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## The Assumption of Non-Gaussianity in Natural and Social Sciences and Its Influence on Detection of Causal Relationships

### Citations

713 |
Synchronization: A Universal Concept in Nonlinear Sciences, ser. Cambridge Nonlinear Science Series
- Pikovsky, Rosenblum, et al.
(Show Context)
Citation Context ...sality which include both linear and nonlinear dependence. Another nonlinear extension of the Granger causality approach was proposed by Chen et al. (Chen et al., 2004) using local linear predictors. An important class of nonlinear predictors are based on so-called radial basis functions (Broomhead & Lowe, 1988) which were used for nonlinear parametric extension of the Granger causality concept (Ancona et al., 2004; Marinazzo, 2006). In physics and nonlinear dynamics, a considerable interest recently emerged in studying cooperative behavior of coupled complex systems (Boccaletti et al., 2002; Pikovsky et al., 2001). Synchronization and related phenomena were observed not only in physical, but also in many biological systems, i.e. (Schäfer et al., 1998; 1999) or in (Paluš et al., 2001a;b; Quyen et al., 1999; Schiff et al., 1996; Tass et al., 1998). In such physiological systems it is not only important to detect synchronized states, but also to identify drive-response relationships and thus the causality in evolution of the interacting (sub)systems. (Schiff et al., 1996) and (Quyen et al., 1999) used ideas similar to those of Granger, however, their cross-prediction models utilize zero-order nonlinear pr... |

600 |
Multivariable functional interpolation and adaptive networks
- Broomhead, Lowe
- 1988
(Show Context)
Citation Context ...is so called correntropy (Park & Principe, 2008). A non-parametric approach to non-linear causality testing, based on non-parametric regression, was proposed in (Bell et al., 1996). Following (Hiemstra & Jones, 1994), (Aparicio & Escribano, 1998) succinctly suggested an information-theoretic definition of causality which include both linear and nonlinear dependence. Another nonlinear extension of the Granger causality approach was proposed by Chen et al. (Chen et al., 2004) using local linear predictors. An important class of nonlinear predictors are based on so-called radial basis functions (Broomhead & Lowe, 1988) which were used for nonlinear parametric extension of the Granger causality concept (Ancona et al., 2004; Marinazzo, 2006). In physics and nonlinear dynamics, a considerable interest recently emerged in studying cooperative behavior of coupled complex systems (Boccaletti et al., 2002; Pikovsky et al., 2001). Synchronization and related phenomena were observed not only in physical, but also in many biological systems, i.e. (Schäfer et al., 1998; 1999) or in (Paluš et al., 2001a;b; Quyen et al., 1999; Schiff et al., 1996; Tass et al., 1998). In such physiological systems it is not only importan... |

514 |
Measuring the strangeness of strange attractors
- Grassberger, Procaccia
- 1983
(Show Context)
Citation Context ...dge Management The Assumption of Non-Gaussianity in Natural and Social Sciences and Its Influence on Detection of Causal Relationships 5 sciences on the other side. In the field of economy, (Baek & Brock, 1992) and (Hiemstra & Jones, 1994) proposed a nonlinear extension of the Granger causality concept. Their non-parametric dependence estimator is based on so-called correlation integral, a probability distribution and entropy estimator, developed by physicists Grassberger and Procaccia in the field of nonlinear dynamics and deterministic chaos as a characterization tool of chaotic attractors (Grassberger & Procaccia, 1983). Another non-linear extension of Granger causality is so called correntropy (Park & Principe, 2008). A non-parametric approach to non-linear causality testing, based on non-parametric regression, was proposed in (Bell et al., 1996). Following (Hiemstra & Jones, 1994), (Aparicio & Escribano, 1998) succinctly suggested an information-theoretic definition of causality which include both linear and nonlinear dependence. Another nonlinear extension of the Granger causality approach was proposed by Chen et al. (Chen et al., 2004) using local linear predictors. An important class of nonlinear predic... |

262 |
Measuring information transfer.
- Schreiber
- 2000
(Show Context)
Citation Context ...pply various probability distributions to model the real-world phenomena. The selection of an appropriate or inappropriate model to fit the real world data has obviously an important influence on the credibility of the achieved conclusions. In the present paper we discuss the influence of the selection of a data model for detection of causal relationships between two or more time series. We focus here on cases when the Gaussianity of the investigated process can be assumed and when not. The causality detection methods considered here are Granger causality (Granger, 1969) and transfer entropy (Schreiber, 2000). We investigated time series with a wider class probability distributions than Gaussian, the generalized Gaussian probability distributions. These distributions are given parametrically. We set conditions on their parameters so that one can from their values decide whether the relationships between the involved time series are unidirectional causal or whether no causality is present. Being aware of outstanding philosophical papers on causality in the sciences, for example (Illari et al., 2011), we are though not aware of any similar publication on mathematically 4 2 Will-be-set-by-IN-TECH con... |

222 |
Philosophiae naturalis principia mathematica, 1687. Numérisé par le SICD des Universités de Strasbourg, http://num-scd-ulp.u-strasbg.fr:8080/73/. Traduction française par Madame la Marquise du Chastelet, sous le titre Principes mathématiques de la ph
- Newton
- 1759
(Show Context)
Citation Context ...ences and Its Influence on Detection of Causal Relationships Katerina Hlavácková-Schindler Commission for Scientific Visualization, Austrian Academy of Sciences Austria 1. Introduction The concept of causality is changing as human knowledge changes. Causality as an abstract notion has been traditionally studied in the field of metaphysics in philosophy. The Greek philosophers understood the time causality as explanation in general (Aristotle, 350 B.C.). The search for causes was a search for "first principles", which were meant to be explanatory. In the more recent philosophy introduced by (Newton, 1687) was causality connected with determinism. The current experimental science reveals the non-deterministic notion of cause, which has to be also taken into consideration. The introduction of probability theory into all scientific disciplines allows to formalize and mathematize the wider conceived notion of cause. This paper does not deal with the philosophical approach to causality, to this we refer the reader for example to the works (Mackie, 1988), (Hume, 1896), (Russo, 2009) or (Pearl, 2000). Here we deal exclusively with the formal mathematical approaches to detect cause-effect relationship... |

217 | Analysis of multiresolution image denoising schemes using generalized Gaussian and complexity priors,”
- Moulin, Liu
- 1999
(Show Context)
Citation Context ...ent The Assumption of Non-Gaussianity in Natural and Social Sciences and Its Influence on Detection of Causal Relationships 3 Generalized normal distribution (generalized Gaussian distribution), first time mathematically defined in (Nadarajah, 1995) can model for example Brownian motion of particles or fractional Brownian motion with a better precision than the normal distribution (Zinde-Walsh & Phillips, 2003). Other experiments have shown a better approximation precision of the generalized Gaussian distributions than of the Gaussian distributions, for example (Sharifi & Leon-Garcia, 1995), (Moulin & Liu, 1999) for in image processing and video analysis, (Bicego et al., 2008) for EEG time series modeling. The modeling in linguistics applies mostly Gaussian mixtures. Mixtures of generalized Gaussian distributions have been recently used in text independent speaker identification (Sailaja et al., 2010) and showed that it outperforms the earlier existing text independent speaker identification models. This model was applied for speaker identification like voice dialing, banking by telephone, telephone shopping information services etc. Exponential distribution has been frequently used in modeling in as... |

172 |
Testing for linear and nonlinear Granger causality in the stock price-volume relation
- Hiemstra, Jones
- 1994
(Show Context)
Citation Context ...4; Kaminski et. al., 2001). Nevertheless, the limitation of the present concept to linear relations required further generalizations. Recent development in nonlinear dynamics (Abarbanel, 1993) evoked lively interactions between statistics and economy (econometrics) on one side, and physics and other natural 80 Theoretical and Methodological Approaches to Social Sciences and Knowledge Management The Assumption of Non-Gaussianity in Natural and Social Sciences and Its Influence on Detection of Causal Relationships 5 sciences on the other side. In the field of economy, (Baek & Brock, 1992) and (Hiemstra & Jones, 1994) proposed a nonlinear extension of the Granger causality concept. Their non-parametric dependence estimator is based on so-called correlation integral, a probability distribution and entropy estimator, developed by physicists Grassberger and Procaccia in the field of nonlinear dynamics and deterministic chaos as a characterization tool of chaotic attractors (Grassberger & Procaccia, 1983). Another non-linear extension of Granger causality is so called correntropy (Park & Principe, 2008). A non-parametric approach to non-linear causality testing, based on non-parametric regression, was proposed... |

156 |
Log-normal distributions across the sciences: Keys and clues
- Limpert, Stahel, et al.
- 2001
(Show Context)
Citation Context ...wn for a relatively long time, is simple and analytically tractable. Its symmetry about its mean value is one of the basic principles realized in nature as well as in human culture. The bell shape of its graph makes the normal distribution attractive for modeling of real world data in many scientific or social disciplines. Indeed, many common natural or social phenomena show to have normal distribution. For example, such phenomena as women’s height, Brownian motion of particles, milk production by cows and random deviations from target values in industrial processes fit a normal distribution (Limpert et al., 2001). However, many phenomena which fit normal distribution, have been shown that they fit also log-normal distribution or generalized normal distribution or, more precisely, fit it even better. What is the difference between normal and log-normal distribution? Both forms of variability are based on a variety of forces (causes) acting independently of one another. A major difference is however that the effects can be additive or multiplicative, thus leading to normal or log-normal distributions, respectively (Limpert et al., 2001). The length of spoken words in phone conversation (Herdan, 1958), t... |

155 | Forecasting Volatility in Financial Markets: A Review.”
- Poon, Granger
- 2003
(Show Context)
Citation Context ...d changes in interand intra-hemispheric connectivity and in the hemispheric predominance of theta and gamma frequency oscillations in sheep infero-temporal cortex. The results provide the first evidence for connectivity changes between and within left and right infero-temporal cortexes as a result of face recognition learning. 3.2 Application of Granger causality in natural and social sciences As already said, the Granger causality was introduced by its author in econometry and applied by him and his followers mainly in econometry, finance and market analysis, for example in (Granger, 1969), (Poon & Granger, 2003). Other applications in humanities and social sciences are in linguistics and psychology (Gilbert & Karahalios, 2009) or demography (Feridun, 2007). 81 The Assumption of Non-Gaussianity in Natural and Social Sciences and Its Influence on D tecti n of Causal Relationships 6 Will-be-set-by-IN-TECH Granger causality has also been extensively applied in natural sciences, for example in medicine, especially to neuroscience (Smith et al., 2011) for the functional magnetic resonance method and (Hesse et al., 2003), analysis of EEG signals or causal interaction in neural populations (Seth & Edelman, 2... |

138 |
The cement of the universe: A study of causation.
- Mackie
- 1974
(Show Context)
Citation Context ... B.C.). The search for causes was a search for "first principles", which were meant to be explanatory. In the more recent philosophy introduced by (Newton, 1687) was causality connected with determinism. The current experimental science reveals the non-deterministic notion of cause, which has to be also taken into consideration. The introduction of probability theory into all scientific disciplines allows to formalize and mathematize the wider conceived notion of cause. This paper does not deal with the philosophical approach to causality, to this we refer the reader for example to the works (Mackie, 1988), (Hume, 1896), (Russo, 2009) or (Pearl, 2000). Here we deal exclusively with the formal mathematical approaches to detect cause-effect relationships, namely with Granger causality and transfer entropy and their application in sciences. The generally non-deterministic approaches to causality apply various probability distributions to model the real-world phenomena. The selection of an appropriate or inappropriate model to fit the real world data has obviously an important influence on the credibility of the achieved conclusions. In the present paper we discuss the influence of the selection of... |

126 | Evaluating causal relations in neural systems: Granger causality, directed transfer function and statistical assessment of significance. - Kaminski, Ding, et al. - 2001 |

113 |
Detection of n:m phase locking from noisy data: application to magnetoencephalography.
- TASS, MG, et al.
- 1998
(Show Context)
Citation Context ...rs are based on so-called radial basis functions (Broomhead & Lowe, 1988) which were used for nonlinear parametric extension of the Granger causality concept (Ancona et al., 2004; Marinazzo, 2006). In physics and nonlinear dynamics, a considerable interest recently emerged in studying cooperative behavior of coupled complex systems (Boccaletti et al., 2002; Pikovsky et al., 2001). Synchronization and related phenomena were observed not only in physical, but also in many biological systems, i.e. (Schäfer et al., 1998; 1999) or in (Paluš et al., 2001a;b; Quyen et al., 1999; Schiff et al., 1996; Tass et al., 1998). In such physiological systems it is not only important to detect synchronized states, but also to identify drive-response relationships and thus the causality in evolution of the interacting (sub)systems. (Schiff et al., 1996) and (Quyen et al., 1999) used ideas similar to those of Granger, however, their cross-prediction models utilize zero-order nonlinear predictors based on mutual nearest neighbors. A careful comparison of these two papers (Quyen et al., 1999; Schiff et al., 1996) reveals how complex is the problem of inferring causality in nonlinear systems. While the latter two papers u... |

104 |
Zhou :The synchronization of chaotic systems.
- Boccaletti, Kurths, et al.
- 2002
(Show Context)
Citation Context ...eoretic definition of causality which include both linear and nonlinear dependence. Another nonlinear extension of the Granger causality approach was proposed by Chen et al. (Chen et al., 2004) using local linear predictors. An important class of nonlinear predictors are based on so-called radial basis functions (Broomhead & Lowe, 1988) which were used for nonlinear parametric extension of the Granger causality concept (Ancona et al., 2004; Marinazzo, 2006). In physics and nonlinear dynamics, a considerable interest recently emerged in studying cooperative behavior of coupled complex systems (Boccaletti et al., 2002; Pikovsky et al., 2001). Synchronization and related phenomena were observed not only in physical, but also in many biological systems, i.e. (Schäfer et al., 1998; 1999) or in (Paluš et al., 2001a;b; Quyen et al., 1999; Schiff et al., 1996; Tass et al., 1998). In such physiological systems it is not only important to detect synchronized states, but also to identify drive-response relationships and thus the causality in evolution of the interacting (sub)systems. (Schiff et al., 1996) and (Quyen et al., 1999) used ideas similar to those of Granger, however, their cross-prediction models utilize... |

80 | A robust method for detecting interdependences: application to intracranially recorded EEG - Arnhold, Grassberger, et al. - 1999 |

75 |
Detecting Dynamical Interdependence and Generalized Synchrony through Mutual Prediction in a Neural Ensemble,” Phys.
- Schiff, So, et al.
- 1996
(Show Context)
Citation Context ...of nonlinear predictors are based on so-called radial basis functions (Broomhead & Lowe, 1988) which were used for nonlinear parametric extension of the Granger causality concept (Ancona et al., 2004; Marinazzo, 2006). In physics and nonlinear dynamics, a considerable interest recently emerged in studying cooperative behavior of coupled complex systems (Boccaletti et al., 2002; Pikovsky et al., 2001). Synchronization and related phenomena were observed not only in physical, but also in many biological systems, i.e. (Schäfer et al., 1998; 1999) or in (Paluš et al., 2001a;b; Quyen et al., 1999; Schiff et al., 1996; Tass et al., 1998). In such physiological systems it is not only important to detect synchronized states, but also to identify drive-response relationships and thus the causality in evolution of the interacting (sub)systems. (Schiff et al., 1996) and (Quyen et al., 1999) used ideas similar to those of Granger, however, their cross-prediction models utilize zero-order nonlinear predictors based on mutual nearest neighbors. A careful comparison of these two papers (Quyen et al., 1999; Schiff et al., 1996) reveals how complex is the problem of inferring causality in nonlinear systems. While the... |

70 |
Estimation of shape parameter for generalized Gaussian distributions in subband decompositions of video,”
- Sharifi, Leon-Garcia
- 1995
(Show Context)
Citation Context ... Sciences and Knowledge Management The Assumption of Non-Gaussianity in Natural and Social Sciences and Its Influence on Detection of Causal Relationships 3 Generalized normal distribution (generalized Gaussian distribution), first time mathematically defined in (Nadarajah, 1995) can model for example Brownian motion of particles or fractional Brownian motion with a better precision than the normal distribution (Zinde-Walsh & Phillips, 2003). Other experiments have shown a better approximation precision of the generalized Gaussian distributions than of the Gaussian distributions, for example (Sharifi & Leon-Garcia, 1995), (Moulin & Liu, 1999) for in image processing and video analysis, (Bicego et al., 2008) for EEG time series modeling. The modeling in linguistics applies mostly Gaussian mixtures. Mixtures of generalized Gaussian distributions have been recently used in text independent speaker identification (Sailaja et al., 2010) and showed that it outperforms the earlier existing text independent speaker identification models. This model was applied for speaker identification like voice dialing, banking by telephone, telephone shopping information services etc. Exponential distribution has been frequently ... |

67 |
The use of time-variant EEG Granger causality for inspecting directed interdependencies of neural assemblies.
- Hesse, Moller, et al.
- 2003
(Show Context)
Citation Context ...s mainly in econometry, finance and market analysis, for example in (Granger, 1969), (Poon & Granger, 2003). Other applications in humanities and social sciences are in linguistics and psychology (Gilbert & Karahalios, 2009) or demography (Feridun, 2007). 81 The Assumption of Non-Gaussianity in Natural and Social Sciences and Its Influence on D tecti n of Causal Relationships 6 Will-be-set-by-IN-TECH Granger causality has also been extensively applied in natural sciences, for example in medicine, especially to neuroscience (Smith et al., 2011) for the functional magnetic resonance method and (Hesse et al., 2003), analysis of EEG signals or causal interaction in neural populations (Seth & Edelman, 2007) and in many other papers. Granger causality was applied as well as in climatology (Kufmann & Stern, 1997), in cognitive and systematical biology, (Kim et al., 2011), (Fujita et al., 2010) etc. The main drawback of Granger causality and its extensions as a model dependent method are their instability which can cause a high variability in the final estimation of errors in (2) and (3). As an alternative, we will present in the following model-free methods whose formal definitions apply information-theoret... |

60 |
A general test for nonlinear Granger causality: Bivariate model,” Working paper
- Baek, Brock
- 1992
(Show Context)
Citation Context ...se (Blinowska et al., 2004; Kaminski et. al., 2001). Nevertheless, the limitation of the present concept to linear relations required further generalizations. Recent development in nonlinear dynamics (Abarbanel, 1993) evoked lively interactions between statistics and economy (econometrics) on one side, and physics and other natural 80 Theoretical and Methodological Approaches to Social Sciences and Knowledge Management The Assumption of Non-Gaussianity in Natural and Social Sciences and Its Influence on Detection of Causal Relationships 5 sciences on the other side. In the field of economy, (Baek & Brock, 1992) and (Hiemstra & Jones, 1994) proposed a nonlinear extension of the Granger causality concept. Their non-parametric dependence estimator is based on so-called correlation integral, a probability distribution and entropy estimator, developed by physicists Grassberger and Procaccia in the field of nonlinear dynamics and deterministic chaos as a characterization tool of chaotic attractors (Grassberger & Procaccia, 1983). Another non-linear extension of Granger causality is so called correntropy (Park & Principe, 2008). A non-parametric approach to non-linear causality testing, based on non-parame... |

60 |
Investigating causal relation by econometric and crosssectional methods.
- Granger
- 1969
(Show Context)
Citation Context ...terministic approaches to causality apply various probability distributions to model the real-world phenomena. The selection of an appropriate or inappropriate model to fit the real world data has obviously an important influence on the credibility of the achieved conclusions. In the present paper we discuss the influence of the selection of a data model for detection of causal relationships between two or more time series. We focus here on cases when the Gaussianity of the investigated process can be assumed and when not. The causality detection methods considered here are Granger causality (Granger, 1969) and transfer entropy (Schreiber, 2000). We investigated time series with a wider class probability distributions than Gaussian, the generalized Gaussian probability distributions. These distributions are given parametrically. We set conditions on their parameters so that one can from their values decide whether the relationships between the involved time series are unidirectional causal or whether no causality is present. Being aware of outstanding philosophical papers on causality in the sciences, for example (Illari et al., 2011), we are though not aware of any similar publication on mathem... |

57 | Causality detection based on information-theoretic approaches in time series analysis. Physics Reports, - Hlavackova-Schindler, Palusb, et al. - 2007 |

53 |
Inference and Causality in Economic Time Series Models’,
- Geweke
- 1984
(Show Context)
Citation Context ...rature is defined for univariate predictor and predictee variables Y and X, and is given by the natural logarithm of the ratio of the residual variance in the restricted regression (2) to that of the unrestricted regression (3). (Barnett, 2009) have shown that G-causality can be expressed as FY→X|Z = ln( Σ(X|X− ⊕ Z−) Σ(X|X− ⊕ Y− ⊕ Z−) ) (4) where ln denotes the natural logarithm. 3.1 Extensions of Granger causality The linear framework of Granger causality given by equations 2 and 3 has been widely applied not only in economy and finance (for a comprehensive survey of the literature see i.e. (Geweke, 1984)), but also in diverse fields of natural sciences, i.e. climatology (see (Triacca, 2005) and references therein) or neurophysiology, where specific problems of multichannel electroencephalogram recordings were solved by generalizing the Granger causality concept to multivariate case (Blinowska et al., 2004; Kaminski et. al., 2001). Nevertheless, the limitation of the present concept to linear relations required further generalizations. Recent development in nonlinear dynamics (Abarbanel, 1993) evoked lively interactions between statistics and economy (econometrics) on one side, and physics an... |

50 |
Network modelling methods for fMRI.
- Smith, Miller, et al.
- 2011
(Show Context)
Citation Context ...oduced by its author in econometry and applied by him and his followers mainly in econometry, finance and market analysis, for example in (Granger, 1969), (Poon & Granger, 2003). Other applications in humanities and social sciences are in linguistics and psychology (Gilbert & Karahalios, 2009) or demography (Feridun, 2007). 81 The Assumption of Non-Gaussianity in Natural and Social Sciences and Its Influence on D tecti n of Causal Relationships 6 Will-be-set-by-IN-TECH Granger causality has also been extensively applied in natural sciences, for example in medicine, especially to neuroscience (Smith et al., 2011) for the functional magnetic resonance method and (Hesse et al., 2003), analysis of EEG signals or causal interaction in neural populations (Seth & Edelman, 2007) and in many other papers. Granger causality was applied as well as in climatology (Kufmann & Stern, 1997), in cognitive and systematical biology, (Kim et al., 2011), (Fujita et al., 2010) etc. The main drawback of Granger causality and its extensions as a model dependent method are their instability which can cause a high variability in the final estimation of errors in (2) and (3). As an alternative, we will present in the following... |

48 | Dynamic causal modelling of evoked responses in EEG/MEG with lead field parameterization.
- SJ, David, et al.
- 2006
(Show Context)
Citation Context ...ctors based on mutual nearest neighbors. A careful comparison of these two papers (Quyen et al., 1999; Schiff et al., 1996) reveals how complex is the problem of inferring causality in nonlinear systems. While the latter two papers use the method of mutual nearest neighbors for mutual prediction, (Arnhold, 1999) proposed asymmetric dependence measures based on averaged relative distances of the (mutual) nearest neighbors. (Ge et al, 2009) presented a novel approach which is an extension of Granger causal model and also shares the features of the bilinear approximation of dynamic causal model (David et al., 2006). The authors demonstrated face discrimination learning-induced changes in interand intra-hemispheric connectivity and in the hemispheric predominance of theta and gamma frequency oscillations in sheep infero-temporal cortex. The results provide the first evidence for connectivity changes between and within left and right infero-temporal cortexes as a result of face recognition learning. 3.2 Application of Granger causality in natural and social sciences As already said, the Granger causality was introduced by its author in econometry and applied by him and his followers mainly in econometry, ... |

41 | Synchronization in the human cardiorespiratory system. - Schäfer, Rosenblum, et al. - 1999 |

39 | Granger causality and transfer entropy are equivalent for Gaussian variables. - Barnett, AB, et al. - 2009 |

38 | Analyzing multiple nonlinear time series with extended Granger causality.
- Chen, Rangarajan, et al.
- 2004
(Show Context)
Citation Context ...c chaos as a characterization tool of chaotic attractors (Grassberger & Procaccia, 1983). Another non-linear extension of Granger causality is so called correntropy (Park & Principe, 2008). A non-parametric approach to non-linear causality testing, based on non-parametric regression, was proposed in (Bell et al., 1996). Following (Hiemstra & Jones, 1994), (Aparicio & Escribano, 1998) succinctly suggested an information-theoretic definition of causality which include both linear and nonlinear dependence. Another nonlinear extension of the Granger causality approach was proposed by Chen et al. (Chen et al., 2004) using local linear predictors. An important class of nonlinear predictors are based on so-called radial basis functions (Broomhead & Lowe, 1988) which were used for nonlinear parametric extension of the Granger causality concept (Ancona et al., 2004; Marinazzo, 2006). In physics and nonlinear dynamics, a considerable interest recently emerged in studying cooperative behavior of coupled complex systems (Boccaletti et al., 2002; Pikovsky et al., 2001). Synchronization and related phenomena were observed not only in physical, but also in many biological systems, i.e. (Schäfer et al., 1998; 1999)... |

38 |
Evidence for human influence on climate from hemispheric temperature relations.
- Kaufmann, Stern
- 1997
(Show Context)
Citation Context ... (Gilbert & Karahalios, 2009) or demography (Feridun, 2007). 81 The Assumption of Non-Gaussianity in Natural and Social Sciences and Its Influence on D tecti n of Causal Relationships 6 Will-be-set-by-IN-TECH Granger causality has also been extensively applied in natural sciences, for example in medicine, especially to neuroscience (Smith et al., 2011) for the functional magnetic resonance method and (Hesse et al., 2003), analysis of EEG signals or causal interaction in neural populations (Seth & Edelman, 2007) and in many other papers. Granger causality was applied as well as in climatology (Kufmann & Stern, 1997), in cognitive and systematical biology, (Kim et al., 2011), (Fujita et al., 2010) etc. The main drawback of Granger causality and its extensions as a model dependent method are their instability which can cause a high variability in the final estimation of errors in (2) and (3). As an alternative, we will present in the following model-free methods whose formal definitions apply information-theoretic functionals. 4. Information-theoretical causality measures Using distributions of random processes and their definitions, introduce the information-theoretic causality measures determinism into t... |

35 | Statistical assessment of nonlinear causality: Application to epileptic EEG signals. - Chávez, Martinerie, et al. - 2003 |

34 |
A Generalized Normal Distribution,
- Nadarajah
- 2005
(Show Context)
Citation Context ...eto distribution or skewed generalized normal distribution. Statistical inference using a normal distribution is not robust to the presence of outliers. When outliers are expected, data may be better described using a heavy-tailed distribution such as the Student’s t-distribution. 78 Theoretical and Methodological Approaches to Social Sciences and Knowledge Management The Assumption of Non-Gaussianity in Natural and Social Sciences and Its Influence on Detection of Causal Relationships 3 Generalized normal distribution (generalized Gaussian distribution), first time mathematically defined in (Nadarajah, 1995) can model for example Brownian motion of particles or fractional Brownian motion with a better precision than the normal distribution (Zinde-Walsh & Phillips, 2003). Other experiments have shown a better approximation precision of the generalized Gaussian distributions than of the Gaussian distributions, for example (Sharifi & Leon-Garcia, 1995), (Moulin & Liu, 1999) for in image processing and video analysis, (Bicego et al., 2008) for EEG time series modeling. The modeling in linguistics applies mostly Gaussian mixtures. Mixtures of generalized Gaussian distributions have been recently used ... |

33 | Direction of Coupling from Phases of Interacting Oscillators: An InformationTheoretic Approach,” Phys. - Palus, Stefanovska - 2003 |

33 | Detecting direction of coupling in interacting oscillators. Physical Review E,
- Rosenblum, Pikovsky
- 2001
(Show Context)
Citation Context ...ion-theoretic approach to the Granger causality plays an important, if not a dominant role in analyses of causal relationships in nonlinear systems. In the following we define a practical criterium for detection of causal relationships among time series by means of transfer entropy. 4.3 Directionality index To measure causal structure on small data sets and to allow conclusions about the dominant direction of the information flow, the (causal) directionality index was defined for transfer entropy or conditional mutual information by Paluš in (Paluš & A. Stefanovska, 2003) and analogically in (Rosenblum & Pikovsky, 2001). It is given by DI(Y → X|Z) = TY→X|Z − TX→Y|Z TY→X|Z + TX→Y|Z , (8) where X, Y, Z are time series. Paluš et al. in Paluš & A. Stefanovska (2003) consider special cases for Z, the so called phase increments of X and Y: DI(Y → X) = TY→X − TX→YTY→X + TX→Y , (9) where TY→X = H(X|X− ⊕ ΔX−) − H(X|X− ⊕ Y− ⊕ ΔX−) and ΔX = X(n + k) − X(n) and similarly TX→Y = H(Y|Y− ⊕ ΔY−)− H(Y|Y− ⊕ X− ⊕ ΔY−) and ΔY = Y(n + k)− Y(n). The index varies between −1 and 1, where negative values imply that the information flow from X to Y dominates and positive vales indicate a large information flow from Y to X. The defini... |

32 |
Analysing the information flow between financial time series. an improved estimator for transfer entropy.
- Marschinski, Kantz
- 2002
(Show Context)
Citation Context ...Influence on Detection of Causal Relationships 7 It was shown in (Hlavácková-Schindler et. al., 2007) that with proper conditioning, the transfer entropy is equivalent to the conditional mutual information (Paluš et al., 2001b). The latter, however, is a standard measure of information theory (Cover & Thomas, 1991). More details on the information-theoretic methods for causality detection can be found in our review paper (Hlavácková-Schindler et. al., 2007). Marschinski and Kanz in 2002 suggested so called effective transfer entropy to reduce the bias of transfer entropy on small data sets (Marschinski & Kantz, 2002). 4.2 Transfer entropy, other information-theoretical measures and their application in natural and social sciences Turning our attention back to econometrics, we can follow further development due to (Diks & DeGoede, 2001). They applied a nonparametric approach to nonlinear Granger causality using the concept of correlation integrals (Grassberger & Procaccia, 1983) and pointed out the connection between the correlation integrals and information theory. (Diks & Panchenko, 2005) critically discussed the previous tests of (Hiemstra & Jones, 1994). As the most recent development in economics, (Ba... |

29 | M. Granger causality and information flow in multivariate processes. - Blinowska, Kus, et al. - 2004 |

29 | Synchronization As Adjustment of Information Rates: Detection from Bivariate Time Series,” Phys. - Palus, Komarek, et al. - 2001 |

26 |
Heartbeat synchronized with ventilation.
- Schäfer, Rosenblum, et al.
- 1998
(Show Context)
Citation Context ... et al. (Chen et al., 2004) using local linear predictors. An important class of nonlinear predictors are based on so-called radial basis functions (Broomhead & Lowe, 1988) which were used for nonlinear parametric extension of the Granger causality concept (Ancona et al., 2004; Marinazzo, 2006). In physics and nonlinear dynamics, a considerable interest recently emerged in studying cooperative behavior of coupled complex systems (Boccaletti et al., 2002; Pikovsky et al., 2001). Synchronization and related phenomena were observed not only in physical, but also in many biological systems, i.e. (Schäfer et al., 1998; 1999) or in (Paluš et al., 2001a;b; Quyen et al., 1999; Schiff et al., 1996; Tass et al., 1998). In such physiological systems it is not only important to detect synchronized states, but also to identify drive-response relationships and thus the causality in evolution of the interacting (sub)systems. (Schiff et al., 1996) and (Quyen et al., 1999) used ideas similar to those of Granger, however, their cross-prediction models utilize zero-order nonlinear predictors based on mutual nearest neighbors. A careful comparison of these two papers (Quyen et al., 1999; Schiff et al., 1996) reveals how ... |

25 |
Nonlinear analyses of interictal EEG map the brain interdependences in human focal epilepsy.
- Quyen, Martinerie, et al.
- 1999
(Show Context)
Citation Context ... An important class of nonlinear predictors are based on so-called radial basis functions (Broomhead & Lowe, 1988) which were used for nonlinear parametric extension of the Granger causality concept (Ancona et al., 2004; Marinazzo, 2006). In physics and nonlinear dynamics, a considerable interest recently emerged in studying cooperative behavior of coupled complex systems (Boccaletti et al., 2002; Pikovsky et al., 2001). Synchronization and related phenomena were observed not only in physical, but also in many biological systems, i.e. (Schäfer et al., 1998; 1999) or in (Paluš et al., 2001a;b; Quyen et al., 1999; Schiff et al., 1996; Tass et al., 1998). In such physiological systems it is not only important to detect synchronized states, but also to identify drive-response relationships and thus the causality in evolution of the interacting (sub)systems. (Schiff et al., 1996) and (Quyen et al., 1999) used ideas similar to those of Granger, however, their cross-prediction models utilize zero-order nonlinear predictors based on mutual nearest neighbors. A careful comparison of these two papers (Quyen et al., 1999; Schiff et al., 1996) reveals how complex is the problem of inferring causality in nonline... |

24 | A note on the Hiemstra-Jones test for Granger non-causality.
- Diks, Panchenko
- 2005
(Show Context)
Citation Context ... in 2002 suggested so called effective transfer entropy to reduce the bias of transfer entropy on small data sets (Marschinski & Kantz, 2002). 4.2 Transfer entropy, other information-theoretical measures and their application in natural and social sciences Turning our attention back to econometrics, we can follow further development due to (Diks & DeGoede, 2001). They applied a nonparametric approach to nonlinear Granger causality using the concept of correlation integrals (Grassberger & Procaccia, 1983) and pointed out the connection between the correlation integrals and information theory. (Diks & Panchenko, 2005) critically discussed the previous tests of (Hiemstra & Jones, 1994). As the most recent development in economics, (Baghli, 2006) proposes information-theoretic statistics for a model-free characterization of causality, based on an evaluation of conditional entropy. The information-theoretical approaches to causality detection are model free and can detect non-linear causal relationships, which are their advantages with respect to the approach of the linear Granger causality. The nonlinear extension of the Granger causality based the information-theoretic formulation has found numerous applica... |

21 | Predicting influential users in online social networks.
- Ghosh, Lerman
- 2010
(Show Context)
Citation Context ...Facebook) serves to researches as an important source for studying social interactions. One important problem is the characterization and identification of influentials, which can be defined as users who influence the behavior of large number of other users. To characterize influence (in other words a causal relationship) in Twitter, researchers have suggested number of followers, mentions, and retweets (Cha et al., 2010), and Pagerank of follower network (Kwak at al., 2010). (Ver Steeg et al., 2011) however argue that the purely structural measures of influence (causality) can be misleading (Ghosh & Lerman, 2010) and high popularity does not necessarily imply high influence (Romero et al., 2010; Ver Steeg et al., 2011). More recent work has used the size of the cascade trees (Bakshy et al., 2011) and influence-passivity score (Romero et al., 2010). One serious drawback of existing methods is that they are based on explicit causal knowledge (i.e., A responds to B), whereas for many data sets such knowledge is not available. (Ver Steeg et al., 2011) suggest a model-free transfer entropy approach to detect causal relationships and identifying influential users based on their capacity to predict the behav... |

21 | A granger causality measure for point process models of ensemble neural spiking activity,”
- Kim, Putrino, et al.
- 2011
(Show Context)
Citation Context ...The Assumption of Non-Gaussianity in Natural and Social Sciences and Its Influence on D tecti n of Causal Relationships 6 Will-be-set-by-IN-TECH Granger causality has also been extensively applied in natural sciences, for example in medicine, especially to neuroscience (Smith et al., 2011) for the functional magnetic resonance method and (Hesse et al., 2003), analysis of EEG signals or causal interaction in neural populations (Seth & Edelman, 2007) and in many other papers. Granger causality was applied as well as in climatology (Kufmann & Stern, 1997), in cognitive and systematical biology, (Kim et al., 2011), (Fujita et al., 2010) etc. The main drawback of Granger causality and its extensions as a model dependent method are their instability which can cause a high variability in the final estimation of errors in (2) and (3). As an alternative, we will present in the following model-free methods whose formal definitions apply information-theoretic functionals. 4. Information-theoretical causality measures Using distributions of random processes and their definitions, introduce the information-theoretic causality measures determinism into the notion of causality. (Paluš et al., 2001b) proposed to s... |

21 |
Causality and causal modelling in the social sciences. Measuring variations.
- Russo
- 2009
(Show Context)
Citation Context ...was a search for "first principles", which were meant to be explanatory. In the more recent philosophy introduced by (Newton, 1687) was causality connected with determinism. The current experimental science reveals the non-deterministic notion of cause, which has to be also taken into consideration. The introduction of probability theory into all scientific disciplines allows to formalize and mathematize the wider conceived notion of cause. This paper does not deal with the philosophical approach to causality, to this we refer the reader for example to the works (Mackie, 1988), (Hume, 1896), (Russo, 2009) or (Pearl, 2000). Here we deal exclusively with the formal mathematical approaches to detect cause-effect relationships, namely with Granger causality and transfer entropy and their application in sciences. The generally non-deterministic approaches to causality apply various probability distributions to model the real-world phenomena. The selection of an appropriate or inappropriate model to fit the real world data has obviously an important influence on the credibility of the achieved conclusions. In the present paper we discuss the influence of the selection of a data model for detection o... |

18 | El Niño Southern Oscillation Drives North Atlantic Oscillation As Revealed with Nonlinear Techniques from Climatic Indices,” Geophys.
- Mokhov, Smirnov
- 2006
(Show Context)
Citation Context ...statistics for a model-free characterization of causality, based on an evaluation of conditional entropy. The information-theoretical approaches to causality detection are model free and can detect non-linear causal relationships, which are their advantages with respect to the approach of the linear Granger causality. The nonlinear extension of the Granger causality based the information-theoretic formulation has found numerous applications in various fields of natural and social sciences. Let us mention just a few examples. The Schreiber’s transfer entropy has been used in climatology, i.e. (Mokhov & Smirnov, 2006; Verdes, 2005), in physiology, i.e. (Verdes, 2005), in neurophysiology, i.e. (Chávez et al., 2003) and also in analysis of financial data, i.e.(Marschinski & Kantz, 2002). (Paluš et al., 2001a;b) applied their conditional mutual information based measures in analysis of electroencephalograms of patients suffering from epilepsy. Other applications of the conditional mutual information in neurophysiology are due to (Hinrichs et. al., 2006) and (Pflieger & Greenblatt, 2005). Causality or coupling directions in multimode laser dynamics is another diverse field where the conditional mutual informa... |

17 | A Novel Extended Granger Causal Model Approach Demonstrates Brain Hemispheric Differences during Face Recognition Learning.
- Ge, Kendrick, et al.
- 2009
(Show Context)
Citation Context ...sub)systems. (Schiff et al., 1996) and (Quyen et al., 1999) used ideas similar to those of Granger, however, their cross-prediction models utilize zero-order nonlinear predictors based on mutual nearest neighbors. A careful comparison of these two papers (Quyen et al., 1999; Schiff et al., 1996) reveals how complex is the problem of inferring causality in nonlinear systems. While the latter two papers use the method of mutual nearest neighbors for mutual prediction, (Arnhold, 1999) proposed asymmetric dependence measures based on averaged relative distances of the (mutual) nearest neighbors. (Ge et al, 2009) presented a novel approach which is an extension of Granger causal model and also shares the features of the bilinear approximation of dynamic causal model (David et al., 2006). The authors demonstrated face discrimination learning-induced changes in interand intra-hemispheric connectivity and in the hemispheric predominance of theta and gamma frequency oscillations in sheep infero-temporal cortex. The results provide the first evidence for connectivity changes between and within left and right infero-temporal cortexes as a result of face recognition learning. 3.2 Application of Granger causa... |

15 |
Assessing causality from multivariate time series.
- Verdes
- 2005
(Show Context)
Citation Context ...ree characterization of causality, based on an evaluation of conditional entropy. The information-theoretical approaches to causality detection are model free and can detect non-linear causal relationships, which are their advantages with respect to the approach of the linear Granger causality. The nonlinear extension of the Granger causality based the information-theoretic formulation has found numerous applications in various fields of natural and social sciences. Let us mention just a few examples. The Schreiber’s transfer entropy has been used in climatology, i.e. (Mokhov & Smirnov, 2006; Verdes, 2005), in physiology, i.e. (Verdes, 2005), in neurophysiology, i.e. (Chávez et al., 2003) and also in analysis of financial data, i.e.(Marschinski & Kantz, 2002). (Paluš et al., 2001a;b) applied their conditional mutual information based measures in analysis of electroencephalograms of patients suffering from epilepsy. Other applications of the conditional mutual information in neurophysiology are due to (Hinrichs et. al., 2006) and (Pflieger & Greenblatt, 2005). Causality or coupling directions in multimode laser dynamics is another diverse field where the conditional mutual information was applie... |

14 | Causal visual interactions as revealed by an information theoretic measure and fMRI. - Hinrichs, Heinze, et al. - 2006 |

13 |
A general nonparametric bootstrap test for Granger causality, in:
- Diks, DeGoede
- 2001
(Show Context)
Citation Context .... The latter, however, is a standard measure of information theory (Cover & Thomas, 1991). More details on the information-theoretic methods for causality detection can be found in our review paper (Hlavácková-Schindler et. al., 2007). Marschinski and Kanz in 2002 suggested so called effective transfer entropy to reduce the bias of transfer entropy on small data sets (Marschinski & Kantz, 2002). 4.2 Transfer entropy, other information-theoretical measures and their application in natural and social sciences Turning our attention back to econometrics, we can follow further development due to (Diks & DeGoede, 2001). They applied a nonparametric approach to nonlinear Granger causality using the concept of correlation integrals (Grassberger & Procaccia, 1983) and pointed out the connection between the correlation integrals and information theory. (Diks & Panchenko, 2005) critically discussed the previous tests of (Hiemstra & Jones, 1994). As the most recent development in economics, (Baghli, 2006) proposes information-theoretic statistics for a model-free characterization of causality, based on an evaluation of conditional entropy. The information-theoretical approaches to causality detection are model fr... |

12 |
Introduction to Nonlinear Dynamics for Physicists.
- Abarbanel
- 1993
(Show Context)
Citation Context ... widely applied not only in economy and finance (for a comprehensive survey of the literature see i.e. (Geweke, 1984)), but also in diverse fields of natural sciences, i.e. climatology (see (Triacca, 2005) and references therein) or neurophysiology, where specific problems of multichannel electroencephalogram recordings were solved by generalizing the Granger causality concept to multivariate case (Blinowska et al., 2004; Kaminski et. al., 2001). Nevertheless, the limitation of the present concept to linear relations required further generalizations. Recent development in nonlinear dynamics (Abarbanel, 1993) evoked lively interactions between statistics and economy (econometrics) on one side, and physics and other natural 80 Theoretical and Methodological Approaches to Social Sciences and Knowledge Management The Assumption of Non-Gaussianity in Natural and Social Sciences and Its Influence on Detection of Causal Relationships 5 sciences on the other side. In the field of economy, (Baek & Brock, 1992) and (Hiemstra & Jones, 1994) proposed a nonlinear extension of the Granger causality concept. Their non-parametric dependence estimator is based on so-called correlation integral, a probability dist... |

12 |
Information-theoretic analysis of serial dependence and cointegration.
- Aparicio, Escribano
- 1998
(Show Context)
Citation Context ...pt. Their non-parametric dependence estimator is based on so-called correlation integral, a probability distribution and entropy estimator, developed by physicists Grassberger and Procaccia in the field of nonlinear dynamics and deterministic chaos as a characterization tool of chaotic attractors (Grassberger & Procaccia, 1983). Another non-linear extension of Granger causality is so called correntropy (Park & Principe, 2008). A non-parametric approach to non-linear causality testing, based on non-parametric regression, was proposed in (Bell et al., 1996). Following (Hiemstra & Jones, 1994), (Aparicio & Escribano, 1998) succinctly suggested an information-theoretic definition of causality which include both linear and nonlinear dependence. Another nonlinear extension of the Granger causality approach was proposed by Chen et al. (Chen et al., 2004) using local linear predictors. An important class of nonlinear predictors are based on so-called radial basis functions (Broomhead & Lowe, 1988) which were used for nonlinear parametric extension of the Granger causality concept (Ancona et al., 2004; Marinazzo, 2006). In physics and nonlinear dynamics, a considerable interest recently emerged in studying cooperativ... |

12 |
A non-parametric approach to non-linear causality testing.
- Bell, Kay, et al.
- 1996
(Show Context)
Citation Context ...osed a nonlinear extension of the Granger causality concept. Their non-parametric dependence estimator is based on so-called correlation integral, a probability distribution and entropy estimator, developed by physicists Grassberger and Procaccia in the field of nonlinear dynamics and deterministic chaos as a characterization tool of chaotic attractors (Grassberger & Procaccia, 1983). Another non-linear extension of Granger causality is so called correntropy (Park & Principe, 2008). A non-parametric approach to non-linear causality testing, based on non-parametric regression, was proposed in (Bell et al., 1996). Following (Hiemstra & Jones, 1994), (Aparicio & Escribano, 1998) succinctly suggested an information-theoretic definition of causality which include both linear and nonlinear dependence. Another nonlinear extension of the Granger causality approach was proposed by Chen et al. (Chen et al., 2004) using local linear predictors. An important class of nonlinear predictors are based on so-called radial basis functions (Broomhead & Lowe, 1988) which were used for nonlinear parametric extension of the Granger causality concept (Ancona et al., 2004; Marinazzo, 2006). In physics and nonlinear dynamic... |

11 | Nonlinear parametric model for granger causality of time series,” - Marinazzo, Pellicoro, et al. - 2004 |

11 |
Distinguishing causal interactions in neural populations.
- Seth, Edelman
- 2007
(Show Context)
Citation Context ... & Granger, 2003). Other applications in humanities and social sciences are in linguistics and psychology (Gilbert & Karahalios, 2009) or demography (Feridun, 2007). 81 The Assumption of Non-Gaussianity in Natural and Social Sciences and Its Influence on D tecti n of Causal Relationships 6 Will-be-set-by-IN-TECH Granger causality has also been extensively applied in natural sciences, for example in medicine, especially to neuroscience (Smith et al., 2011) for the functional magnetic resonance method and (Hesse et al., 2003), analysis of EEG signals or causal interaction in neural populations (Seth & Edelman, 2007) and in many other papers. Granger causality was applied as well as in climatology (Kufmann & Stern, 1997), in cognitive and systematical biology, (Kim et al., 2011), (Fujita et al., 2010) etc. The main drawback of Granger causality and its extensions as a model dependent method are their instability which can cause a high variability in the final estimation of errors in (2) and (3). As an alternative, we will present in the following model-free methods whose formal definitions apply information-theoretic functionals. 4. Information-theoretical causality measures Using distributions of random ... |

11 | Information transfer in social media.
- Steeg, Galstyan
- 2012
(Show Context)
Citation Context ... of transfer entropy in linguistics can be found in the book (Baeyer, 2005). Social media (for example Twitter or Facebook) serves to researches as an important source for studying social interactions. One important problem is the characterization and identification of influentials, which can be defined as users who influence the behavior of large number of other users. To characterize influence (in other words a causal relationship) in Twitter, researchers have suggested number of followers, mentions, and retweets (Cha et al., 2010), and Pagerank of follower network (Kwak at al., 2010). (Ver Steeg et al., 2011) however argue that the purely structural measures of influence (causality) can be misleading (Ghosh & Lerman, 2010) and high popularity does not necessarily imply high influence (Romero et al., 2010; Ver Steeg et al., 2011). More recent work has used the size of the cascade trees (Bakshy et al., 2011) and influence-passivity score (Romero et al., 2010). One serious drawback of existing methods is that they are based on explicit causal knowledge (i.e., A responds to B), whereas for many data sets such knowledge is not available. (Ver Steeg et al., 2011) suggest a model-free transfer entropy ap... |

10 |
Transfer entropy: a model-free measure of effective connectivity for the neurosciences.
- Vicente, Wibral, et al.
- 2010
(Show Context)
Citation Context ...(Paluš & A. Stefanovska, 2003) adapted the conditional mutual information approach (Paluš et al., 2001b) to analysis of instantaneous phases of interacting oscillators and demonstrated suitability of this approach for analyzing causality in cardio-respiratory interaction (Paluš et al., 2001b). The later approach has also been applied in neurophysiology (Brea et al., 2006). More recent applications of information-theoretical functionals in natural sciences (medicine) are for example in (Van Dijck et al., 2007), inferring and quantifying causality in neuronal networks (Chicharro et al., 2011), (Vicente et al., 2010), in the computer simulation of human-robot interaction in (Sumioka et al., 1997) or in the relationship of predator-prey in etiology (Bochmann, 2007). The information-theoretical functionals applied in social sciences are mostly in financial applications: i.e. application of transfer entropy to the information flow between various 83 The Assumption of Non-Gaussianity in Natural and Social Sciences and Its Influence on D tecti n of Causal Relationships 8 Will-be-set-by-IN-TECH financial time series (Dimpfl et al., 2011) or analysis of the Korean stock market by transfer entropy (Baek et al., 2... |

6 |
Using transfer entropy to measure information flows from and to the CDS market.
- Dimpfl, Huergo, et al.
- 2011
(Show Context)
Citation Context ...and quantifying causality in neuronal networks (Chicharro et al., 2011), (Vicente et al., 2010), in the computer simulation of human-robot interaction in (Sumioka et al., 1997) or in the relationship of predator-prey in etiology (Bochmann, 2007). The information-theoretical functionals applied in social sciences are mostly in financial applications: i.e. application of transfer entropy to the information flow between various 83 The Assumption of Non-Gaussianity in Natural and Social Sciences and Its Influence on D tecti n of Causal Relationships 8 Will-be-set-by-IN-TECH financial time series (Dimpfl et al., 2011) or analysis of the Korean stock market by transfer entropy (Baek et al., 2006). Applications of transfer entropy in linguistics can be found in the book (Baeyer, 2005). Social media (for example Twitter or Facebook) serves to researches as an important source for studying social interactions. One important problem is the characterization and identification of influentials, which can be defined as users who influence the behavior of large number of other users. To characterize influence (in other words a causal relationship) in Twitter, researchers have suggested number of followers, mentions,... |

6 |
The relations between the dictionary distribution and the occurrence distribution of word length and its importance for the study of quantitative linguistics.
- Herdan
- 1958
(Show Context)
Citation Context ...rt et al., 2001). However, many phenomena which fit normal distribution, have been shown that they fit also log-normal distribution or generalized normal distribution or, more precisely, fit it even better. What is the difference between normal and log-normal distribution? Both forms of variability are based on a variety of forces (causes) acting independently of one another. A major difference is however that the effects can be additive or multiplicative, thus leading to normal or log-normal distributions, respectively (Limpert et al., 2001). The length of spoken words in phone conversation (Herdan, 1958), the length of sentences (Williams, 1940) have been shown to have log-normal distribution, as well as the age of marriage (Preston, 1981) or income (Statistical yearbook in Switzerland, 1997). Prices, incomes or populations, i.e. phenomena which grow exponentially, are often skewed to the right, and hence may be better modeled by other distributions than by the normal one, such as the log-normal distribution, Pareto distribution or skewed generalized normal distribution. Statistical inference using a normal distribution is not robust to the presence of outliers. When outliers are expected, da... |

5 |
Time series analysis, cointegration, and applications. Nobel Lecture.
- Granger
- 2003
(Show Context)
Citation Context ...enomena are investigated. A crucial question is whether there are causal relationships among the studied phenomena. This leads to a formal definition of causality and causal measures. In the following chapters we define formally two causality detection measures, namely the Granger causality and transfer entropy. 3. Granger causality The introduction of the concept of causality into the experimental science, namely into analyses of data observed in consecutive time instants (time series), is due to C.W.J. Granger in (Granger, 1969), the 2003 Nobel prize winner in economy. In his Nobel lecture (Granger, 2003) he recalled the inspiration by the Wiener’s work and identified two components of the statement about causality: 1. The cause occurs before the effect; and 2. The cause contains information about the effect that is unique, and is in no other variable. As Granger put it, a consequence of these statements is that the causal variable can help to forecast the effect variable after other data has been first used (Granger, 2003). This restricted sense of causality, referred to as Granger causality, G-causality thereafter, characterizes the extent to which a process Xt is leading another process Yt,... |

5 |
Pseudo-log-normal distributions.
- Preston
- 1981
(Show Context)
Citation Context ...neralized normal distribution or, more precisely, fit it even better. What is the difference between normal and log-normal distribution? Both forms of variability are based on a variety of forces (causes) acting independently of one another. A major difference is however that the effects can be additive or multiplicative, thus leading to normal or log-normal distributions, respectively (Limpert et al., 2001). The length of spoken words in phone conversation (Herdan, 1958), the length of sentences (Williams, 1940) have been shown to have log-normal distribution, as well as the age of marriage (Preston, 1981) or income (Statistical yearbook in Switzerland, 1997). Prices, incomes or populations, i.e. phenomena which grow exponentially, are often skewed to the right, and hence may be better modeled by other distributions than by the normal one, such as the log-normal distribution, Pareto distribution or skewed generalized normal distribution. Statistical inference using a normal distribution is not robust to the presence of outliers. When outliers are expected, data may be better described using a heavy-tailed distribution such as the Student’s t-distribution. 78 Theoretical and Methodological Appro... |

4 | Generalized Gaussian distributions for sequential data classification.
- Bicego, Gonzalez-Jimenez, et al.
- 2008
(Show Context)
Citation Context ...ces and Its Influence on Detection of Causal Relationships 3 Generalized normal distribution (generalized Gaussian distribution), first time mathematically defined in (Nadarajah, 1995) can model for example Brownian motion of particles or fractional Brownian motion with a better precision than the normal distribution (Zinde-Walsh & Phillips, 2003). Other experiments have shown a better approximation precision of the generalized Gaussian distributions than of the Gaussian distributions, for example (Sharifi & Leon-Garcia, 1995), (Moulin & Liu, 1999) for in image processing and video analysis, (Bicego et al., 2008) for EEG time series modeling. The modeling in linguistics applies mostly Gaussian mixtures. Mixtures of generalized Gaussian distributions have been recently used in text independent speaker identification (Sailaja et al., 2010) and showed that it outperforms the earlier existing text independent speaker identification models. This model was applied for speaker identification like voice dialing, banking by telephone, telephone shopping information services etc. Exponential distribution has been frequently used in modeling in astrophysics, for example the Weinman exponential distribution has b... |

4 |
Measuring direction in the coupling of biological oscillators: A case study for electroreceptors of paddlefish.
- Brea, Russell, et al.
- 2006
(Show Context)
Citation Context ...physiology are due to (Hinrichs et. al., 2006) and (Pflieger & Greenblatt, 2005). Causality or coupling directions in multimode laser dynamics is another diverse field where the conditional mutual information was applied (Otsuka et al., 2004). (Paluš & A. Stefanovska, 2003) adapted the conditional mutual information approach (Paluš et al., 2001b) to analysis of instantaneous phases of interacting oscillators and demonstrated suitability of this approach for analyzing causality in cardio-respiratory interaction (Paluš et al., 2001b). The later approach has also been applied in neurophysiology (Brea et al., 2006). More recent applications of information-theoretical functionals in natural sciences (medicine) are for example in (Van Dijck et al., 2007), inferring and quantifying causality in neuronal networks (Chicharro et al., 2011), (Vicente et al., 2010), in the computer simulation of human-robot interaction in (Sumioka et al., 1997) or in the relationship of predator-prey in etiology (Bochmann, 2007). The information-theoretical functionals applied in social sciences are mostly in financial applications: i.e. application of transfer entropy to the information flow between various 83 The Assumption o... |

4 | Causality detected by transfer entropy leads acquisition of joint attention. - Sumioka, Asada, et al. - 2007 |

3 |
A model-free characterization of causality
- Baghli
- 2006
(Show Context)
Citation Context ...2). 4.2 Transfer entropy, other information-theoretical measures and their application in natural and social sciences Turning our attention back to econometrics, we can follow further development due to (Diks & DeGoede, 2001). They applied a nonparametric approach to nonlinear Granger causality using the concept of correlation integrals (Grassberger & Procaccia, 1983) and pointed out the connection between the correlation integrals and information theory. (Diks & Panchenko, 2005) critically discussed the previous tests of (Hiemstra & Jones, 1994). As the most recent development in economics, (Baghli, 2006) proposes information-theoretic statistics for a model-free characterization of causality, based on an evaluation of conditional entropy. The information-theoretical approaches to causality detection are model free and can detect non-linear causal relationships, which are their advantages with respect to the approach of the linear Granger causality. The nonlinear extension of the Granger causality based the information-theoretic formulation has found numerous applications in various fields of natural and social sciences. Let us mention just a few examples. The Schreiber’s transfer entropy has ... |

3 |
Is the exponential distribution a good approximation of dusty galactic disks?
- Misiriotis, Kylafis, et al.
- 2000
(Show Context)
Citation Context ...ics applies mostly Gaussian mixtures. Mixtures of generalized Gaussian distributions have been recently used in text independent speaker identification (Sailaja et al., 2010) and showed that it outperforms the earlier existing text independent speaker identification models. This model was applied for speaker identification like voice dialing, banking by telephone, telephone shopping information services etc. Exponential distribution has been frequently used in modeling in astrophysics, for example the Weinman exponential distribution has been shown to be a good model for dusty galactic discs (Misiriotis et al., 2000). To summarize, other probability distributions than the normal one have an important role in modeling both in natural and social sciences. We will call them non-Gaussian distributions in the following. The selection of a correct distributions for modeling natural or social phenomena is of great importance, especially when mutual interactions among these phenomena are investigated. A crucial question is whether there are causal relationships among the studied phenomena. This leads to a formal definition of causality and causal measures. In the following chapters we define formally two causalit... |

3 |
Formation of an information network in a self-pulsating multimode laser.
- Otsuka, Miyasaka, et al.
- 2004
(Show Context)
Citation Context ...n physiology, i.e. (Verdes, 2005), in neurophysiology, i.e. (Chávez et al., 2003) and also in analysis of financial data, i.e.(Marschinski & Kantz, 2002). (Paluš et al., 2001a;b) applied their conditional mutual information based measures in analysis of electroencephalograms of patients suffering from epilepsy. Other applications of the conditional mutual information in neurophysiology are due to (Hinrichs et. al., 2006) and (Pflieger & Greenblatt, 2005). Causality or coupling directions in multimode laser dynamics is another diverse field where the conditional mutual information was applied (Otsuka et al., 2004). (Paluš & A. Stefanovska, 2003) adapted the conditional mutual information approach (Paluš et al., 2001b) to analysis of instantaneous phases of interacting oscillators and demonstrated suitability of this approach for analyzing causality in cardio-respiratory interaction (Paluš et al., 2001b). The later approach has also been applied in neurophysiology (Brea et al., 2006). More recent applications of information-theoretical functionals in natural sciences (medicine) are for example in (Van Dijck et al., 2007), inferring and quantifying causality in neuronal networks (Chicharro et al., 2011),... |

3 | Synchronization and information flow in EEG of epileptic patients. - Paluš, Komárek, et al. - 2001 |

3 |
Text independent speaker identification with finite multivariate generalized gaussian mixture model and hierarchical clustering algorithm.
- Sailaja, Rao, et al.
- 2010
(Show Context)
Citation Context ...rticles or fractional Brownian motion with a better precision than the normal distribution (Zinde-Walsh & Phillips, 2003). Other experiments have shown a better approximation precision of the generalized Gaussian distributions than of the Gaussian distributions, for example (Sharifi & Leon-Garcia, 1995), (Moulin & Liu, 1999) for in image processing and video analysis, (Bicego et al., 2008) for EEG time series modeling. The modeling in linguistics applies mostly Gaussian mixtures. Mixtures of generalized Gaussian distributions have been recently used in text independent speaker identification (Sailaja et al., 2010) and showed that it outperforms the earlier existing text independent speaker identification models. This model was applied for speaker identification like voice dialing, banking by telephone, telephone shopping information services etc. Exponential distribution has been frequently used in modeling in astrophysics, for example the Weinman exponential distribution has been shown to be a good model for dusty galactic discs (Misiriotis et al., 2000). To summarize, other probability distributions than the normal one have an important role in modeling both in natural and social sciences. We will ca... |

3 |
A note on the statistical analysis of sentence length as a criterion of literry style.
- Williams
- 1940
(Show Context)
Citation Context ...a which fit normal distribution, have been shown that they fit also log-normal distribution or generalized normal distribution or, more precisely, fit it even better. What is the difference between normal and log-normal distribution? Both forms of variability are based on a variety of forces (causes) acting independently of one another. A major difference is however that the effects can be additive or multiplicative, thus leading to normal or log-normal distributions, respectively (Limpert et al., 2001). The length of spoken words in phone conversation (Herdan, 1958), the length of sentences (Williams, 1940) have been shown to have log-normal distribution, as well as the age of marriage (Preston, 1981) or income (Statistical yearbook in Switzerland, 1997). Prices, incomes or populations, i.e. phenomena which grow exponentially, are often skewed to the right, and hence may be better modeled by other distributions than by the normal one, such as the log-normal distribution, Pareto distribution or skewed generalized normal distribution. Statistical inference using a normal distribution is not robust to the presence of outliers. When outliers are expected, data may be better described using a heavy-t... |

2 | Information: The New Language of Science. - Bayer - 2005 |

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Inferring and quantifying causality in neuronal networks.
- Chicharro, Andrzejak, et al.
- 2011
(Show Context)
Citation Context ...ed (Otsuka et al., 2004). (Paluš & A. Stefanovska, 2003) adapted the conditional mutual information approach (Paluš et al., 2001b) to analysis of instantaneous phases of interacting oscillators and demonstrated suitability of this approach for analyzing causality in cardio-respiratory interaction (Paluš et al., 2001b). The later approach has also been applied in neurophysiology (Brea et al., 2006). More recent applications of information-theoretical functionals in natural sciences (medicine) are for example in (Van Dijck et al., 2007), inferring and quantifying causality in neuronal networks (Chicharro et al., 2011), (Vicente et al., 2010), in the computer simulation of human-robot interaction in (Sumioka et al., 1997) or in the relationship of predator-prey in etiology (Bochmann, 2007). The information-theoretical functionals applied in social sciences are mostly in financial applications: i.e. application of transfer entropy to the information flow between various 83 The Assumption of Non-Gaussianity in Natural and Social Sciences and Its Influence on D tecti n of Causal Relationships 8 Will-be-set-by-IN-TECH financial time series (Dimpfl et al., 2011) or analysis of the Korean stock market by transfer... |

2 |
Immigration, income and unemployment: An application of the bounds testing approach to cointegration.
- Feridun
- 2007
(Show Context)
Citation Context ...l cortex. The results provide the first evidence for connectivity changes between and within left and right infero-temporal cortexes as a result of face recognition learning. 3.2 Application of Granger causality in natural and social sciences As already said, the Granger causality was introduced by its author in econometry and applied by him and his followers mainly in econometry, finance and market analysis, for example in (Granger, 1969), (Poon & Granger, 2003). Other applications in humanities and social sciences are in linguistics and psychology (Gilbert & Karahalios, 2009) or demography (Feridun, 2007). 81 The Assumption of Non-Gaussianity in Natural and Social Sciences and Its Influence on D tecti n of Causal Relationships 6 Will-be-set-by-IN-TECH Granger causality has also been extensively applied in natural sciences, for example in medicine, especially to neuroscience (Smith et al., 2011) for the functional magnetic resonance method and (Hesse et al., 2003), analysis of EEG signals or causal interaction in neural populations (Seth & Edelman, 2007) and in many other papers. Granger causality was applied as well as in climatology (Kufmann & Stern, 1997), in cognitive and systematical biolo... |

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Granger causality in systems biology: Modeling gene networks in time series microarray data using vector autoregressive models.
- Fujita, Severino, et al.
- 2010
(Show Context)
Citation Context ...n-Gaussianity in Natural and Social Sciences and Its Influence on D tecti n of Causal Relationships 6 Will-be-set-by-IN-TECH Granger causality has also been extensively applied in natural sciences, for example in medicine, especially to neuroscience (Smith et al., 2011) for the functional magnetic resonance method and (Hesse et al., 2003), analysis of EEG signals or causal interaction in neural populations (Seth & Edelman, 2007) and in many other papers. Granger causality was applied as well as in climatology (Kufmann & Stern, 1997), in cognitive and systematical biology, (Kim et al., 2011), (Fujita et al., 2010) etc. The main drawback of Granger causality and its extensions as a model dependent method are their instability which can cause a high variability in the final estimation of errors in (2) and (3). As an alternative, we will present in the following model-free methods whose formal definitions apply information-theoretic functionals. 4. Information-theoretical causality measures Using distributions of random processes and their definitions, introduce the information-theoretic causality measures determinism into the notion of causality. (Paluš et al., 2001b) proposed to study synchronization ph... |

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Using conditional mututal information to approximate causality for mutlivariate physiological time series.
- Pflieger, Greenblatt
- 2005
(Show Context)
Citation Context ...ral and social sciences. Let us mention just a few examples. The Schreiber’s transfer entropy has been used in climatology, i.e. (Mokhov & Smirnov, 2006; Verdes, 2005), in physiology, i.e. (Verdes, 2005), in neurophysiology, i.e. (Chávez et al., 2003) and also in analysis of financial data, i.e.(Marschinski & Kantz, 2002). (Paluš et al., 2001a;b) applied their conditional mutual information based measures in analysis of electroencephalograms of patients suffering from epilepsy. Other applications of the conditional mutual information in neurophysiology are due to (Hinrichs et. al., 2006) and (Pflieger & Greenblatt, 2005). Causality or coupling directions in multimode laser dynamics is another diverse field where the conditional mutual information was applied (Otsuka et al., 2004). (Paluš & A. Stefanovska, 2003) adapted the conditional mutual information approach (Paluš et al., 2001b) to analysis of instantaneous phases of interacting oscillators and demonstrated suitability of this approach for analyzing causality in cardio-respiratory interaction (Paluš et al., 2001b). The later approach has also been applied in neurophysiology (Brea et al., 2006). More recent applications of information-theoretical function... |

2 |
Fractional Brownian motion as a differential generalized Gaussian process.
- Zinde-Walsh, Phillips
- 2003
(Show Context)
Citation Context ... When outliers are expected, data may be better described using a heavy-tailed distribution such as the Student’s t-distribution. 78 Theoretical and Methodological Approaches to Social Sciences and Knowledge Management The Assumption of Non-Gaussianity in Natural and Social Sciences and Its Influence on Detection of Causal Relationships 3 Generalized normal distribution (generalized Gaussian distribution), first time mathematically defined in (Nadarajah, 1995) can model for example Brownian motion of particles or fractional Brownian motion with a better precision than the normal distribution (Zinde-Walsh & Phillips, 2003). Other experiments have shown a better approximation precision of the generalized Gaussian distributions than of the Gaussian distributions, for example (Sharifi & Leon-Garcia, 1995), (Moulin & Liu, 1999) for in image processing and video analysis, (Bicego et al., 2008) for EEG time series modeling. The modeling in linguistics applies mostly Gaussian mixtures. Mixtures of generalized Gaussian distributions have been recently used in text independent speaker identification (Sailaja et al., 2010) and showed that it outperforms the earlier existing text independent speaker identification models.... |

1 | The Assumption of Non-Gaussianity in Natural and Social Sciences and Its Influence on D tecti n of Causal Relationships 14 Will-be-set-by-IN-TECH - Marinazzo, D, et al. - 2004 |

1 |
Transfer entropy analysis of the Korean stock market. Physica A: Statistical Mechanics and its Applications,
- Baek, Jung, et al.
- 2006
(Show Context)
Citation Context ... et al., 2010), in the computer simulation of human-robot interaction in (Sumioka et al., 1997) or in the relationship of predator-prey in etiology (Bochmann, 2007). The information-theoretical functionals applied in social sciences are mostly in financial applications: i.e. application of transfer entropy to the information flow between various 83 The Assumption of Non-Gaussianity in Natural and Social Sciences and Its Influence on D tecti n of Causal Relationships 8 Will-be-set-by-IN-TECH financial time series (Dimpfl et al., 2011) or analysis of the Korean stock market by transfer entropy (Baek et al., 2006). Applications of transfer entropy in linguistics can be found in the book (Baeyer, 2005). Social media (for example Twitter or Facebook) serves to researches as an important source for studying social interactions. One important problem is the characterization and identification of influentials, which can be defined as users who influence the behavior of large number of other users. To characterize influence (in other words a causal relationship) in Twitter, researchers have suggested number of followers, mentions, and retweets (Cha et al., 2010), and Pagerank of follower network (Kwak at al.... |

1 |
Everyone’s an inluencer: quatifying influence on twitter.
- Bakshy, Hofman, et al.
- 2011
(Show Context)
Citation Context ...ed as users who influence the behavior of large number of other users. To characterize influence (in other words a causal relationship) in Twitter, researchers have suggested number of followers, mentions, and retweets (Cha et al., 2010), and Pagerank of follower network (Kwak at al., 2010). (Ver Steeg et al., 2011) however argue that the purely structural measures of influence (causality) can be misleading (Ghosh & Lerman, 2010) and high popularity does not necessarily imply high influence (Romero et al., 2010; Ver Steeg et al., 2011). More recent work has used the size of the cascade trees (Bakshy et al., 2011) and influence-passivity score (Romero et al., 2010). One serious drawback of existing methods is that they are based on explicit causal knowledge (i.e., A responds to B), whereas for many data sets such knowledge is not available. (Ver Steeg et al., 2011) suggest a model-free transfer entropy approach to detect causal relationships and identifying influential users based on their capacity to predict the behavior of other users. Having reviewed the relevant literature and also after extensive practical experience, we can state that the information-theoretic approach to the Granger causality pl... |

1 | Computational mechanics and information measures in food webs. - Bochmann, Lizier, et al. - 2007 |

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Measuring user influence in twitter: The milion follower fallacy. ICMSM’10:
- Cha, Haddadi, et al.
- 2010
(Show Context)
Citation Context ... the Korean stock market by transfer entropy (Baek et al., 2006). Applications of transfer entropy in linguistics can be found in the book (Baeyer, 2005). Social media (for example Twitter or Facebook) serves to researches as an important source for studying social interactions. One important problem is the characterization and identification of influentials, which can be defined as users who influence the behavior of large number of other users. To characterize influence (in other words a causal relationship) in Twitter, researchers have suggested number of followers, mentions, and retweets (Cha et al., 2010), and Pagerank of follower network (Kwak at al., 2010). (Ver Steeg et al., 2011) however argue that the purely structural measures of influence (causality) can be misleading (Ghosh & Lerman, 2010) and high popularity does not necessarily imply high influence (Romero et al., 2010; Ver Steeg et al., 2011). More recent work has used the size of the cascade trees (Bakshy et al., 2011) and influence-passivity score (Romero et al., 2010). One serious drawback of existing methods is that they are based on explicit causal knowledge (i.e., A responds to B), whereas for many data sets such knowledge is ... |

1 |
90 Theoretical and Methodological Approaches to Social Sciences and Knowledge Management The Assumption of Non-Gaussianity in Natural and Social Sciences and Its Influence on
- Cover, Thomas
- 1991
(Show Context)
Citation Context ... entropy does not depend on t, so we omitted it from labeling. Transfer entropy is a a Kullback-Leibler distance of transition probabilities. 82 Theoretical and Methodological Approaches to Social Sciences and Knowledge Management The Assumption of Non-Gaussianity in Natural and Social Sciences and Its Influence on Detection of Causal Relationships 7 It was shown in (Hlavácková-Schindler et. al., 2007) that with proper conditioning, the transfer entropy is equivalent to the conditional mutual information (Paluš et al., 2001b). The latter, however, is a standard measure of information theory (Cover & Thomas, 1991). More details on the information-theoretic methods for causality detection can be found in our review paper (Hlavácková-Schindler et. al., 2007). Marschinski and Kanz in 2002 suggested so called effective transfer entropy to reduce the bias of transfer entropy on small data sets (Marschinski & Kantz, 2002). 4.2 Transfer entropy, other information-theoretical measures and their application in natural and social sciences Turning our attention back to econometrics, we can follow further development due to (Diks & DeGoede, 2001). They applied a nonparametric approach to nonlinear Granger causali... |

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Widespread worry and the stock market. Association for the Advancement of Artificial Intelligence.
- Gilbert, Karahalios
- 2009
(Show Context)
Citation Context ...quency oscillations in sheep infero-temporal cortex. The results provide the first evidence for connectivity changes between and within left and right infero-temporal cortexes as a result of face recognition learning. 3.2 Application of Granger causality in natural and social sciences As already said, the Granger causality was introduced by its author in econometry and applied by him and his followers mainly in econometry, finance and market analysis, for example in (Granger, 1969), (Poon & Granger, 2003). Other applications in humanities and social sciences are in linguistics and psychology (Gilbert & Karahalios, 2009) or demography (Feridun, 2007). 81 The Assumption of Non-Gaussianity in Natural and Social Sciences and Its Influence on D tecti n of Causal Relationships 6 Will-be-set-by-IN-TECH Granger causality has also been extensively applied in natural sciences, for example in medicine, especially to neuroscience (Smith et al., 2011) for the functional magnetic resonance method and (Hesse et al., 2003), analysis of EEG signals or causal interaction in neural populations (Seth & Edelman, 2007) and in many other papers. Granger causality was applied as well as in climatology (Kufmann & Stern, 1997), in co... |

1 | Causality in the Sciences.
- Illari, Russo, et al.
- 2011
(Show Context)
Citation Context ... causality detection methods considered here are Granger causality (Granger, 1969) and transfer entropy (Schreiber, 2000). We investigated time series with a wider class probability distributions than Gaussian, the generalized Gaussian probability distributions. These distributions are given parametrically. We set conditions on their parameters so that one can from their values decide whether the relationships between the involved time series are unidirectional causal or whether no causality is present. Being aware of outstanding philosophical papers on causality in the sciences, for example (Illari et al., 2011), we are though not aware of any similar publication on mathematically 4 2 Will-be-set-by-IN-TECH conceived causality and their application in natural and social sciences, neither of any analysis of the probabilistic assumptions about the investigated time series and their influence on causality detection by Granger causality or transfer entropy. The paper is organized as follows. The application of various probabilistic models in natural and social sciences is discussed in Section 2. Granger causality and its application in natural and social sciences is treated in Section 3. Section 4 deals ... |

1 | What is twitter, a socila network or a news media? - Kwak, Lee, et al. - 2010 |

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92 Theoretical and Methodological Approaches to Social Sciences and Knowledge Management The Assumption of Non-Gaussianity in Natural and Social Sciences and Its Influence on Detection of
- Park, Principe
- 2008
(Show Context)
Citation Context ...on of Causal Relationships 5 sciences on the other side. In the field of economy, (Baek & Brock, 1992) and (Hiemstra & Jones, 1994) proposed a nonlinear extension of the Granger causality concept. Their non-parametric dependence estimator is based on so-called correlation integral, a probability distribution and entropy estimator, developed by physicists Grassberger and Procaccia in the field of nonlinear dynamics and deterministic chaos as a characterization tool of chaotic attractors (Grassberger & Procaccia, 1983). Another non-linear extension of Granger causality is so called correntropy (Park & Principe, 2008). A non-parametric approach to non-linear causality testing, based on non-parametric regression, was proposed in (Bell et al., 1996). Following (Hiemstra & Jones, 1994), (Aparicio & Escribano, 1998) succinctly suggested an information-theoretic definition of causality which include both linear and nonlinear dependence. Another nonlinear extension of the Granger causality approach was proposed by Chen et al. (Chen et al., 2004) using local linear predictors. An important class of nonlinear predictors are based on so-called radial basis functions (Broomhead & Lowe, 1988) which were used for nonl... |

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Influence and passivity in social media. Social Science Research Newtor Working Paper Series,
- Romero, Galuba, et al.
- 2010
(Show Context)
Citation Context ...s. One important problem is the characterization and identification of influentials, which can be defined as users who influence the behavior of large number of other users. To characterize influence (in other words a causal relationship) in Twitter, researchers have suggested number of followers, mentions, and retweets (Cha et al., 2010), and Pagerank of follower network (Kwak at al., 2010). (Ver Steeg et al., 2011) however argue that the purely structural measures of influence (causality) can be misleading (Ghosh & Lerman, 2010) and high popularity does not necessarily imply high influence (Romero et al., 2010; Ver Steeg et al., 2011). More recent work has used the size of the cascade trees (Bakshy et al., 2011) and influence-passivity score (Romero et al., 2010). One serious drawback of existing methods is that they are based on explicit causal knowledge (i.e., A responds to B), whereas for many data sets such knowledge is not available. (Ver Steeg et al., 2011) suggest a model-free transfer entropy approach to detect causal relationships and identifying influential users based on their capacity to predict the behavior of other users. Having reviewed the relevant literature and also after extensiv... |

1 | Information theoretic derivations for causality detection: Application to human gait, - Dijck, Vaerenbergh, et al. - 2007 |