We present a framework for the rational analysis of elemental causal induction – learning about the existence of a relationship between a single cause and effect – based upon causal graphical models. This framework makes precise the distinction between causal structure and causal strength: the difference between asking whether a causal relationship exists and asking how strong that causal relationship might be. We show that two leading rational models of elemental causal induction, ∆P and causal power, both estimate causal strength, and introduce a new rational model, causal support, that assesses causal structure. Causal support predicts several key phenomena of causal induction that cannot be accounted for by other rational models, which we explore through a series of experiments. These phenomena include the complex interaction between ∆P and the base-rate probability of the effect in the absence of the cause, sample size effects, inferences from incomplete contingency tables, and causal learning from rates. Causal support also provides a better account of a number of existing datasets than either ∆P or causal power.

Inducing causal relationships from observations is a classic problem in scientific inference, statistics, and machine learning. It is also a central part of human learning, and a task that people perform remarkably well given its notorious difficulties. People can learn causal structure in various settings, from diverse forms of data: observations of the co-occurrence frequencies between causes and effects, interactions between physical objects, or patterns of spatial or temporal coincidence. These different modes of learning are typically thought of as distinct psychological processes and are rarely studied together, but at heart they present the same inductive challenge—identifying the unobservable mechanisms that generate observable relations between variables, objects, or events, given only sparse and limited data. We present a computational-level analysis of this inductive problem and a framework for its solution, which allows us to model all these forms of causal learning in a common language. In this framework, causal induction is the product of domain-general statistical inference guided by domain-specific prior knowledge, in the form of an abstract causal theory. We identify 3 key aspects of abstract prior knowledge—the ontology of entities, properties, and relations that organizes a domain; the plausibility of specific causal relationships; and the functional form of those relationships—and show how they provide the constraints that people need to induce useful causal models from sparse data.

In this paper we give a general definition of residuals for regression models with independent responses. Our definition produces residuals which are exactly normal, apart from sampling variability in the estimated parameters, by inverting the fitted distribution function for each response value and finding the equivalent standard normal quantile. Our definition includes some randomization to achieve continuous residuals when the response variable is discrete. Quantile residuals are easily computed in computer packages such as SAS, S-Plus, GLIM or LispStat, and allow residual analyses to be carried out in many commonly occurring situations in which the customary definitions of residuals fail. Quantile residuals are applied in this paper to three example data sets. Keywords: deviance residual; exponential regression; generalized linear model; logistic regression; normal probability plot; Pearson residual. 1 Introduction Residuals, and especially plots of residuals, play a central role ...

We first describe a number of inter-related issues that need to be considered by the researcher when comparing frequencies of linguistic features in two or more corpora. We then describe the chi-squared and log-likelihood tests used in previous research for the comparison of word frequencies. Our focus, in this paper, is on the issue of reliability of the statistical tests, and we describe simulation experiments to compare the reliability of the chisquared and log-likelihood statistics under conditions of different-sized corpora and probability of a word occurring in text. We observe that the Cochran rule provides a good guide to accuracy of both statistics in general, but in some cases it needs to be extended. We conclude by recommending higher cut-off values for the Cochran rule at the 5%, 1 % and 0.1 % levels. In order to extend applicability of the frequency comparisons to expected values of 1 or more, use of the log-likelihood statistic is preferred over the chi-squared statistic, at the 0.01 % level. The trade-off for corpus linguists is that the new critical value is 15.13.

Abstract — In this paper, the distribution of mutual information between two discrete random variables is approximated by means of a second-order Taylor series expansion. Approximative expressions for the distribution of mutual information (MI) between independent random variables, conditional MI between conditionally independent variables, and MI between (weakly) dependent random variables are derived. These distributions are functions of the available sample size and the number of realisations of the random variables only; knowledge of the variables ’ PMF is not required. The results are verified numerically for various cases. Exemplary application ideas in statistics and communications engineering are proposed. I.

In this paper, we present a framework for categorical data analysis which allows such data sets to be explored using a rich set of techniques that are only applicable to continuous data sets. We introduce the concept of separability statistics in the context of exploratory categorical data analysis. We show how these statistics can be used as a way to map categorical data to continuous space given a labeled reference data set. This mapping enables visualization of categorical data using techniques that are applicable to continuous data. We show that in the transformed continuous space, the performance of the standard k-nn based outlier detection technique is comparable to the performance of the k-nn based outlier detection technique using the best of the similarity measures designed for categorical data. The proposed framework can also be used to devise similarity measures best suited for a particular type of data set. 1

An integrated approach for visual analysis of a multi-source moving objects knowledge base

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An expressive and comprehensive situation picture is necessary for a reliable decision making in various application fields. The domain knowledge, however, is often too complex to be handled individually, and thus geographical information systems (GIS) with powerful modeling tools are nowadays availed to support the process. Data to be considered are becoming available at an increasing speed and level of detail, thus the challenge of obtaining a useful resulting model lies in utilization of suitable methods. In our research, we deal with a systematic risk assessment model for Helsinki Fire&Rescue services. The model shall serve as a basis for preparedness of fire brigades. In this paper, we aim to use contingency tables, which are known from statistics, to assist valuing new variables for the developing risk model. In the case study, we analyze spatial relationships between the incident data points and distribution of population age. Derived information shall be implemented into the spatial model, which is the basis for further risk modeling process. The methods for the analysis of spatial data suggested in this paper support reliability of the risk model and advance understanding of how GIScientist can contribute to the process of decision making. 1.

Objective: To evaluate the ability of the fellow eye to detect stimuli in the area corresponding to the ring scotoma (blind area) of a monocular bioptic telescope in simple conditions (conventional perimetry) and in more visually demanding conditions. Methods: A computerized dichoptic perimeter enabled separate stimuli to be presented to each eye of 7 bioptic users and 7 nonusers. The bioptic ring scotoma was mapped by presenting the stimulus to the telescope eye only. Detection tests were then conducted under binocular viewing, with stimuli presented only to the fellow eye in a 2�2�2 design with or without telescope, on plain gray or patterned (spatial noise) background, and with passive (looking at cross) or active (reading letters) fixation task. Results: No significant differences were noted in felloweye detection with (86%) and without (87%) a bioptic. The detection rate was significantly reduced on the patterned background and in the active fixation task. Conclusions: To our knowledge, this is the first study to demonstrate fellow-eye detection in the area of the ring scotoma with a monocular bioptic telescope under more realistic and visually demanding conditions than conventional perimetry. These results should ease the concern that the monocular ring scotoma might cause blindness to traffic outside the field of the telescope.