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Assessment and Propagation of Model Uncertainty
, 1995
"... this paper I discuss a Bayesian approach to solving this problem that has long been available in principle but is only now becoming routinely feasible, by virtue of recent computational advances, and examine its implementation in examples that involve forecasting the price of oil and estimating the ..."
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Cited by 108 (0 self)
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this paper I discuss a Bayesian approach to solving this problem that has long been available in principle but is only now becoming routinely feasible, by virtue of recent computational advances, and examine its implementation in examples that involve forecasting the price of oil and estimating the chance of catastrophic failure of the U.S. Space Shuttle.
Cluster: An unsupervised algorithm for modeling Gaussian mixtures
, 1997
"... without fee, and without written agreement is hereby granted, provided that the above copyright notice and the following two paragraphs appear in all copies of this software. In no event shall Purdue University be liable to any party for direct, indirect, special, incidental, or consequential damage ..."
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Cited by 47 (6 self)
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without fee, and without written agreement is hereby granted, provided that the above copyright notice and the following two paragraphs appear in all copies of this software. In no event shall Purdue University be liable to any party for direct, indirect, special, incidental, or consequential damages arising out of the use of this software and its documentation, even if Purdue University has been advised of the possibility of such damage. Purdue University specifically disclaims any warranties, including, but not limited to, the implied warranties of merchantability and fitness for a particular purpose. The software provided hereunder is on an “as is ” basis, and Purdue Univeristy has no obligation to provide maintenance, support, updates, enhancements, or modifications. 1 Contents
Regression And Time Series Model Selection Using Variants Of The Schwarz Information Criterion
, 1997
"... The Schwarz (1978) information criterion, SIC, is a widelyused tool in model selection, largely due to its computational simplicity and effective performance in many modeling frameworks. The derivation of SIC (Schwarz, 1978) establishes the criterion as an asymptotic approximation to a transformati ..."
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Cited by 16 (1 self)
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The Schwarz (1978) information criterion, SIC, is a widelyused tool in model selection, largely due to its computational simplicity and effective performance in many modeling frameworks. The derivation of SIC (Schwarz, 1978) establishes the criterion as an asymptotic approximation to a transformation of the Bayesian posterior probability of a candidate model. In this paper, we investigate the derivation for the identification of terms which are discarded as being asymptotically negligible, but which may be significant in small to moderate samplesize applications. We suggest several SIC variants based on the inclusion of these terms. The results of a simulation study show that the variants improve upon the performance of SIC in two important areas of application: multiple linear regression and time series analysis. 1. Introduction One of the most important problems confronting an investigator in statistical modeling is the choice of an appropriate model to characterize the underlyin...
Statistics and Music: Fitting a Local Harmonic Model to Musical Sound Signals
, 1998
"... Statistical modeling and analysis have been applied to different music related fields. One of them is sound synthesis and analysis. Sound can be represented as a realvalued function of time. This function can be sampled at a small enough rate so that the resulting discrete version is almost as goo ..."
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Cited by 8 (4 self)
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Statistical modeling and analysis have been applied to different music related fields. One of them is sound synthesis and analysis. Sound can be represented as a realvalued function of time. This function can be sampled at a small enough rate so that the resulting discrete version is almost as good as the continuous one. This permits one to study musical sounds as a discrete time series, an entity for whichmany statistical techniques are available. Physical modeling suggests that manymusical instruments' sounds are characterized bya harmonic and an additive noise signal. The noise is not something to get rid of rather it's an important part of the signal. In this research the interest is in separating these two elements of the sound. To do so a local harmonic model that tracks ch...
Modelling of ECoG in Temporal Lobe Epilepsy
 Proceedings of the 25 th Annual Rocky Mountains Bioengineering Symposium
, 1988
"... Subdural recordings of the electrical activity of the human brain give electrocorticograms (ECoG) almost free of artifacts and distortions by the skull and other intervening material. This paper discusses the modelling of the ECoG during the preictal, ictal and postictal phases of an epileptic sei ..."
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Cited by 5 (3 self)
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Subdural recordings of the electrical activity of the human brain give electrocorticograms (ECoG) almost free of artifacts and distortions by the skull and other intervening material. This paper discusses the modelling of the ECoG during the preictal, ictal and postictal phases of an epileptic seizure. Optimum order linear autoregressive (AR) models are formed and the movement of the poles of the models are traced with time. Nonlinear extension to the AR models (NAR) is formulated based on the assumption of existenceof nonlinear oscillations in the data. The optimum order of this model is determined and its performance is compared with that of the linear AR models. The analysis of the data with NAR resulted in the satisfaction of sufficient conditions for limit cycles in the ictal phase. KEY WORDS: Electrocorticography; focal epilepsy; nonlinear modelling; limit cycles. I. INTRODUCTION In this paper we are concerned with the building of models for discrete time domain ECoG data. Ou...
Generalizing The Derivation Of The Schwarz Information Criterion
, 1999
"... The Schwarz information criterion (SIC, BIC, SBC) is one of the most widely known and used tools in statistical model selection. The criterion was derived by Schwarz (1978) to serve as an asymptotic approximation to a transformation of the Bayesian posterior probability of a candidate model. Althoug ..."
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Cited by 4 (1 self)
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The Schwarz information criterion (SIC, BIC, SBC) is one of the most widely known and used tools in statistical model selection. The criterion was derived by Schwarz (1978) to serve as an asymptotic approximation to a transformation of the Bayesian posterior probability of a candidate model. Although the original derivation assumes that the observed data is independent, identically distributed, and arising from a probability distribution in the regular exponential family, SIC has traditionally been used in a much larger scope of model selection problems. To better justify the widespread applicability of SIC, we derive the criterion in a very general framework: one which does not assume any specific form for the likelihood function, but only requires that it satisfies certain nonrestrictive regularity conditions.
Information and Posterior Probability Criteria for Model Selection in Local Likelihood Estimation
 J Amer. Stat. Ass
, 1998
"... this paper we propose a modification to the methods used to motivate many information and posterior probability criteria for the weighted likelihood case. We derive weighted versions for two of the most widely known criteria, namely the AIC and BIC. Via a simple modification, the criteria are also m ..."
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Cited by 2 (0 self)
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this paper we propose a modification to the methods used to motivate many information and posterior probability criteria for the weighted likelihood case. We derive weighted versions for two of the most widely known criteria, namely the AIC and BIC. Via a simple modification, the criteria are also made useful for window span selection. The usefulness of the weighted version of these criteria are demonstrated through a simulation study and an application to three data sets. KEY WORDS: Information Criteria; Posterior Probability Criteria; Model Selection; Local Likelihood. 1. INTRODUCTION Local regression has become a popular method for smoothing scatterplots and for nonparametric regression in general. It has proven to be a useful tool in finding structure in datasets (Cleveland and Devlin 1988). Local regression estimation is a method for smoothing scatterplots (x i ; y i ), i = 1; : : : ; n in which the fitted value at x 0 is the value of a polynomial fit to the data using weighted least squares where the weight given to (x i ; y i ) is related to the distance between x i and x 0 . Stone (1977) shows that estimates obtained using the local regression methods have desirable theoretical properties. Recently, Fan (1993) has studied minimax properties of local linear regression. Tibshirani and Hastie (1987) extend the ideas of local regression to a local likelihood procedure. This procedure is designed for nonparametric regression modeling in situations where weighted least squares is inappropriate as an estimation method, for example binary data. Local regression may be viewed as a special case of local likelihood estimation. Tibshirani and Hastie (1987), Staniswalis (1989), and Loader (1999) apply local likelihood estimation to several types of data where local regressio...
COMPARATIVE SIMULATIONS OF A LARGESCALE FIELD INFILTRATION EXPERIMENT 3
"... TOUGH2 and iTOUGH2 are used to conduct forward and inverse simulations of a largescale infiltration experiment at the Maricopa Agricultural Center (MAC) near Phoenix, Arizona. Three site representations are considered: uniform horizontal layers, layers composed of uniform segments, and layers havin ..."
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TOUGH2 and iTOUGH2 are used to conduct forward and inverse simulations of a largescale infiltration experiment at the Maricopa Agricultural Center (MAC) near Phoenix, Arizona. Three site representations are considered: uniform horizontal layers, layers composed of uniform segments, and layers having randomly varying properties. Due to a paucity of hydraulic parameter measurements at the MAC, these are inferred from soil compositional data using generic data bases and pedotransfer functions. Variogram analyses of these data support the laterally nonuniform and randomly variable site representations. To reproduce observed water contents it is necessary to modify the inferred hydraulic parameters through inverse modeling based on preliminary sensitivity and error analyses. Model discrimination criteria are used to rank the three calibrated site models. Layers composed of uniform segments are ranked highest due to their superior performance and relative simplicity. The choice representation is validated by using it to reproduce water contents during another infiltration experiment.