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Bayesian measures of model complexity and fit
 Journal of the Royal Statistical Society, Series B
, 2002
"... [Read before The Royal Statistical Society at a meeting organized by the Research ..."
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Cited by 132 (2 self)
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[Read before The Royal Statistical Society at a meeting organized by the Research
Deviance Information Criterion for Comparing Stochastic Volatility Models
 Journal of Business and Economic Statistics
, 2002
"... Bayesian methods have been efficient in estimating parameters of stochastic volatility models for analyzing financial time series. Recent advances made it possible to fit stochastic volatility models of increasing complexity, including covariates, leverage effects, jump components and heavytailed d ..."
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Cited by 26 (7 self)
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Bayesian methods have been efficient in estimating parameters of stochastic volatility models for analyzing financial time series. Recent advances made it possible to fit stochastic volatility models of increasing complexity, including covariates, leverage effects, jump components and heavytailed distributions. However, a formal model comparison via Bayes factors remains difficult. The main objective of this paper is to demonstrate that model selection is more easily performed using the deviance information criterion (DIC). It combines a Bayesian measureoffit with a measure of model complexity. We illustrate the performance of DIC in discriminating between various different stochastic volatility models using simulated data and daily returns data on the S&P100 index.
Training Samples in Objective Bayesian Model Selection
 Ann. Statist
, 2004
"... Central to several objective approaches to Bayesian model selection is the use of training samples (subsets of the data), so as to allow utilization of improper objective priors. The most common prescription for choosing training samples is to choose them to be as small as possible, subject to yield ..."
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Cited by 7 (2 self)
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Central to several objective approaches to Bayesian model selection is the use of training samples (subsets of the data), so as to allow utilization of improper objective priors. The most common prescription for choosing training samples is to choose them to be as small as possible, subject to yielding proper posteriors; these are called minimal training samples.
Bayesian Estimation and Model Choice in Item Response Models
, 1999
"... Item response models are essential tools for analyzing results from many placement tests. Such models are used to quantify the probability of correct response as a function of unobserved examinee ability and other parameters explaining the difficulty and the discriminatory power of the questions in ..."
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Cited by 4 (1 self)
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Item response models are essential tools for analyzing results from many placement tests. Such models are used to quantify the probability of correct response as a function of unobserved examinee ability and other parameters explaining the difficulty and the discriminatory power of the questions in the test. Some of these models also incorporate a threshold parameter for the probability of the correct response to eliminate the effect of guessing the correct answer in multiple choice type tests. In this article we consider fitting of these models using the Gibbs sampler. A data augmentation method to analyze a normalogive model incorporating a threshold guessing parameter is introduced and compared with a MetropolisHastings sampling method. The proposed method is an order of magnitude better than the existing method. Another objective of this paper is to develop Bayesian model choice techniques for model discrimination. A predictive approach based on a variant of the Bayes factor is ...
Strategies for Inference Robustness in Complex Modelling: An Application to Longitudinal Performance Measures.
, 1999
"... Advances in computation mean it is now possible to fit a wide range of complex models, but selecting a model on which to base reported inferences is a difficult problem. Following an early suggestion of Box and Tiao, it seems reasonable to seek `inference robustness' in reported models, so that a ..."
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Cited by 1 (0 self)
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Advances in computation mean it is now possible to fit a wide range of complex models, but selecting a model on which to base reported inferences is a difficult problem. Following an early suggestion of Box and Tiao, it seems reasonable to seek `inference robustness' in reported models, so that alternative assumptions that are reasonably well supported would not lead to substantially different conclusions. We propose a fourstage modelling strategy in which we: iteratively assess and elaborate an initial model, measure the support for each of the resulting family of models, assess the influence of adopting alternative models on the conclusions of primary interest, and identify whether an approximate model can be reported. These stages are semiformal, in that they are embedded in a decisiontheoretic framework but require substantive input for any specific application. The ideas are illustrated on a dataset comprising the success rates of 46 invitro fertilisation clinics over three years. The analysis supports a model that assumes 43 of the 46 clinics have odds on success that are evolving at a constant proportional rate (i.e. linear on a logit scale), while three clinics are outliers in the sense of showing nonlinear trends. For the 43 `linear' clinics, the intercepts and gradients can be assumed to follow a bivariate normal distribution except for one outlying intercept: the odds on success are significantly increasing for four clinics and significantly decreasing for three. This model displays considerable inference robustness and, although its conclusions could be approximated by other lesssupported models, these would not be any more parsimonious. Technical issues include fitting mixture models of alternative hierarchical longitudinal models, t...
A Comparison of Frailty and Other Models for Bivariate Survival Data
, 1999
"... ... In this article, we compare the frailty models for bivariate data with the models based on bivariate exponential and Weibull distributions. Bayesian methods provide a convenient paradigm for comparing the two sets of models we consider. Our techniques are illustrated using two examples. One simu ..."
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... In this article, we compare the frailty models for bivariate data with the models based on bivariate exponential and Weibull distributions. Bayesian methods provide a convenient paradigm for comparing the two sets of models we consider. Our techniques are illustrated using two examples. One simulated example demonstrates model choice methods developed in this paper and the other example, based on a practical data set of onset of blindness for diabetic Retinopathy patients, considers Bayesian inference using different models.
Expected Posterior Prior Distributions for Model Selection
"... Consider the problem of comparing parametric models M 1 ; : : : ; M k , when at least one of the models has an improper prior ß N i (` i ). Using the Bayes factor for comparing among these is not feasible due to arbitrary multiplicative constants in ß N (` i ). In this work we suggest adjusting t ..."
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Consider the problem of comparing parametric models M 1 ; : : : ; M k , when at least one of the models has an improper prior ß N i (` i ). Using the Bayes factor for comparing among these is not feasible due to arbitrary multiplicative constants in ß N (` i ). In this work we suggest adjusting the initial priors for each model, ß N i , by ß i (` i ) = Z ß N i (` i jy )m (y )dy where m is a suitable predictive measure on (imaginary) training samples, y . The updated prior, ß , is called the expected posterior prior under m . Some properties of this approach include: (1) The resulting Bayes factors depend only on sufficient statistics. (2) The resulting Bayesian inference is coherent and allows for multiple comparisons. (3) In many cases, it is possible to find m such that, for a sample of minimal size, there is predictive matching for the comparisons of model M i to M j ,i.e., the Bayes factor B ij = 1. (4) In the case of nested models, where M 1 is ...
& Gynecology)
"... ❙ X: Επίπεδο εστριόλης (estriol) των εγκύων γυναικών ❚ Υ i ~ Normal(μ i, σ 2) ❚ μ i =η i =α+βΧ i 6 … ΑΠΛΟΙ ΕΛΕΓΧΟΙ ΥΠΟΘΕΣΕΩΝ 6.1. Εισαγωγή: ΕκτωνΥστερων Λόγος ..."
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❙ X: Επίπεδο εστριόλης (estriol) των εγκύων γυναικών ❚ Υ i ~ Normal(μ i, σ 2) ❚ μ i =η i =α+βΧ i 6 … ΑΠΛΟΙ ΕΛΕΓΧΟΙ ΥΠΟΘΕΣΕΩΝ 6.1. Εισαγωγή: ΕκτωνΥστερων Λόγος
59, Part 2, pp. 233–253 Structural and parameter uncertainty in Bayesian costeffectiveness models
, 2008
"... Summary. Health economic decision models are subject to various forms of uncertainty, including uncertainty about the parameters of the model and about the model structure. These uncertainties can be handled within a Bayesian framework, which also allows evidence from previous studies to be combined ..."
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Summary. Health economic decision models are subject to various forms of uncertainty, including uncertainty about the parameters of the model and about the model structure. These uncertainties can be handled within a Bayesian framework, which also allows evidence from previous studies to be combined with the data. As an example, we consider a Markov model for assessing the costeffectiveness of implantable cardioverter defibrillators. Using Markov chain Monte Carlo posterior simulation, uncertainty about the parameters of the model is formally incorporated in the estimates of expected cost and effectiveness. We extend these methods to include uncertainty about the choice between plausible model structures. This is accounted for by averaging the posterior distributions from the competing models using weights that are derived from the pseudomarginallikelihood and the deviance information criterion, which are measures of expected predictive utility. We also show how these costeffectiveness calculations can be performed efficiently in the widely used software WinBUGS.