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Bayesian Deviance, the Effective Number of Parameters, and the Comparison of Arbitrarily Complex Models
, 1998
"... We consider the problem of comparing complex hierarchical models in which the number of parameters is not clearly defined. We follow Dempster in examining the posterior distribution of the loglikelihood under each model, from which we derive measures of fit and complexity (the effective number of p ..."
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Cited by 35 (7 self)
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We consider the problem of comparing complex hierarchical models in which the number of parameters is not clearly defined. We follow Dempster in examining the posterior distribution of the loglikelihood under each model, from which we derive measures of fit and complexity (the effective number of parameters). These may be combined into a Deviance Information Criterion (DIC), which is shown to have an approximate decisiontheoretic justification. Analytic and asymptotic identities reveal the measure of complexity to be a generalisation of a wide range of previous suggestions, with particular reference to the neural network literature. The contributions of individual observations to fit and complexity can give rise to a diagnostic plot of deviance residuals against leverages. The procedure is illustrated in a number of examples, and throughout it is emphasised that the required quantities are trivial to compute in a Markov chain Monte Carlo analysis, and require no analytic work for new...
Logicist Statistics I. Models and Modeling
 Statistical Science
, 1998
"... Abstract. Arguments are presented to support increased emphasis on logical aspects of formal methods of analysis, depending on probability in the sense of R. A. Fisher. Formulating probabilistic models that convey uncertain knowledge of objective phenomena and using such models for inductive reasoni ..."
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Cited by 6 (0 self)
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Abstract. Arguments are presented to support increased emphasis on logical aspects of formal methods of analysis, depending on probability in the sense of R. A. Fisher. Formulating probabilistic models that convey uncertain knowledge of objective phenomena and using such models for inductive reasoning are central activities of individuals that introduce limited but necessary subjectivity into science. Statistical models are classified into overlapping types called here empirical, stochastic and predictive, all drawing on a common mathematical theory of probability, and all facilitating statements with logical and epistemic content. Contexts in which these ideas are intended to apply are discussed via three major examples. Key words and phrases: Logicism and proceduralism; specificity of analysis; formal subjective probability; complementarity; subjective and objective; formal and informal; empirical, stochastic and predictive models; U.S. national census; screening for chronic disease; global climate change.
Bayesian point null hypothesis testing via the posterior likelihood ratio. Statist. and Computing
, 2005
"... ratio ..."
Spike and Slab Prior Distributions for Simultaneous Bayesian Hypothesis Testing, Model Selection, and Prediction, of Nonlinear Outcomes
"... A small body of literature has used the spike and slab prior specification for model selection with strictly linear outcomes. In this setup a twocomponent mixture distribution is stipulated for coefficients of interest with one part centered at zero with very high precision (the spike) and the oth ..."
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Cited by 1 (0 self)
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A small body of literature has used the spike and slab prior specification for model selection with strictly linear outcomes. In this setup a twocomponent mixture distribution is stipulated for coefficients of interest with one part centered at zero with very high precision (the spike) and the other as a distribution diffusely centered at the research hypothesis (the slab). With the selective shrinkage, this setup incorporates the zero coefficient contingency directly into the modeling process to produce posterior probabilities for hypothesized outcomes. We extend the model to qualitative responses by designing a hierarchy of forms over both the parameter and model spaces to achieve variable selection, model averaging, and individual coefficient hypothesis testing. To overcome the technical challenges in estimating the marginal posterior distributions possibly with a dramatic ratio of density heights of the spike to the slab, we develop a hybrid Gibbs sampling algorithm using an adaptive rejection approach for various discrete outcome models, including dichotomous, polychotomous, and count responses. The performance of the models and methods are assessed with both Monte Carlo experiments and empirical applications in political science.
Bayesian Inference for Model Choice
"... This manuscript is currently being revised. Once the revision is completed, the revised manuscript will be posted on my webpage at ..."
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This manuscript is currently being revised. Once the revision is completed, the revised manuscript will be posted on my webpage at
BAYESIAN MODEL COMPARISON AND MODEL AVERAGING FOR SMALLAREA ESTIMATION 1
, 2008
"... This paper considers smallarea estimation with lung cancer mortality data, and discusses the choice of upperlevel model for the variation over areas. Inference about the random effects for the areas may depend strongly on the choice of this model, but this choice is not a straightforward matter. W ..."
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This paper considers smallarea estimation with lung cancer mortality data, and discusses the choice of upperlevel model for the variation over areas. Inference about the random effects for the areas may depend strongly on the choice of this model, but this choice is not a straightforward matter. We give a general methodology for both evaluating the data evidence for different models and averaging over plausible models to give robust area effect distributions. We reanalyze the data of Tsutakawa [Biometrics 41 (1985) 69–79] on lung cancer mortality rates in Missouri cities, and show the differences in conclusions about the city rates from this methodology. 1. The lung cancer data. The data are male lung cancer mortality frequencies and population sizes for the period 1972–1981 in N = 84 Missouri cities (see Table 1). The variables, given in Tsutakawa and reproduced below, are the number r of men aged 45–54 dying from lung cancer in each city over the period 1972–1981 and the city size n. Most of the “cities ” are small, though three are large. The mortality rates are poorly defined in small cities; four cities with populations less than 200 have no deaths at all, so the observed rate is zero. Our aim is to estimate the mortality rates in each city, using the information from other cities in the most appropriate way. 2. Smallarea estimation. Variance component models are widely used in smallarea estimation; the term borrowing strength is commonly used to
Application to the Spanish Continuous Stock Market
, 2007
"... Firstly, I would like to thank my director, Carlos Maté Jiménez, PhD, for giving me the chance of making this project. With him, I have learnt, not only about Statistics and investigation, but also about how to enjoy with them. Special thanks to my parents. Their love and all they have taught me in ..."
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Firstly, I would like to thank my director, Carlos Maté Jiménez, PhD, for giving me the chance of making this project. With him, I have learnt, not only about Statistics and investigation, but also about how to enjoy with them. Special thanks to my parents. Their love and all they have taught me in this life are the things what have made possible being the person I am now. Thanks to my brothers, my sister and the rest of my family for their support and for the stolen time. Thanks to Charo for standing my bad mood in the bad moments, for supporting me and for giving me the inspiration to go ahead. i
Bayesian Model Comparison: Review and Discussion
"... This paper provides a brief review of the more popular methods for comparing models in a Bayesian framework. Personal experience in implementing these methods in problems requiring mixture models is also referenced. 1 ..."
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This paper provides a brief review of the more popular methods for comparing models in a Bayesian framework. Personal experience in implementing these methods in problems requiring mixture models is also referenced. 1