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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 111 (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.
Inference and Hierarchical Modeling in the Social Sciences
, 1995
"... this paper I (1) examine three levels of inferential strength supported by typical social science datagathering methods, and call for a greater degree of explicitness, when HMs and other models are applied, in identifying which level is appropriate; (2) reconsider the use of HMs in school effective ..."
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Cited by 22 (6 self)
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this paper I (1) examine three levels of inferential strength supported by typical social science datagathering methods, and call for a greater degree of explicitness, when HMs and other models are applied, in identifying which level is appropriate; (2) reconsider the use of HMs in school effectiveness studies and metaanalysis from the perspective of causal inference; and (3) recommend the increased use of Gibbs sampling and other Markovchain Monte Carlo (MCMC) methods in the application of HMs in the social sciences, so that comparisons between MCMC and betterestablished fitting methodsincluding full or restricted maximum likelihood estimation based on the EM algorithm, Fisher scoring or iterative generalized least squaresmay be more fully informed by empirical practice.
Bayesian Hierarchical Modeling
, 2000
"... Introduction This tutorial provides a very brief introduction to the formulation, tting, and checking of hierarchical or multilevel models from the Bayesian point of view. Hierarchical models (HMs) arise frequently in ve main kinds of applications: 1 HMs are common in elds such as health and educa ..."
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Cited by 13 (3 self)
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Introduction This tutorial provides a very brief introduction to the formulation, tting, and checking of hierarchical or multilevel models from the Bayesian point of view. Hierarchical models (HMs) arise frequently in ve main kinds of applications: 1 HMs are common in elds such as health and education, in which databoth outcomes and predictorsare often gathered in a nested or hierarchical fashion, e.g., patients within hospitals, or students within classrooms within schools. HMs are thus also ideally suited to the wide range of applications in government and business in which single or multistage cluster samples are routinely drawn, and oer a unied approach to the analysis of randomeects (variancecomponents) and mixed models. 2 Introduction (continued) 2 A dierent kind
Enhancing the Predictive Performance of Bayesian Graphical Models
 Communications in Statistics – Theory and Methods
, 1995
"... Both knowledgebased systems and statistical models are typically concerned with making predictions about future observables. Here we focus on assessment of predictive performance and provide two techniques for improving the predictive performance of Bayesian graphical models. First, we present Baye ..."
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Cited by 7 (4 self)
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Both knowledgebased systems and statistical models are typically concerned with making predictions about future observables. Here we focus on assessment of predictive performance and provide two techniques for improving the predictive performance of Bayesian graphical models. First, we present Bayesian model averaging, a technique for accounting for model uncertainty. Second, we describe a technique for eliciting a prior distribution for competing models from domain experts. We explore the predictive performance of both techniques in the context of a urological diagnostic problem. KEYWORDS: Prediction; Bayesian graphical model; Bayesian network; Decomposable model; Model uncertainty; Elicitation. 1 Introduction Both statistical methods and knowledgebased systems are typically concerned with combining information from various sources to make inferences about prospective measurements. Inevitably, to combine information, we must make modeling assumptions. It follows that we should car...
Bayesian Data Analysis for Data Mining
 In Handbook of Data Mining
, 2002
"... Introduction The Bayesian approach to data analysis computes conditional probability distribu tions of quantities of interest (such as future observables) given the observed data. Bayesian analyses usually begin with a .full probability model  a joint probability dis tribution for all the observ ..."
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Introduction The Bayesian approach to data analysis computes conditional probability distribu tions of quantities of interest (such as future observables) given the observed data. Bayesian analyses usually begin with a .full probability model  a joint probability dis tribution for all the observable and unobservable quantities under study  and then use Bayes' theorem (Bayes, 1763) to compute the requisite conditional probability distributions (called poster'Joy distributions). The theorem itself is innocuous enough. In its simplest form, if Q denotes a quantity of interest and D denotes data, the theorem states: P(ql D) P(;lq) X P(q)/P(). This theorem prescribes the basis for statistical learning in the probabilistic frame work. With p(Q) regarded as a probabilistic statement of prior knowledge about Q before obtaining the data D, p(QI D) becomes a revised probabilistic statement of our knowledge about Q in the light of the data (Bernardo and Smith, 1994, p.2). The marginal lik
Volume I Theory and Methods for Quality Evaluation Preface
"... The Model Quality Report in Business Statistics project was set up to develop a detailed description of the methods for assessing the quality of surveys, with particular application in the context of business surveys, and then to apply these methods in some example surveys to evaluate their quality. ..."
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The Model Quality Report in Business Statistics project was set up to develop a detailed description of the methods for assessing the quality of surveys, with particular application in the context of business surveys, and then to apply these methods in some example surveys to evaluate their quality. The work was specified and initiated by Eurostat following on from the Working Group on Quality of Business Statsitics. It was funded by Eurostat under SUPCOM 1997, lot 6, and has been undertaken by a consortium of the UK Office for National Statistics, Statistics Sweden, the University of Southampton and the University of Bath, with the Office for National Statistics managing the contract. The report is divided into four volumes, of which this is the first. This volume deals with the theory and methods for assessing quality in business surveys in nine chapters following the survey process through its various stages in order. These fall into three parts, one dealing with sampling errors, one with a variety of nonsampling errors, and one covering coherence and comparability of statistics. Other volumes of the report contain: • a comparison of the software methods and packages available for variance estimation in sample surveys (volume II); • example assessments of quality for an annual and a monthly business survey from Sweden and the UK (volume III); • guidelines for and experiences of implementing the methods (volume IV). An outline of the chapters in the report is given on the following page. Acknowledgements Apart from the authors, several other people have made large contributions without which this report would not have reached its current form. In particular we would like to mention
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"... In probability theory, the random variables Y1,...,YN are said to be exchangeable (or permutable or symmetric) if their joint distribution F(y1,...,yN) is symmetric; that is, if F is invariant under permutation of its arguments, so that F(z1,...,zN) = F(y1,...,yN) whenever z1,...,zN is a permutatio ..."
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In probability theory, the random variables Y1,...,YN are said to be exchangeable (or permutable or symmetric) if their joint distribution F(y1,...,yN) is symmetric; that is, if F is invariant under permutation of its arguments, so that F(z1,...,zN) = F(y1,...,yN) whenever z1,...,zN is a permutation of y1,...,yN. There is a related epidemiologic usage which is described in the article on confounding. In many ways, sequences of exchangeable random variables play a role in subjective Bayesian theory analogous to that played by independent identically distributed (iid) sequences in classical frequentist theory. In particular, the assumption that a sequence of random variables is exchangeable allows the development of inductive statistical procedures for inference from observed to unobserved members of the sequence [1–3, 5, 6, 9]. Exchangeable random variables are identically distributed, and iid variables are exchangeable. Now suppose that Y1,...,YN are iid given an unknown parameter θ that indexes their joint distribution (see Identifiability). Such variables will not be unconditionally independent when θ is a random variable, but will be exchangeable. Consider, for example, the case in which Y1,...,YN have a joint density. The unconditional density of Y1,...,YN will be f(y1,...,yN) = f(y1,...,yNθ) dF(θ)
1.1 Quantification of uncertainty: classical, frequentist, and Bayesian definitions of probability. Subjectivity and objectivity. Case study: Diagnostic screening for HIV 1.2 Sequential learning; Bayes ’ Theorem. Inference (science)
"... and decisionmaking (policy and business). 1.3 Bayesian decision theory; coherence. Maximization of expected utility ..."
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and decisionmaking (policy and business). 1.3 Bayesian decision theory; coherence. Maximization of expected utility