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Approximate Bayes Factors and Accounting for Model Uncertainty in Generalized Linear Models
, 1993
"... Ways of obtaining approximate Bayes factors for generalized linear models are described, based on the Laplace method for integrals. I propose a new approximation which uses only the output of standard computer programs such as GUM; this appears to be quite accurate. A reference set of proper priors ..."
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Cited by 96 (28 self)
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Ways of obtaining approximate Bayes factors for generalized linear models are described, based on the Laplace method for integrals. I propose a new approximation which uses only the output of standard computer programs such as GUM; this appears to be quite accurate. A reference set of proper priors is suggested, both to represent the situation where there is not much prior information, and to assess the sensitivity of the results to the prior distribution. The methods can be used when the dispersion parameter is unknown, when there is overdispersion, to compare link functions, and to compare error distributions and variance functions. The methods can be used to implement the Bayesian approach to accounting for model uncertainty. I describe an application to inference about relative risks in the presence of control factors where model uncertainty is large and important. Software to implement the
Bayesian Selection of LogLinear Models
 Canadian Journal of Statistics
, 1995
"... A general methodology is presented for finding suitable Poisson loglinear models with applications to multiway contingency tables. Mixtures of multivariate normal distributions are used to model prior opinion when a subset of the regression vector is believed to be nonzero. This prior distribution ..."
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Cited by 7 (2 self)
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A general methodology is presented for finding suitable Poisson loglinear models with applications to multiway contingency tables. Mixtures of multivariate normal distributions are used to model prior opinion when a subset of the regression vector is believed to be nonzero. This prior distribution is studied for two and threeway contingency tables, in which the regression coefficients are interpretable in terms of oddsratios in the table. Efficient and accurate schemes are proposed for calculating the posterior model probabilities. The methods are illustrated for a large number of twoway simulated tables and for two threeway tables. These methods appear to be useful in selecting the best loglinear model and in estimating parameters of interest that reflect uncertainty in the true model. Key words and phrases: Bayes factors, Laplace method, Gibbs sampling, Model selection, Odds ratios. AMS subject classifications: Primary 62H17, 62F15, 62J12. 1 Introduction 1.1 Bayesian testing...
TEACHING BAYESIAN METHODS IN BIOMEDICAL RESEARCH
"... This paper considers experiences of teaching Bayesian statistical methods within a biomedical research setting to both statisticians and nonstatisticians at postgraduate level. In particular, it considers topics covered, level of mathematical exposition, software and texts. ..."
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This paper considers experiences of teaching Bayesian statistical methods within a biomedical research setting to both statisticians and nonstatisticians at postgraduate level. In particular, it considers topics covered, level of mathematical exposition, software and texts.
The Bayesian Score Statistic
"... We propose a novel Bayesian test under a (noninformative) Jeffreys ’ prior specification. We check whether the fixed scalar value of the socalled Bayesian Score Statistic (BSS) under the null hypothesis is a plausible realization from its known and standardized distribution under the alternative. U ..."
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We propose a novel Bayesian test under a (noninformative) Jeffreys ’ prior specification. We check whether the fixed scalar value of the socalled Bayesian Score Statistic (BSS) under the null hypothesis is a plausible realization from its known and standardized distribution under the alternative. Unlike highest posterior density regions the BSS is invariant to reparameterizations. The BSS equals the posterior expectation of the classical score statistic and it provides an exact test procedure, whereas classical tests often rely on asymptotic results. Since the statistic is evaluated under the null hypothesis it provides the Bayesian counterpart of diagnostic checking. This result extends the similarity of classical sampling densities of maximum likelihood estimators and Bayesian posterior distributions based on Jeffreys ’ priors, towards score statistics. We illustrate the BSS as a diagnostic to test for misspecification in linear and cointegration models. 1