For the problem of variable selection for the normal linear model, fixed penalty selection criteria such as AIC, Cp, BIC and RIC correspond to the posterior modes of a hierarchical Bayes model for various fixed hyperparameter settings. Adaptive selection criteria obtained by empirical Bayes estimation of the hyperparameters have been shown by George and Foster [2000. Calibration and Empirical B...

Consider an experiment yielding an observable random quantity X whose distribution Fθ depends on a parameter θ with θ being distributed according to some distribution G0. We study the Bayesian estimation problem of θ under squared error loss function based on X, as well as some additional data available from other similar experiments according to an empirical Bayes structure. In a recent paper,...

Wheeler WC and Pickett KM (2008. Topology-Bayes versus clade-Bayes in phylogenetic analysis. Mol Biol Evol. 25:447-453.) discuss two ways of summarizing the posterior probability distribution of a Bayesian phylogenetic analysis, which they refer to as "topology-Bayes" and "clade-Bayes." They claim that the clade-Bayes approach leads to problems such as "exaggerated clade support, inconsistently...

Naive Bayes The multinomial Naive Bayes model on a dictionary is a familiar option for text classification, e.g. (Gale, Church, & Yarowski 1992), (McCallum & Nigam 1998). When there are additional features, the Naive Bayes model has also a natural extension: We simply assume that each additional feature is independent of all the others, conditional upon . In this case, we invert Bayes’ Law by o...

BACKGROUND AND AIMS It has been proposed that more use should be made of Bayes factors in hypothesis testing in addiction research. Bayes factors are the ratios of the likelihood of a specified hypothesis (e.g. an intervention effect within a given range) to another hypothesis (e.g. no effect). They are particularly important for differentiating lack of strong evidence for an effect and evidenc...

We generalize the approach of Liu and Lawrence (1999) for multiple changepoint problems where the number of changepoints is unknown. The approach is based on dynamic programming recursion for efficient calculation of the marginal probability of the data with the hidden parameters integrated out. For the estimation of the hyperparameters, we propose to use Monte Carlo EM when training data are a...

Recent work in supervised learning has shown that a surprisingly simple Bayesian classifier with assumptions of conditional independence among features given the class, called naı̈ve Bayes, is competitive with state of the art classifiers. On this paper a new naive Bayes classifier called Interval Estimation naı̈ve Bayes is proposed. Interval Estimation naı̈ve Bayes performs on two phases. On the ...

An estimation problem of the mean µ of an inverse Gaussian distribution IG(µ, C µ) with known coefficient of variation c is treated as a decision problem with entropy loss function. A class of Bayes estimators is constructed, and shown to include MRSE estimator as its closure. Two important members of this class can easily be computed using continued fractions