This paper considers mixtures of structural equation models with an unknown number of components. A Bayesian model selection approach is developed based on the Bayes factor. A procedure for computing the Bayes factor is developed via path sampling, which has a number of nice features. The key idea is to construct a continuous path linking the competing models; then the Bayes factor can be estim...

Bayes factors comparing two or more competing hypotheses are often estimated by constructing a Markov chain Monte Carlo (MCMC) sampler to explore the joint space of the hypotheses. To obtain efficient Bayes factor estimates, Carlin and Chib (1995, Journal of the Royal Statistical Society, Series B57, 473-484) suggest adjusting the prior odds of the competing hypotheses so that the posterior odd...

Progress in science often comes from discovering invariances in relationships among variables; these invariances often correspond to null hypotheses. As is commonly known, it is not possible to state evidence for the null hypothesis in conventional significance testing. Here we highlight a Bayes factor alternative to the conventional t test that will allow researchers to express preference for ...

For hypotheses of the type H0 : θ = θ0 vs H1 : θ 6= θ0 we demonstrate the equivalence of a Bayesian hypothesis test using a Bayes factor and the corresponding classical test, for a large class of models, which are detailed in the paper. In particular, we show that the role of the prior and critical region for the Bayes factor test is only to specify the type I error. This is their only role sin...

BACKGROUND In the context of genome-wide association studies we critique a number of methods that have been suggested for flagging associations for further investigation. METHODS The P-value is by far the most commonly used measure, but requires careful calibration when the a priori probability of an association is small, and discards information by not considering the power associated with e...

A method is given for design of experiments to detect associations (linkage disequilibrium) in a random population between a marker and a quantitative trait locus (QTL), or gene, with a given strength of evidence, as defined by the Bayes factor. Using a version of the Bayes factor that can be linked to the value of an F-statistic with an existing deterministic power calculation makes it possibl...

A key problem when fitting a model to data consists in the appropriate choice of the complexity of the model. On one side, the more complex model (that is, a model with more parameters) will usually follow the data more closely. On the other hand, the more complex model is likely to over fit the data. Several solutions to this problem have been proposed in the literature. Basically, the complex...

The relative performance of diierent methods for classiier learning varies across domains. Some recent Instance Based Learning (IBL) methods, such as IB1-MVDM* 10 , use similarity measures based on conditional class probabilities. These probabilities are a key component of Naive Bayes methods. Given this commonality of approach, it is of interest to consider how the diierences between the two m...