Bayesian analysis of factorial experiments by mixture modelling

by Agostino Nobile and Peter J. Green (University of Bristol)
A Bayesian analysis for factorial experiments is presented, using finite mixture distributions to model the main effects and interactions. This allows both estimation and an analogue of hypothesis testing in a posterior analysis using a single prior specification. A detailed formulation based on this approach is provided for the case of the two-way model with replication, allowing interactions. Issues in formulating a suitable prior are discussed in detail, and, in the context of three illustrative applications, we discuss implementation, presentation of posterior distributions, sensitivity, and performance of the MCMC methods that are used.

Some key words: Analysis of Variance, Bayes linear model, Finite mixture distributions, Identifiability, Markov chain Monte Carlo, Partial exchangeability, Random partitions, Reversible jump, Sensitivity analysis.

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