We describe two interesting and innovative strands of Murray Aitkin's research publications, dealing with mixture models and with Bayesian inference. Of his considerable publications on mixture models, we focus on a nonparametric random effects approach in generalized linear mixed modelling, which has proven useful in a wide variety of applications. As an early proponent of ways of implementing the Bayesian paradigm, Aitkin proposed an alternative Bayes factor based on a posterior mean likelihood. We discuss these innovative approaches and some research lines motivated by them and also suggest future related methodological implementations.
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