Statistical Modelling 22 (1&2) (2022), 33–45

Reflections on Murray Aitkin's contributions to nonparametric mixture models and Bayes factors

Alan Agresti,
University of Florida,
Gainesville, Florida,
USA.
e-mail: agresti@ufl.edu

Francesco Bartolucci,
University of Perugia,
Perugia,
Italy.

Antonietta Mira,
Università della Svizzera italiana,
Lugano,
Switzerland;
University of Insubria,
Como,
Italy.

Abstract:

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.

Keywords:

Bayes factor, Bayesian inference, generalized linear mixed model, mean likelihood, mixture models, nonparametric random effects

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