Priors play a key role in Bayesian modelling, computation and inference. There is interest in the formulation of so-called uninformative or weakly informative priors, which carry little to no information in the posterior distribution, given the data. Although there has been a substantial amount of research on these types of priors, the increasing complexity of models and the expansion of computational algorithms motivates new ideas and insights. In this presentation, I will discuss some recent research into the formulation of such priors for mixture models, hypothesis testing and model evaluation. The integral role of approximate Bayesian computation (ABC) as a computational tool will also be highlighted. This work is joint with a number of co-authors, listed below.
References
Z van Havre, N White, J Rousseau, K Mengersen (2015) Overfitting Bayesian Mixture Models with an Unknown Number of Components. PLoS One. 10, 1-27.
K Kanary, K Mengersen, CP Robert, J Rousseau (2018) Testing hypotheses via a mixture estimation model. arXiv:1412.2044.
DJ Nott, CC Drovandi, K Mengersen, M Evans (2018) Approximation of Bayesian predictive p-values with regression ABC. Bayesian Analysis. 13, 59-83.
J Rousseau, K Mengersen (2011) Asymptotic behaviour of the posterior distribution in overfitted mixture models. JRSS Series B. 73, 689?710
W Xueou, DJ Nott, CC Drovandi, K Mengersen, M Evans (2018) Using history matching for prior choice. Technometrics. To appear.