Abstract

Statisticians divide into two broad schools: frequentists, who assume there is a fixed but unknown process governing observed data, and Bayesians, for whom statistics is about modelling our beliefs and updating sensibly when we see data. The Bayesian methodology has many attractive properties, for example that essentially the same method is used in any possible set-up. But one can ask how well this method works if there is indeed a fixed process governing the data; this is the goal of frequentist analysis of Bayesian procedures. I will provide a gentle introduction to this field, with reference made throughout to the specific problem I’m researching, that of finding posterior contraction rates (i.e. how fast a Bayesian’s beliefs converge to the truth) for estimation in stochastic diffusion models.