Seminar - Duality between the Approximate Bayesian Methods and Prior Robustness
School of Mathematics and Statistics Research Seminar
Speaker: Chaitanya Joshi
Time: Friday 3rd April 2020 at 02:00 PM - 03:00 PM
Location: Cotton Club, Cotton 350
Groups: "Mathematics" "Statistics and Operations Research"
In this paper, we show that there is a link between approximate Bayesian methods and prior robustness. We show that what is typically recognized as an approximation to the likelihood, either due to the simulated data as in the Approximate Bayesian Computation (ABC) methods or due to the functional approximation to the likelihood, can instead also be viewed upon as an implicit exercise in prior robustness. We first define two new classes of priors for the cases where the sufficient statistics is available, establish their mathematical properties and show, for a simple illustrative example, that these classes of priors can also be used to obtain the posterior distribution that would be obtained by implementing ABC. We then generalize and define two further classes of priors that are applicable in very general scenarios; one where the sufficient statistics is not available and another where the likelihood is approximated using a functional approximation. We then discuss the interpretation, elicitation and computational aspects of the classes proposed here. These classes establish the duality between approximate Bayesian inference and prior robustness for a wide category of Bayesian inference methods.