A Principled Approach to Bayesian Transfer Learning

Updating $\textit{a priori}$ information given some observed data is the core tenet of Bayesian inference. Bayesian transfer learning extends this idea by incorporating information from a related dataset to improve the inference on the observed data which may have been collected under slightly different settings. The use of related information can be useful when the observed data is scarce, for example. Current Bayesian transfer learning methods that are based on the so-called $\textit{power prior}$ can adaptively transfer information from related data. Unfortunately, it is not always clear under which scenario Bayesian transfer learning performs best or even if it will improve Bayesian inference. Additionally, current power prior methods rely on conjugacy to evaluate the posterior of interest. We propose using leave-one-out cross validation on the target dataset as a means of evaluating Bayesian transfer learning methods. Further, we introduce a new framework, $\textit{transfer sequential Monte Carlo}$, for power prior approaches that efficiently chooses the transfer parameter while avoiding the need for conjugate priors. We assess the performance of our proposed methods in two comprehensive simulation studies.