Seminar by Mr. Yann McLatchie, Department of Statistical Science, University College London

We analyse the impact of using tempered likelihoods in the production of posterior predictions. While the choice of temperature has an impact on predictive performance in small samples, we formally show that in moderate-to-large samples, tempering does not impact posterior predictions. Consequently, choosing the temperature to optimise predictive performance is an ill-defined problem. Our results constitute formal evidence of the common folklore that, in terms of predictive accuracy, parameter uncertainty is of second-order importance relative to data and model uncertainty. In particular, predictive distributions obtained with different temperatures, and thus different assessments of posterior uncertainty, merge inline with posterior concentration. This is not without precedence, and is often employed informally to justify using posteriors based on approximate and simulation-based inference to form forecast distributions: even though they produce slightly different measures of posterior uncertainty, their predictives are quickly indistinguishable. Crucially, our results make no assumptions on correct model specification, and hold when the model is misspecified.

Yann McLatchie is a doctoral researcher at University College London in the Department of Statistical Science, supervised by Jeremias Knoblauch and Edwin Fong. His research aims to extend the paradigm of probabilistic forecasting to cope with the challenges posed by modern machine learning techniques and big data.