On Entropic Tilting and Predictive Conditioning

TL;DR

This paper reviews entropic tilting (ET), a Bayesian method for constraining predictive distributions, introduces relaxed ET (RET) for bounds, and explores applications like quantile constraints and Bayesian forecasting.

Contribution

It presents new theoretical connections between ET and exponential families, extends ET to RET with bounds, and provides practical examples for quantile and forecasting constraints.

Findings

Connections between ET and exponential family distributions

Extension of ET to relaxed bounds (RET)

Application examples in quantile constraints and Bayesian forecasting

Abstract

Entropic tilting (ET) is a Bayesian decision-analytic method for constraining distributions to satisfy defined targets or bounds for sets of expectations. This report recapitulates the foundations and basic theory of ET for conditioning predictive distributions on such constraints, recognising the increasing interest in ET in several application areas. Contributions include new results related to connections with regular exponential families of distributions, and the extension of ET to relaxed entropic tilting (RET) where specified values for expectations define bounds rather than exact targets. Additional new developments include theory and examples that condition on quantile constraints for modified predictive distributions and examples relevant to Bayesian forecasting applications.