On Entropic Tilting and Predictive Conditioning

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.