Bayesian improver of a distribution

 An estimate of a distribution obtained from a sample by any method of classical statistics may be erroneous when the sample is not representative of the population. A subjective distribution elicited from an expert may be miscalibrated when information is scanty and experience limited. The Bayesian Improver of a Distribution (BID) exploits a coherence principle and improves, in the ex ante sense, an initial estimate of a continuous distribution by using (i) the known distribution of a related variate and (ii) information about the dependence structure between the two variates. The theory of BID is developed into an applied (ABID) procedure. The ABID estimator is applicable to any continuous, monotone likelihood ratio dependent variates with arbitrary, strictly increasing marginal distributions, parametric or nonparametric; it is analytic in form and easy to implement via statistical or judgmental methods; it converges to the true distribution, provided the initial estimator does, as the sample size n→∞; it outperforms the initial estimator in the expected Kolmogorov–Smirnov distance for all n; and it offers the greatest gains when n is small – precisely when improved estimates are needed most.