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Predictive Concordance for Parameter Optimisation and Mixture Synthesis
[Submitted on 12 Jun 2026] · 2026-06-15 · via stat updates on arXiv.org

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Abstract:We discuss probabilistic measures of concordance between two probability distributions based on the expected misclassification rate (EMR). The focus is on comparing a given reference distribution with other distributions in a parametrised class, and optimising concordance by identifying parameter values maximising EMR or a regularised variant. EMR is a practical and decision-theoretically meaningful measure, and its optimisation has direct interpretation as a Bayesian decision analysis with a bounded utility function. We explore theoretical properties of EMR, discuss relationships with other measures including Küllback-Leibler divergence, and recognise that its optimisation has a synthetic Bayesian emulation interpretation that aids understanding and specification of regularisation penalties. A main area of methodology is in mixture synthesis where the parametrised family is a discrete mixture of given distributions. A detailed example comes from scenario forecasting in macroeconomic policy settings, a key applied area motivating the new methodology. Theoretical developments underlie efficient numerical optimisation and analysis is easily implemented using direct Monte Carlo simulation.

Submission history

From: Mike West [view email]
[v1] Fri, 12 Jun 2026 12:17:36 UTC (237 KB)