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arXiv · 2606.14382

Predictive Concordance for Parameter Optimisation and Mixture Synthesis

Tobias Adrian·Domenico Giannone·Matteo Luciani·Mike West
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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.

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Tobias Adrian, Domenico Giannone, Matteo Luciani, Mike West. 2026-06-12. Predictive Concordance for Parameter Optimisation and Mixture Synthesis. https://arxiv.org/abs/2606.14382

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