Recovering Posterior Beliefs in Credit Risk: A Latent-State EM Extension of the Information-Geometric Framework

RESUMO

This paper develops a latent-state framework for recovering borrower-level posterior beliefs in credit-risk analysis. Creditworthiness and financial fragility are represented as latent dimensions, while observed borrower scores follow a finite Gaussian mixture model where default depends on the profile. Borrower-specific probabilities of default are obtained by averaging profile-specific default probabilities over the posterior distribution of latent states. A joint Expectation–Maximization procedure is used to estimate mixture structure and parameters from observed score–default pairs. After estimation, predictive posterior beliefs are computed using scores alone, thereby preserving information available before default realization. A controlled simulation experiment evaluates the recovery of structural parameters, posterior beliefs, and default probabilities. Posterior distributions are interpreted as points on probability simplex, and their recovery is assessed using both conventional error measures and information-geometric divergences. The results provide a controlled benchmark for studying the interaction between latent economic structure, uncertainty, and prediction.