Bayesian nonparametric density estimation, ordinal regression, and hidden Markov models under likelihood ratio order constraints

A. Olivares Canal, V. Peña Pizarro, M. Jauch, A. F. Barrientos

Domain knowledge often suggests that distributions satisfy a stochastic order. Jauch et al. (2025) introduced a mixture representation for two distributions, F <= G, under the likelihood ratio (LR) order, showing that f/g is non-increasing if and only if one density is a mixture of one-sided truncations of the other. We extend this to K LR-ordered continuous distributions F_1​ <= ... <= F_K​.

This framework enables Bayesian nonparametric (BNP) density estimation, ordinal regression, and hidden Markov models (HMMs). We developed slice-within-Gibbs MCMC samplers using Dirichlet Process Mixtures (DPM). We use simulations to investigate whether, when the LR order is appropriate, these constrained mixtures improve inference over independent DPMs for small or unbalanced samples. We illustrate the approach on applications to animal movement, intergenerational income mobility data, and retinopathy. LR ordering constraints on emission densities eliminate label-switching issues in BNP-HMMs.

Palabras clave: Bayesian nonparametrics, mixture representations, monotone likelihood ratio order, hidden Markov models, stochastic order.

Métodos Bayesianos
4 de septiembre de 2026  11:10
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