A. Olivares Canal, V. Peña Pizarro, M. Jauch
In many applications, domain knowledge often suggests that two distributions should satisfy a stochastic order. Jauch et al. (2023) introduced univariate mixture representations for a distribution function G in terms of F when F <= G with respect to the likelihood ratio order. The ratio of two probability density functions is monotone if and only if one can be expressed as a mixture of one-sided truncations of the other. They proposed a Bayesian nonparametric density estimation model using Dirichlet Process Mixtures to enforce this constraint and applied it to medical data. We extend this framework using the weak likelihood ratio order, a multivariate generalization, first in the bivariate case and then to a full multivariate mixture representation. Additionally, we consider the case of sequences of K+1 stochastically ordered distributions F_0 <= F_1 <=, ..., <= F_K. These extensions enable multivariate Bayesian nonparametric logistic and ordinal regression models.
Palabras clave: Mixture representations, Bayesian methods, Monotone likelihood ratio order, Stochastic order, Regression models
Programado
Sesión de pósters II
13 de junio de 2025 15:30
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