Mixture representations and bayesian nonparametric inference for likelihood ratio ordered distributions
In this article, we introduce mixture representations for likelihood ratio ordered distributions. Essentially, the ratio of two probability densities, or mass functions, is monotone if and only if one can be expressed as a mixture of one-sided truncations of the other. To illustrate the practical va...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2025 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/433736 |
| Acceso en línea: | https://hdl.handle.net/2117/433736 https://dx.doi.org/10.1214/25-BA1519 |
| Access Level: | acceso abierto |
| Palabra clave: | Mathematical statistics density estimation Dirichlet process monotone likelihood ratio shape constrained estimation stochastic order Estadística matemàtica Classificació AMS::62 Statistics::62F Parametric inference Classificació AMS::62 Statistics::62G Nonparametric inference Àrees temàtiques de la UPC::Matemàtiques i estadística::Estadística matemàtica::Inferència estadística |
| Sumario: | In this article, we introduce mixture representations for likelihood ratio ordered distributions. Essentially, the ratio of two probability densities, or mass functions, is monotone if and only if one can be expressed as a mixture of one-sided truncations of the other. To illustrate the practical value of the mixture representations, we address the problem of density estimation for likelihood ratio ordered distributions. In particular, we propose a nonparametric Bayesian solution which takes advantage of the mixture representations. The prior distribution is constructed from Dirichlet process mixtures and has large support on the space of pairs of densities satisfying the monotone ratio constraint. Posterior consistency holds under reasonable conditions on the prior specification and the true unknown densities. To our knowledge, this is the first posterior consistency result in the literature on order constrained inference. With a simple modification to the prior distribution, we can test the equality of two distributions against the alternative of likelihood ratio ordering. We develop a Markov chain Monte Carlo algorithm for posterior inference and demonstrate the method in a biomedical application. |
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