On the inferential implications of decreasing weight structures in mixture models
| Autor: | Pierpaolo De Blasi, Ramsés H. Mena, Asael Fabian Martínez, Igor Prünster |
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| Rok vydání: | 2020 |
| Předmět: |
Statistics and Probability
Model based clustering Context (language use) 01 natural sciences Bayesian nonparametrics 010104 statistics & probability BAYESIAN NONPARAMETRICS DENSITY ESTIMATION GEOMETRIC PROCESS MODEL BASED CLUSTERING 0502 economics and business Density estimation Geometric process Statistical physics 0101 mathematics Mixing (physics) 050205 econometrics Mathematics Bayes estimator Applied Mathematics 05 social sciences Nonparametric statistics Mixture model Dirichlet process Computational Mathematics Computational Theory and Mathematics Identifiability |
| Zdroj: | Computational Statistics & Data Analysis. 147:106940 |
| ISSN: | 0167-9473 |
| DOI: | 10.1016/j.csda.2020.106940 |
| Popis: | Bayesian estimation of nonparametric mixture models strongly relies on available representations of discrete random probability measures. In particular, the order of the mixing weights plays an important role for the identifiability of component-specific parameters which, in turn, affects the convergence properties of posterior samplers. The geometric process mixture model provides a simple alternative to models based on the Dirichlet process that effectively addresses these issues. However, the rate of decay of the mixing weights for this model may be too fast for modeling data with a large number of components. The need for different decay rates arises. Some variants of the geometric process featuring different decay behaviors, while preserving the decreasing structure, are presented and investigated. An asymptotic characterization of the number of distinct values in a sample from the corresponding mixing measure is also given, highlighting the inferential implications of different prior specifications. The analysis is completed by a simulation study in the context of density estimation. It shows that by controlling the decaying rate, the mixture model is able to capture data with a large number of components. |
| Databáze: | OpenAIRE |
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