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EnglishInference for bivariate distributions with fixed marginals is very important in applications. When a bayesian approach is followed, the problem of defining a (prior) distribution on a class of probabilities having given marginals arises. We consider the class of Lancaster distributions. It is a convex and compact set, so that any element may be represented as a mixture of extreme points. Therefore a prior distribution can be assigned to the Lancaster class by assuming the mixing measure as a random probability. We analyse in detail the Lancaster class with Gamma marginals. Choosing as mixing measure a Dirichlet process, the model turns out to be a Dirichlet process mixture model. Many quantities relevant for statistical purposes are linear functionals of the Dirichlet process. Posterior laws are determined; in order to approximate these laws a MCMC algorithm is suggested. Results of an example with simulated data are discussed.
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| Titolo: | Bayesian Inference for Lancaster Probabilities |
| Data di pubblicazione: | 2008 |
| Autori: | |
| Autori: | Cifarelli, DONATO MICHELE; Graziani, Rebecca; Melilli, Eugenio |
| Rivista: | APPLIED MATHEMATICAL SCIENCES |
| Abstract: | Inference for bivariate distributions with fixed marginals is very important in applications. When a bayesian approach is followed, the problem of defining a (prior) distribution on a class of probabilities having given marginals arises. We consider the class of Lancaster distributions. It is a convex and compact set, so that any element may be represented as a mixture of extreme points. Therefore a prior distribution can be assigned to the Lancaster class by assuming the mixing measure as a random probability. We analyse in detail the Lancaster class with Gamma marginals. Choosing as mixing measure a Dirichlet process, the model turns out to be a Dirichlet process mixture model. Many quantities relevant for statistical purposes are linear functionals of the Dirichlet process. Posterior laws are determined; in order to approximate these laws a MCMC algorithm is suggested. Results of an example with simulated data are discussed. |
| Appare nelle tipologie: | 01 - Article in academic journal / Articolo su rivista Scientifica |
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