Title On the non-singularity issue for the Poisson-gamma model /
Another Title Apie nesinguliarumo sąlygą taikant Puasono-gama modelį.
Authors Jakimauskas, Gintautas
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Is Part of Jaunųjų mokslininkų darbai.. Šiauliai : Šiaulių universitetas. 2014, Nr. 1, p. 99-103.. ISSN 1648-8776
Keywords [eng] Empirical Bayesian estimation ; Poisson-gamma model
Abstract [eng] The problem of estimation of small probabilities in large populations (e.g., the estimation of probability of some disease, death, suicides, etc.) is considered. The number of corresponding events depends on the size of the population and the probability of the single event. It is assumed that the number of events in populations has a Poisson distribution with certain parameters. Let us have two models of distribution of unknown probabilities: the probabilities have a gamrna distribution (Poisson-gamma model), or logits of the probabilities have a Gaussian distribution (Poisson-Gaussian model). In the case of the Poisson-Gaussian model it is known that if a certain non-singularity condition does not hold then empirical Bayes estimates of unknown probabilities are equal to mean relative risk estimates, and corresponding distribution of logits of the probabilities have singular distribution with zero variance. In the case of the Poisson-gamma model we have a similar non-singularity issue. In practice it means that the shape and scale parameters given by iterative procedures for finding distribution parameters converge to infinity and we do not obtain finite values of shape and scale parameters. The non-singularity condition depends only on population sizes and the number of observed events. We will consider the Poisson-gamma model for some sets of data and we will show the behaviour of iterative procedures. We will focus on the behaviour of a partial derivative of the maximum likelihood function, which is essential for the non-singularity condition for the Poisson-gamma model.
Published Šiauliai : Šiaulių universitetas
Type Journal article
Language English
Publication date 2014