NDLI: Exact Bayesian modeling for bivariate Poisson data and extensions

Content Provider	Springer Nature Link
Author	Karlis, Dimitris Tsiamyrtzis, Panagiotis
Copyright Year	2007
Abstract	Bivariate count data arise in several different disciplines (epidemiology, marketing, sports statistics just to name a few) and the bivariate Poisson distribution being a generalization of the Poisson distribution plays an important role in modelling such data. In the present paper we present a Bayesian estimation approach for the parameters of the bivariate Poisson model and provide the posterior distributions in closed forms. It is shown that the joint posterior distributions are finite mixtures of conditionally independent gamma distributions for which their full form can be easily deduced by a recursively updating scheme. Thus, the need of applying computationally demanding MCMC schemes for Bayesian inference in such models will be removed, since direct sampling from the posterior will become available, even in cases where the posterior distribution of functions of the parameters is not available in closed form. In addition, we define a class of prior distributions that possess an interesting conjugacy property which extends the typical notion of conjugacy, in the sense that both prior and posteriors belong to the same family of finite mixture models but with different number of components. Extension to certain other models including multivariate models or models with other marginal distributions are discussed.
Starting Page	27
Ending Page	40
Page Count	14
File Format	PDF
ISSN	09603174
Journal	Statistics and Computing
Volume Number	18
Issue Number	1
e-ISSN	15731375
Language	English
Publisher	Springer US
Publisher Date	2007-09-11
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Bayesian sequentially updated mixtures Conjugacy Direct sampling Gamma mixtures Artificial Intelligence (incl. Robotics) Mathematics Numeric Computing Statistics Statistics and Computing/Statistics Programs
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Theoretical Computer Science Computational Theory and Mathematics Statistics, Probability and Uncertainty

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4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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