A Bayesian Approach to the Estimation of Expected Cell Counts by Using Log-Linear Models |
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Authors: | H Demirhan C Hamurkaroglu |
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Institution: | 1. Department of Statistics , Hacettepe University , Beytepe, Ankara, Turkey haydarde@hacettepe.edu.tr;3. Department of Statistics , Hacettepe University , Beytepe, Ankara, Turkey |
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Abstract: | ABSTRACT In this article, Bayesian estimation of the expected cell counts for log-linear models is considered. The prior specified for log-linear parameters is used to determine a prior for expected cell counts, by means of the family and parameters of prior distributions. This approach is more cost-effective than working directly with cell counts because converting prior information into a prior distribution on the log-linear parameters is easier than that of on the expected cell counts. While proceeding from the prior on log-linear parameters to the prior of the expected cell counts, we faced with a singularity problem of variance matrix of the prior distribution, and added a new precision parameter to solve the problem. A numerical example is also given to illustrate the usage of the new parameter. |
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Keywords: | Bayesian posterior estimates Expected cell counts Geweke's modified z-test Gibbs sampling Hierarchical modeling Log-linear model Log-normal prior Multivariate log-normal distribution Multivariate normal distribution |
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