On Bayesian Estimation in Mixed Linear Models Using the Gibbs Sampler
IRAQI JOURNAL OF STATISTICAL SCIENCES,
2008, Volume 8, Issue 1, Pages 10-34
AbstractThis paper tackles the estimation of parameters of linear mixed random effect one–classification model by Bayesian technique which includes Gibbs sampling. Gibbs sampling is a special case of Monte Carlo Method which uses Markov Chain and so called MCMC (Markov Chain Monte Carlo).
This MCMC method depends on partition of difficult and compound models into simple ones which can be manipulated and easily analyzed, specially for the posterior distribution which are not easy to find their final formulae.
In this research the mixed random effect linear one–classification model is proposed on a population of 15 treatments including 15 types of cotton plant. A random sample of 5 types is taken and using the analysis of variance method to test the hypothesis that all the 15 types have equal effect and the estimation of the parameters is obtained Gibbs sampling is also used in order to estimate the parameters and then testing the hypothesis of equal effects of treatments. The results obtained in both ANOVA and Gibbs sampling are nearly the same and encouraging. All algorithms are programmed in this research using WinBUGS program.
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