Bayesian analysis for sire model using Gibbs sampling in animal breeding

ABSTRACT BAYESIAN ANALYSIS FOR SIRE MODEL USING GIBBS SAMPLING IN ANIMAL BREEDING AŞKIN GALIÇ M Sc. in Animal Science Adviser: Assoc. Prof. Dr. M. Ziya FIRAT November, 2002, 40 pages Variance is most often used value in the description of a population or samples that are taken from the population. It is necessary for the computation of the statistics such as standard deviation and coefficient of variation, which are useful to describe variability within a population. Also, the heritability, that is the answer to the question " what percentage of the observed variability is attributable to genetics?' and a cornerstone of quantitative genetics, plays an important role in animal breeding. Generally the methods based on probability theory (ML and REML) and Bayesian are used in the estimation of genetic parameters. From the point of view of using the latest techniques in solving problems that are faced with in animal breeding experiments, Gibbs sampling approach is considered in this study. Gibbs sampling is a method of numerical integration that allows inferences to be made about joint or marginal densities, even those densities cannot be evaluated directly. It is based on generation, in sequence, of variables from all of the full conditional densities. Full conditional density is the density of a variable given all other parameters in the model. In this study, 500 data sets using different number and sizes of families and heritabilities for half-sib sire family structure are simulated using Monte Carlo method. For each data set, the estimates of variance components and functions of them are obtained employing different statistical methods and the results of these methods are then compared. KEY WORDS: Gibbs sampling, heritability, parameter estimation, variance. COMMITTEE : Assoc. Prof. M.Ziya FIRAT Assist. Prof. M. Soner BALCIO?LU Assoc. Prof. Yavuz AKBAŞ