IntroductionVariance sources are the basis for organization of progeny testing, calculation of genetic-environment interaction, construction of selection index, calculation of mixed model BLUP, estimation of phenotype-environment correlation, planning of improvement program with identified genetic structure in quantitative characters, estimation of variance components, and estimation of accurate breeding value [1,2]. Accuracy of estimation of variance components depends on factors that include observations, statistical model used, and method [3]. Therefore, many researchers have tried to improve different methods for estimation of variance components [4][5][6][7][8][9]. ANOVA, ML, and REML are the most used methods for estimation of genetic variance [10]. These methods have been called classical approaches (frequentist, Berkeley methods) and are based on normality assumption. However, the existence of threshold traits and the observation of binary data in animal breeding violates the rule of normality assumption [11,12]. Therefore, the Bayesian approach, another alternative method to overcome this concern, has been developed and this approach that does not require normality can be alternatively used to estimate variance components by using posterior distribution in discrete and continuous distributed traits [13][14][15][16]. In this respect, the Bayesian approach has more advantages than the classical approach in practice [17]. At the same time, no negative variance can be estimated under the Bayesian approach [18]. In the genetic evaluation of animals, the use of the MCMC algorithm in Bayesian approach has been a good option and this approach has been reducing bias in the estimations even when the dataset is too small [19]. At the same time, the Bayesian approach is statistically more flexible for estimations of variance components than the REML procedure [15]. In addition, some researchers have suggested that the use of the MCMC algorithm in the Bayesian approach is more feasible although it is computationally more expensive [20,21]. However, with the developed computer technology, various programs such as MTGSAM [22], GIBANAL [23], MCMCglmm [24], and FlexQTLs [25,26] have increased the popularity of the Bayesian approach. Under the National Small