Abstract
  The Bayesian model was applied for analyzing the first lactation in Karan Fries cattle. First lactation data of production (305-day or less milk yield and daily milk yield) were collected from the history-cum pedigree sheet and daily milk yield registers of the division of Dairy Cattle Breeding (DCB), National Dairy Research Institute (NDRI), Karnal. In the Bayesian paradigm, MCMC methods are applied to solve complex mathematical problems to estimate a large number of unknown parameters. Assuming linear mixed model and using the different prior set up, diagnostic of MCMC (Markov Chain Monte Carlo) was carried out graphically as well as by Heidelberg stationarity test. Variance estimates of the random effects (VA) and residual variance estimation (VR) and Variance estimate location effects i.e. fixed effects were calculated along with effective sample size. Finally, heritability (h2) estimates for First lactation 305 days or less milk yield (FL305DMY) was estimated along with its credible interval.
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