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Bayesian Inference on Variance Components Using Gibbs Sampling with Various Priors |
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C. Lee, C. D. Wang |
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| Abstract |
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Data for teat number for Landrace (L), Yorkshire (Y), crossbred of Landrace and Yorkshire (LY), and crossbred of Landrace, Yorkshire and Chinese indigenous Min Pig (LYM) were analyzed using Gibbs sampling. In Bayesian inference, flat priors and some informative priors were used to examine their influence on posterior estimates. The posterior mean estimates of heritabilities with flat priors were 0.661 0.035 for L, 0.540 0.072 for Y, 0.789 0.074 for LY, and 0.577 0.058 for LYM, and they did not differ (p>0.05) from their corresponding estimates of REML. When inverse Gamma densities for variance components were used as priors with the shape parameter of 4, the posterior estimates were still corresponding (p>0.05) to REML estimates and mean estimates using Gibbs sampling with flat priors. However, when the inverse Gamma densities with the shape parameter of 10 were utilized, some posterior estimates differed (p<0.10) from REML estimates and/or from other Gibbs mean estimates. The use of moderate degree of belief was influential to the posterior estimates, especially for Y and for LY where data sizes were small. When the data size is small, REML estimates of variance components have unknown distributions. On the other hand, Bayesian approach gives exact posterior densities of variance components. However, when the data size is small and prior knowledge is lacked, researchers should be careful with even moderate priors. |
| Keywords:
Teat Number; Variance Component; REML; Bayesian Inference |
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