Flexible prior specification for the genetic covariance matrix via the generalized inverted Wishart distribution

MUNILLA, S.; CANTET, R. J. C.

Stavanger

Congreso; 62nd Annual Meeting of the European Federation of Animal Science; 2011

European Federation of Animal Science

Consider the estimation of genetic (co)variance components from a maternal animal model (MAM) using a conjugated Bayesian approach. Usually, more uncertainty is expected a priori on the maternal additive variance than on the direct additive variance. However, it is not possible to model such differential uncertainty using the standard approach based on assuming an inverted Wishart (IW) distribution for the genetic covariance matrix. Instead, consider setting a generalized inverted Wishart (GIW) distribution. The GIW is essentially characterized by a larger set of hyperparameters, a feature that offers more flexibility while specifying prior knowledge. Taking advantage of this property, we present an elicitation method based on using previously estimated values of the (co)variance components to assess the hyperparameters on the next round. This Bayesian updating strategy stems naturally from the standard practice of genetic evaluations, where genetic parameters are frequently re-estimated as data is accrued over the years. A stochastic simulation study using the MAM as the data generator process was carried out to test the procedure. Genetic parameters were estimated through a Bayesian analysis via the Gibbs sampler. Posterior means, posterior standard deviations, and autocorrelations for the direct heritability, the maternal heritability and the direct-maternal genetic correlation were used as the criteria for comparison against more standard prior specifications. The elicitation method returned on average accurate estimates and reduced standard errors compared with non informative prior settings, while improving the convergence rates. In general, faster convergence was always observed when a stronger weight was placed on the prior distributions. However, analyses based on the IW distribution and initialized with over-dispersed starting values produced biased estimates with respect to the true simulated values.