Reparametrization-based estimation of genetic parameters in multi-trait animal model using Integrated Nested Laplace Approximation

Abstract

Key messageA novel reparametrization-based INLA approach as a fast alternative to MCMC for the Bayesian estimation of genetic parameters in multivariate animal model is presented.Abstract Multi-trait genetic parameter estimation is a relevant topic in animal and plant breeding programs because multi-trait analysis can take into account the genetic correlation between different traits and that significantly improves the accuracy of the genetic parameter estimates. Generally, multi-trait analysis is computationally demanding and requires initial estimates of genetic and residual correlations among the traits, while those are difficult to obtain. In this study, we illustrate how to reparametrize covariance matrices of a multivariate animal model/animal models using modified Cholesky decompositions. This reparametrization-based approach is used in the Integrated Nested Laplace Approximation (INLA) methodology to estimate genetic parameters of multivariate animal model. Immediate benefits are: (1) to avoid difficulties of finding good starting values for analysis which can be a problem, for example in Restricted Maximum Likelihood (REML); (2) Bayesian estimation of (co)variance components using INLA is faster to execute than using Markov Chain Monte Carlo (MCMC) especially when realized relationship matrices are dense. The slight drawback is that priors for covariance matrices are assigned for elements of the Cholesky factor but not directly to the covariance matrix elements as in MCMC. Additionally, we illustrate the concordance of the INLA results with the traditional methods like MCMC and REML approaches. We also present results obtained from simulated data sets with replicates and field data in rice.

Yielding stability of early maturing potato varieties: Bayesian analysis

“…A similar approach was used in Mathew et al . (2016), where the authors applied the multi-trait animal model in the analysis of plant breeding trials. However, instead of using empirical variances, one can use the knowledge about varieties from the previous studies.…”

“…(2013), a similar assumption regarding the degrees of belief in the inverse-Wishart distribution was used in Mathew et al . (2016). However, in literature concerning Bayesian statistics, it was argued against using inverse-Wishart priors for covariance matrices because they impose a degree of informativity and the posterior inferences are sensitive to the choice of hyper-parameters.…”

“…In the present work, as a prior knowledge about the tested varieties, the values of empirical variances of each variety were used. A similar approach was used in Mathew et al (2016), where the authors applied the multi-trait animal model in the analysis of plant breeding trials. However, instead of using empirical variances, one can use the knowledge about varieties from the previous studies.…”

Eigen structure of a new class of covariance and inverse covariance matrices

“…Despite receiving considerable attention, the problem of large covariance estimation is a persistent obstacle in numerous applied works (e.g. Cribben et al, 2012;Mathew et al, 2016). It is well understood that when the dimension p is larger than the sample size n, it is impossible to construct a consistent estimator of Σ (in any non-trivial matrix norm) on the basis of the i.i.d.…”

Fine mapping and genomic prediction for detailed milk composition : Unraveling the genetics of milk composition towards implementing selective breeding

“…Some studies based on real (Eaglen et al, 2012) and simulated data (e.g. Mathew et al, 2016) indicate that different variance components can be estimated with higher accuracies and/or lower standard errors of prediction using multi-traits analysis. By allowing incorporation of information on genetic correlations into analysis, multi-trait models significantly improve the accuracy of the genetic parameter estimates.…”