title: Reparametrization-based estimation of genetic parameters in multi-trait animal model using Integrated Nested Laplace Approximation.
abstract: CONCLUSIONS
  A novel reparametrization-based INLA approach as a fast alternative to MCMC for the Bayesian estimation of genetic parameters in multivariate animal model is presented.
  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.
authors.affiliation: Institute of Crop Science and Resource Conservation, University of Bonn, 53115, Bonn, Germany. boby.mathew@hotmail.com.
authors.forename: Boby
authors.initials: B
authors.lastname: Mathew
authors.affiliation: Department of Mathematical Sciences, Norwegian University of Science and Technology, 7491, Trondheim, Norway.
authors.forename: Anna Marie
authors.initials: AM
authors.lastname: Holand
authors.affiliation: Department of Mathematics and Statistics, University of Helsinki, 00014, Helsinki, Finland.
authors.forename: Petri
authors.initials: P
authors.lastname: Koistinen
authors.affiliation: Institute of Crop Science and Resource Conservation, University of Bonn, 53115, Bonn, Germany.
authors.forename: Jens
authors.initials: J
authors.lastname: Léon
authors.affiliation: Department of Mathematical Sciences and Biocenter Oulu, University of Oulu, 90014, Oulu, Finland.
authors.forename: Mikko J
authors.initials: MJ
authors.lastname: Sillanpää
mesh_terms: D000465:Algorithms; D000818:Animals; D001499:Bayes Theorem; D001947:Breeding; D003198:Computer Simulation; D016013:Likelihood Functions; D008390:Markov Chains; D008957:Models, Genetic; D009010:Monte Carlo Method; D010375:Pedigree; D019655:Quantitative Trait, Heritable