Monte Carlo approximation of the logarithm of the determinant of large matrices with applications for linear mixed models in quantitative genetics.

ABSTRACT.- Background: Likelihood-based inferences such as variance components estimation and hypothesis testing need logarithms of the determinant (log-determinant) of high dimensional matrices. Calculating the log-determinant is memory and time-consuming, making it impossible to perform likelihood-based inferences for large datasets. Conclusions: The method presented in this study allows to approximate the log-determinant of positive semi-definite matrices and, therefore, the likelihood for datasets of any size.