Tunings for leapfrog integration of Hamiltonian Monte Carlo for estimating genetic parameters

Abstract

A Hamiltonian Monte Carlo algorithm is a Markov Chain Monte Carlo method that is considered more effective than the conventional Gibbs sampling method. Hamiltonian Monte Carlo is based on Hamiltonian dynamics, and it follows Hamiltons equations, which are expressed as two differential equations. In the sampling process of Hamiltonian Monte Carlo, a numerical integration method called leapfrog integration is used to approximately solve Hamiltons equations, and the integration is required to set the number of discrete time steps and the integration stepsize. These two parameters require some amount of tuning and calibration for effective sampling. In this study, we applied the Hamiltonian Monte Carlo method to animal breeding data and identified the optimal tunings of leapfrog integration for normal and inverse chi-square distributions. Then, using real pig data, we revealed the properties of the Hamiltonian Monte Carlo method with the optimal tuning by applying models including variance explained by pedigree information or genomic information. Compared with the Gibbs sampling method, the Hamiltonian Monte Carlo method had superior performance in both models. We have provided the source codes of this method written in the R language.