A Hamiltonian Monte Carlo algorithm is a Markov chain Monte Carlo method, and the method has a potential to improve estimating parameters effectively. Hamiltonian Monte Carlo is based on Hamiltonian dynamics, and it follows Hamilton's 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 Hamilton's 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 Fortran language at https://github.com/A-ARAKAWA/HMC.

中文翻译：

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估计方差分量的哈密顿蒙特卡洛方法

哈密​​顿蒙特卡洛算法是一种马尔可夫链蒙特卡洛方法，该方法具有有效改进参数估计的潜力。哈密​​顿蒙特卡洛基于哈密顿动力学，它遵循哈密顿方程，该方程表示为两个微分方程。在哈密顿蒙特卡洛的采样过程中，采用了一种称为leapfrog integration的数值积分方法来近似求解Hamilton方程，积分需要设置离散时间步数和积分步长。这两个参数需要一定量的调整和校准才能有效采样。在这项研究中，我们将哈密顿蒙特卡罗方法应用于动物育种数据，并确定了正态和逆卡方分布的蛙跳积分的最佳调整。然后，使用真实的猪数据，我们通过应用模型（包括由谱系信息或基因组信息解释的方差）揭示了哈密顿蒙特卡洛方法的特性和最佳调整。与吉布斯抽样法相比，哈密顿蒙特卡洛法在两种模型中均具有优越的性能。我们在 https://github.com/A-ARAKAWA/HMC 提供了用 Fortran 语言编写的此方法的源代码。