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Performance of Hamiltonian Monte Carlo and No-U-Turn Sampler for estimating genetic parameters and breeding values.
Genetics Selection Evolution ( IF 3.6 ) Pub Date : 2019-12-10 , DOI: 10.1186/s12711-019-0515-1
Motohide Nishio 1 , Aisaku Arakawa 1
Affiliation  

BACKGROUND Hamiltonian Monte Carlo is one of the algorithms of the Markov chain Monte Carlo method that uses Hamiltonian dynamics to propose samples that follow a target distribution. The method can avoid the random walk behavior to achieve a more effective and consistent exploration of the probability space and sensitivity to correlated parameters, which are shortcomings that plague many Markov chain Monte Carlo methods. However, the performance of Hamiltonian Monte Carlo is highly sensitive to two hyperparameters. The No-U-Turn Sampler, an extension of Hamiltonian Monte Carlo, was recently introduced to automate the tuning of these hyperparameters. Thus, this study compared the performances of Gibbs sampling, Hamiltonian Monte Carlo, and the No-U-Turn Sampler for estimating genetic parameters and breeding values as well as sampling qualities in both simulated and real pig data. For all datasets, we used a pedigree-based univariate linear mixed model. RESULTS For all datasets, the No-U-Turn Sampler and Gibbs sampling performed comparably regarding the estimation of heritabilities and accuracies of breeding values. Compared with Gibbs sampling, the estimates of effective sample sizes for simulated and pig data with the No-U-Turn Sampler were 3.2 to 22.6 and 3.5 to 5.9 times larger, respectively. Autocorrelations decreased more quickly with the No-U-Turn Sampler than with Gibbs sampling. When true heritability was low in the simulated data, the skewness of the marginal posterior distributions with the No-U-Turn Sampler was smaller than that with Gibbs sampling. The performance of Hamiltonian Monte Carlo for sampling quality was inferior to that of No-U-Turn Sampler in the simulated data. Moreover, Hamiltonian Monte Carlo could not estimate genetic parameters because of difficulties with the hyperparameter settings with pig data. CONCLUSIONS The No-U-Turn Sampler is a promising sampling method for animal breeding because of its good sampling qualities: large effective sample sizes, low autocorrelations, and low skewness of marginal posterior distributions, particularly when heritability is low. Meanwhile, Hamiltonian Monte Carlo failed to converge with a simple univariate model for pig data. Thus, it might be difficult to use Hamiltonian Monte Carlo for usual complex models in animal breeding.

中文翻译:

哈密​​尔顿蒙特卡罗和无掉头采样器在估算遗传参数和育种值方面的性能。

背景技术哈密顿量蒙特卡罗是马尔可夫链蒙特卡罗方法的算法之一,该算法使用哈密顿动力学来提出遵循目标分布的样本。该方法可以避免随机游走行为,以实现对概率空间和对相关参数的敏感性的更有效和一致的探索,这些缺点困扰着许多马尔可夫链蒙特卡罗方法。但是,汉密尔顿蒙地卡罗的性能对两个超参数高度敏感。最近引入了汉密尔顿蒙特卡洛(Hamiltonian Monte Carlo)的扩展的No-U-Turn采样器,以自动调整这些超参数。因此,本研究比较了吉布斯采样,汉密尔顿蒙特卡洛,以及No-U-Turn采样器,用于估算模拟和真实猪数据中的遗传参数,育种值以及采样质量。对于所有数据集,我们使用基于谱系的单变量线性混合模型。结果对于所有数据集,在遗传力和育种值准确性的估算上,无调车采样器和吉布斯采样的执行情况相当。与Gibbs采样相比,使用No-U-Turn采样器对模拟和猪数据的有效样本大小的估计分别大3.2到22.6倍和3.5到5.9倍。使用No-U-Turn采样器的自相关下降比使用Gibbs采样更快。当模拟数据中的真实遗传力较低时,使用No-U-Turn采样器的边缘后验分布的偏度要小于使用Gibbs采样的偏度。在模拟数据中,汉密尔顿蒙特卡洛的采样质量性能不如非掉头采样器。此外,由于猪数据的超参数设置存在困难,汉密尔顿蒙特卡洛法无法估算遗传参数。结论No-U-Turn采样器具有良好的采样质量:有效样本量大,自相关性低以及边缘后验分布偏斜度低,尤其是在遗传力较低时,因此是用于动物育种的有前途的采样方法。同时,哈密顿量蒙特卡洛(Hamiltonian Monte Carlo)未能通过简单的单变量猪数据模型收敛。因此,可能难以将汉密尔顿·蒙特卡洛法用于动物育种中的常规复杂模型。此外,由于猪数据的超参数设置存在困难,汉密尔顿蒙特卡洛法无法估算遗传参数。结论No-U-Turn采样器是一种有前途的动物育种采样方法,因为它具有良好的采样质量:有效样本量大,自相关性低以及边缘后验分布的偏度低,尤其是在遗传力较低时。同时,哈密顿量蒙特卡洛(Hamiltonian Monte Carlo)未能通过简单的单变量猪数据模型收敛。因此,可能难以将汉密尔顿蒙特卡洛法用于动物育种中的常规复杂模型。此外,由于猪数据的超参数设置存在困难,汉密尔顿蒙特卡洛法无法估算遗传参数。结论No-U-Turn采样器具有良好的采样质量:有效样本量大,自相关性低以及边缘后验分布偏斜度低,尤其是在遗传力较低时,因此是用于动物育种的有前途的采样方法。同时,哈密顿量蒙特卡洛(Hamiltonian Monte Carlo)未能通过简单的单变量猪数据模型收敛。因此,可能难以将汉密尔顿·蒙特卡洛法用于动物育种中的常规复杂模型。结论No-U-Turn采样器具有良好的采样质量:有效样本量大,自相关性低以及边缘后验分布偏斜度低,尤其是在遗传力较低时,因此是用于动物育种的有前途的采样方法。同时,哈密顿量蒙特卡洛(Hamiltonian Monte Carlo)未能通过简单的单变量猪数据模型收敛。因此,可能难以将汉密尔顿·蒙特卡洛法用于动物育种中的常规复杂模型。结论No-U-Turn采样器是一种有前途的动物育种采样方法,因为它具有良好的采样质量:有效样本量大,自相关性低以及边缘后验分布的偏度低,尤其是在遗传力较低时。同时,哈密顿量蒙特卡洛(Hamiltonian Monte Carlo)未能通过简单的单变量猪数据模型收敛。因此,可能难以将汉密尔顿蒙特卡洛法用于动物育种中的常规复杂模型。
更新日期:2020-04-22
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