Dataset Information

Performance of Hamiltonian Monte Carlo and No-U-Turn Sampler for estimating genetic parameters and breeding values.

ABSTRACT: 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.

SUBMITTER: Nishio M

PROVIDER: S-EPMC6902603 | biostudies-literature | 2019 Dec

REPOSITORIES: biostudies-literature

ACCESS DATA

Publications

Performance of Hamiltonian Monte Carlo and No-U-Turn Sampler for estimating genetic parameters and breeding values.

Nishio Motohide M Arakawa Aisaku A

Genetics, selection, evolution : GSE 20191210 1

<h4>Background</h4>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 sens ...[more]

PMID: 31823719

Similar Datasets

Project description:BackgroundRunning multiple-chain Markov Chain Monte Carlo (MCMC) provides an efficient parallel computing method for complex Bayesian models, although the efficiency of the approach critically depends on the length of the non-parallelizable burn-in period, for which all simulated data are discarded. In practice, this burn-in period is set arbitrarily and often leads to the performance of far more iterations than required. In addition, the accuracy of genomic predictions does not improve after the MCMC reaches equilibrium.ResultsAutomatic tuning of the burn-in length for running multiple-chain MCMC was proposed in the context of genomic predictions using BayesA and BayesCπ models. The performance of parallel computing versus sequential computing and tunable burn-in MCMC versus fixed burn-in MCMC was assessed using simulation data sets as well by applying these methods to genomic predictions of a Chinese Simmental beef cattle population. The results showed that tunable burn-in parallel MCMC had greater speedups than fixed burn-in parallel MCMC, and both had greater speedups relative to sequential (single-chain) MCMC. Nevertheless, genomic estimated breeding values (GEBVs) and genomic prediction accuracies were highly comparable between the various computing approaches. When applied to the genomic predictions of four quantitative traits in a Chinese Simmental population of 1217 beef cattle genotyped by an Illumina Bovine 770 K SNP BeadChip, tunable burn-in multiple-chain BayesCπ (TBM-BayesCπ) outperformed tunable burn-in multiple-chain BayesCπ (TBM-BayesA) and Genomic Best Linear Unbiased Prediction (GBLUP) in terms of the prediction accuracy, although the differences were not necessarily caused by computational factors and could have been intrinsic to the statistical models per se.ConclusionsAutomatically tunable burn-in multiple-chain MCMC provides an accurate and cost-effective tool for high-performance computing of Bayesian genomic prediction models, and this algorithm is generally applicable to high-performance computing of any complex Bayesian statistical model.

Project description:BACKGROUND: Parameter estimation for differential equation models of intracellular processes is a highly relevant bu challenging task. The available experimental data do not usually contain enough information to identify all parameters uniquely, resulting in ill-posed estimation problems with often highly correlated parameters. Sampling-based Bayesian statistical approaches are appropriate for tackling this problem. The samples are typically generated via Markov chain Monte Carlo, however such methods are computationally expensive and their convergence may be slow, especially if there are strong correlations between parameters. Monte Carlo methods based on Euclidean or Riemannian Hamiltonian dynamics have been shown to outperform other samplers by making proposal moves that take the local sensitivities of the system's states into account and accepting these moves with high probability. However, the high computational cost involved with calculating the Hamiltonian trajectories prevents their widespread use for all but the smallest differential equation models. The further development of efficient sampling algorithms is therefore an important step towards improving the statistical analysis of predictive models of intracellular processes. RESULTS: We show how state of the art Hamiltonian Monte Carlo methods may be significantly improved for steady state dynamical models. We present a novel approach for efficiently calculating the required geometric quantities by tracking steady states across the Hamiltonian trajectories using a Newton-Raphson method and employing local sensitivity information. Using our approach, we compare both Euclidean and Riemannian versions of Hamiltonian Monte Carlo on three models for intracellular processes with real data and demonstrate at least an order of magnitude improvement in the effective sampling speed. We further demonstrate the wider applicability of our approach to other gradient based MCMC methods, such as those based on Langevin diffusions. CONCLUSION: Our approach is strictly benefitial in all test cases. The Matlab sources implementing our MCMC methodology is available from https://github.com/a-kramer/ode_rmhmc.

Dataset Information

Performance of Hamiltonian Monte Carlo and No-U-Turn Sampler for estimating genetic parameters and breeding values.

Publications

Performance of Hamiltonian Monte Carlo and No-U-Turn Sampler for estimating genetic parameters and breeding values.

Similar Datasets

OmicsDI is part of the ELIXIR infrastructure

Tweets