scholarly journals Hamiltonian Monte Carlo for Hierarchical Models

2015 ◽  
pp. 79-101 ◽  
Author(s):  
Michael Betancourt ◽  
Mark Girolami
Keyword(s):  
Monte Carlo ◽  
Hierarchical Models ◽  
Hamiltonian Monte Carlo

On L2 convergence of the Hamiltonian Monte Carlo

2021 ◽  
pp. 107811
Author(s):  
Soumyadip Ghosh ◽  
Yingdong Lu ◽  
Tomasz Nowicki
Keyword(s):  
Monte Carlo ◽  
Hamiltonian Monte Carlo

PSV-14 Using Bayesian Hamiltonian Monte Carlo and a nonlinear model for the estimation of genetic parameters for lactation curves in goats

2021 ◽  
Vol 99 (Supplement_3) ◽  
pp. 305-307
Author(s):  
Andre C Araujo ◽  
Leonardo Gloria ◽  
Paulo Abreu ◽  
Fabyano Silva ◽  
Marcelo Rodrigues ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Milk Yield ◽  
Nonlinear Model ◽  
Genetic Parameters ◽  
Model Parameters ◽  
Promising Alternative ◽  
Hamiltonian Monte Carlo ◽  
Heritability Estimates ◽  
Correlated Parameters ◽  
Wood Model

Abstract Hamiltonian Monte Carlo (HMC) is an algorithm of the Markov Chain Monte Carlo (MCMC) method that uses dynamics to propose samples that follow a target distribution. This algorithm enables more effective and consistent exploration of the probability interval and is more sensitive to correlated parameters. Therefore, Bayesian-HMC is a promising alternative to estimate individual parameters of complex functions such as nonlinear models, especially when using small datasets. Our objective was to estimate genetic parameters for milk traits defined based on nonlinear model parameters predicted using the Bayesian-HMC algorithm. A total of 64,680 milk yield test-day records from 2,624 first, second, and third lactations of Saanen and Alpine goats were used. First, the Wood model was fitted to the data. Second, lactation persistency (LP), peak time (PT), peak yield (PY), and total milk yield [estimated from zero to 50 (TMY50), 100(TMY100), 150(TMY150), 200(TMY200), 250(TMY250), and 300(TMY300) days-in-milk] were predicted for each animal and parity based on the output of the first step (the individual phenotypic parameters of the Wood model). Thereafter, these predicted phenotypes were used for estimating genetic parameters for each trait. In general, the heritability estimates across lactations ranged from 0.10 to 0.20 for LP, 0.04 to 0.07 for PT, 0.26 to 0.27 for PY, and 0.21 to 0.28 for TMY (considering the different intervals). Lower heritabilities were obtained for the nonlinear function parameters (A, b and l) compared to its predicted traits (except PT), especially for the first and second lactations (range: 0.09 to 0.18). Higher heritability estimates were obtained for the third lactation traits. To our best knowledge, this study is the first attempt to use the HMC algorithm to fit a nonlinear model in animal breeding. The two-step method proposed here allowed us to estimate genetic parameters for all traits evaluated.

Hamiltonian Monte Carlo calculation in two-dimensional SU(2) QCD with fermions

1985 ◽  
Vol 31 (6) ◽  
pp. 1453-1459 ◽  
Author(s):  
Jen-Fa Min ◽  
Joel A. Shapiro ◽  
Thomas A. DeGrand
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Calculation ◽  
Two Dimensional ◽  
Hamiltonian Monte Carlo
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