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

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.

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Seismic source inversion using Hamiltonian Monte Carlo and a 3-D Earth model in the Japanese Islands

10.5194/egusphere-egu2020-9229 ◽

2020 ◽

Author(s):

Saulė Simutė ◽

Lion Krischer ◽

Christian Boehm ◽

Martin Vallée ◽

Andreas Fichtner

Keyword(s):

Monte Carlo ◽

Moment Tensor ◽

Seismic Source ◽

Monte Carlo Algorithm ◽

Earth Model ◽

Model Parameters ◽

Hamiltonian Monte Carlo ◽

Double Couple ◽

Full Moment Tensor ◽

Japanese Islands

We present a proof-of-concept catalogue of full-waveform seismic source solutions for the Japanese Islands area. Our method is based on the Bayesian inference of source parameters and a tomographically derived heterogeneous Earth model, used to compute Green&#8217;s strain tensors. We infer the full moment tensor, location and centroid time of the seismic events in the study area.To compute spatial derivatives of Green&#8217;s functions, we use a previously derived regional Earth model (Simut&#279; et al., 2016). The model is radially anisotropic, visco-elastic, and fully heterogeneous. It was constructed using full waveforms in the period band of 15&#8211;80 s.Green&#8217;s strains are computed numerically with the spectral-element solver SES3D (Gokhberg & Fichtner, 2016). We exploit reciprocity, and by treating seismic stations as virtual sources we compute and store the wavefield across the domain. This gives us a strain database for all potential source-receiver pairs. We store the wavefield for more than 50 F-net broadband stations (www.fnet.bosai.go.jp). By assuming an impulse response as the source time function, the displacements are then promptly obtained by linear combination of the pre-computed strains scaled by the moment tensor elements.With a feasible number of model parameters and the fast forward problem we infer the unknowns in a Bayesian framework. The fully probabilistic approach allows us to obtain uncertainty information as well as inter-parameter trade-offs. The sampling is performed with a variant of the Hamiltonian Monte Carlo algorithm, which we developed previously (Fichtner and Simut&#279;, 2017). We apply an L2 misfit on waveform data, and we work in the period band of 15&#8211;80 s.We jointly infer three location parameters, timing and moment tensor components. We present two sets of source solutions: 1) full moment tensor solutions, where the trace is free to vary away from zero, and 2) moment tensor solutions with the isotropic part constrained to be zero. In particular, we study events with significant non-double-couple component. Preliminary results of ~Mw 5 shallow to intermediate depth events indicate that proper incorporation of 3-D Earth structure results in solutions becoming more double-couple like. We also find that improving the Global CMT solutions in terms of waveform fit requires a very good 3-D Earth model and is not trivial.

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Random regression models to estimate genetic parameters for test-day milk yield and composition in Iranian buffaloes

Archives Animal Breeding ◽

10.7482/0003-9438-56-027 ◽

2013 ◽

Vol 56 (1) ◽

pp. 276-284 ◽

Cited By ~ 1

Author(s):

M. Madad ◽

N. Ghavi Hossein-Zadeh ◽

A. A. Shadparvar ◽

D. Kianzad

Keyword(s):

Milk Yield ◽

Milk Fat ◽

Milk Protein ◽

Genetic Parameters ◽

Genetic Correlations ◽

Random Regression ◽

Production Traits ◽

Environmental Correlations ◽

Protein Percentage ◽

Heritability Estimates

Abstract. The objective of this study was to estimate genetic parameters for milk yield and milk percentages of fat and protein in Iranian buffaloes. A total of 9,278 test-day production records obtained from 1,501 first lactation buffaloes on 414 herds in Iran between 1993 and 2009 were used for the analysis. Genetic parameters for productive traits were estimated using random regression test-day models. Regression curves were modeled using Legendre polynomials (LPs). Heritability estimates were low to moderate for milk production traits and ranged from 0.09 to 0.33 for milk yield, 0.01 to 0.27 for milk protein percentage and 0.03 to 0.24 for milk fat percentage, respectively. Genetic correlations ranged from −0.24 to 1 for milk yield between different days in milk over the lactation. Genetic correlations of milk yield at different days in milk were often higher than permanent environmental correlations. Genetic correlations for milk protein percentage ranged from −0.89 to 1 between different days in milk. Also, genetic correlations for milk percentage of fat ranged from −0.60 to 1 between different days in milk. The highest estimates of genetic and permanent environmental correlations for milk traits were observed at adjacent test-days. Ignoring heritability estimates for milk yield and milk protein percentage in the first and final days of lactation, these estimates were higher in the 120 days of lactation. Test-day milk yield heritability estimates were moderate in the course of the lactation, suggesting that this trait could be applied as selection criteria in Iranian milking buffaloes.

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Transdimensional seismic inversion using the reversible jump Hamiltonian Monte Carlo algorithm

Geophysics ◽

10.1190/geo2016-0010.1 ◽

2017 ◽

Vol 82 (3) ◽

pp. R119-R134 ◽

Cited By ~ 42

Author(s):

Mrinal K. Sen ◽

Reetam Biswas

Keyword(s):

Monte Carlo ◽

A Priori ◽

Seismic Inversion ◽

Monte Carlo Algorithm ◽

Model Parameters ◽

Reversible Jump ◽

Step Method ◽

Acceptance Probability ◽

Hamiltonian Monte Carlo ◽

Impedance Inversion

Prestack or angle stack gathers are inverted to estimate pseudologs at every surface location for building reservoir models. Recently, several methods have been proposed to increase the resolution of the inverted models. All of these methods, however, require that the total number of model parameters be fixed a priori. We have investigated an alternate approach in which we allow the data themselves to choose model parameterization. In other words, in addition to the layer properties, the number of layers is also treated as a variable in our formulation. Such transdimensional inverse problems are generally solved by using the reversible jump Markov chain Monte Carlo (RJMCMC) approach, which is a tool for model exploration and uncertainty quantification. This method, however, has very low acceptance. We have developed a two-step method by combining RJMCMC with a fixed-dimensional MCMC called Hamiltonian Monte Carlo, which makes use of gradient information to take large steps. Acceptance probability for such a transition is also derived. We call this new method “reversible jump Hamiltonian Monte Carlo (RJHMC).” We have applied this technique to poststack acoustic impedance inversion and to prestack (angle stack) AVA inversion for estimating acoustic and shear impedance profiles. We have determined that the marginal posteriors estimated by RJMCMC and RJHMC are in good agreement. Our results demonstrate that RJHMC converges faster than RJMCMC, and it therefore can be a practical tool for inverting seismic data when the gradient can be computed efficiently.

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Estimation the Genetic Parameters for Milk Yield in Romanian Spotted, Simmental Type Cattle Breed

Archiva Zootechnica ◽

10.2478/azibna-2021-0017 ◽

2021 ◽

Vol 24 (2) ◽

pp. 105-121

Author(s):

Rodica Stefania Pelmuș ◽

Mircea Cătălin Rotar ◽

Cristina Lazăr ◽

Răzvan Alexandru Uță

Keyword(s):

Animal Model ◽

Milk Yield ◽

Genetic Parameters ◽

Genetic Correlations ◽

Cattle Breed ◽

Random Regression ◽

Breeding Value ◽

Regression Test ◽

Fat Yield ◽

Heritability Estimates

Abstract The aim of this study was to estimate the genetic parameters for test-day traits milk yield and the breeding value in Romanian Spotted, Simmental type cattle. Random regression test-day animal model was used to estimate the genetic parameters. The number of records were 2062 test-day from 302 cows. The data were obtained from Romanian Breeding Association Romanian Spotted, Simmental type. The heritability estimates values for milk yield ranged between 0.377 and 0.417. The heritability for fat test-day yield in our study was low the values ranged between 0.117 and 0.236 and for protein test-day yield was medium, the values ranged between 0.308 and 0.372. The breeding value for the best ten cows for milk yield ranged from 1946.57 to 3250.38 kg, for fat yield were between 64.92 and 98.86 kg and for protein ranged from 67.26 to 102.21 kg. The correlations between test-day milk yields ranging from 0.28 to 1. Genetic correlations between test day fat and protein yields were high.

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Schätzung genetischer Parameter für Testtagsergebnisse der Milchleistung bei ostfriesischen Milchschafen mit Bayes-Methoden für longitudinale Daten

Archives Animal Breeding ◽

10.5194/aab-45-61-2002 ◽

2002 ◽

Vol 45 (1) ◽

pp. 61-68

Author(s):

A. Horstick ◽

O. Distl

Keyword(s):

Protein Content ◽

Milk Yield ◽

Bayesian Methods ◽

Regression Models ◽

Genetic Parameters ◽

Fat Content ◽

Random Regression ◽

Lower Saxony ◽

Milk Performance ◽

Heritability Estimates

Abstract. Title of the paper: Estimation of genetic parameters for test day results of milk performance in East Friesian milk sheep using Bayesian methods for longitudinal data The objectives of this study were to estimate genetic parameters of milk performance traits in East Friesian milk sheep by using test day models with random regresssion. The analysis was based on 7545 test day records of 918 East Friesian milk sheep with 1380 lactation records. The data were provided by the sheep breeding organizations of Lower-Saxony, Westphalia, and Bavaria. The milk recordings were collected in the years 1992 to 2000. The average values of the heritability estimates by using random regression models were for the milk yield h2 = 0.25 ± 0.03, for the fat content h2 = 0.46 ± 0.09, and for the protein content h2 = 0.63 ± 0.12. The range of heritability estimates in dependence of the days in milk was for milk yield h2 = 0.03 to 0.70, for fat content h2 = 0.30 to 0.70, and for protein content h2 = 0.44 to 0.92.

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Hamiltonian Monte Carlo sampling to estimate past population dynamics using the skygrid coalescent model in a Bayesian phylogenetics framework

Wellcome Open Research ◽

10.12688/wellcomeopenres.15770.1 ◽

2020 ◽

Vol 5 ◽

pp. 53

Author(s):

Guy Baele ◽

Mandev S. Gill ◽

Philippe Lemey ◽

Marc A. Suchard

Keyword(s):

Monte Carlo ◽

Population Dynamics ◽

Monte Carlo Sampling ◽

Estimation Methods ◽

Model Parameters ◽

Effective Sample Size ◽

Hamiltonian Monte Carlo ◽

Gradient Based ◽

Past Population ◽

Over Time

Nonparametric coalescent-based models are often employed to infer past population dynamics over time. Several of these models, such as the skyride and skygrid models, are equipped with a block-updating Markov chain Monte Carlo sampling scheme to efficiently estimate model parameters. The advent of powerful computational hardware along with the use of high-performance libraries for statistical phylogenetics has, however, made the development of alternative estimation methods feasible. We here present the implementation and performance assessment of a Hamiltonian Monte Carlo gradient-based sampler to infer the parameters of the skygrid model. The skygrid is a popular and flexible coalescent-based model for estimating population dynamics over time and is available in BEAST 1.10.5, a widely-used software package for Bayesian pylogenetic and phylodynamic analysis. Taking into account the increased computational cost of gradient evaluation, we report substantial increases in effective sample size per time unit compared to the established block-updating sampler. We expect gradient-based samplers to assume an increasingly important role for different classes of parameters typically estimated in Bayesian phylogenetic and phylodynamic analyses.

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Genetic parameters of test day records of British Holstein-Friesian heifers

Animal Science ◽

10.1017/s0003356100037211 ◽

1992 ◽

Vol 55 (1) ◽

pp. 11-21 ◽

Cited By ~ 64

Author(s):

B. L. Pander ◽

W. G. Hill ◽

R. Thompson

Keyword(s):

Maximum Likelihood ◽

Milk Yield ◽

Milk Fat ◽

Genetic Parameters ◽

Genetic Correlations ◽

Lactation Performance ◽

Likelihood Methods ◽

Holstein Friesian ◽

Maximum Likelihood Methods ◽

Heritability Estimates

AbstractEstimates of genetic parameters for test day records of yields of milk, fat and protein and concentrations of fat and protein were obtained on 47 736 British Holstein-Friesian heifers in 7973 herds, progeny of 40 proven (to improve connectedness) and 707 young sires (comprising about one-fifth of the progeny), using multivariate restricted maximum likelihood methods with a sire model.Heritability estimates for lactation yields of milk, fat and protein and concentrations of fat and protein were 0·49, 0·39, 0·43, 0·63 and 0·47, respectively. Estimates for individual test day records of these traits ranged from 0·27 to 0·43, 0·16 to 0·34, 0·22 to 0·33, 0·11 to 0·48 and 0·21 to 0·43, respectively. Generally, heritability estimates for test day records were lowest at start and highest in mid lactation.Estimates of genetic correlations among yields of a trait on different test days ranged from 0·57 to 0·99, and for fat and protein concentrations from 0·34 to 0·99, the correlations being highest for adjacent tests. Phenotypic correlations were lower than genetic correlations. Genetic correlations of test day records with corresponding lactation traits were high (0·76 to 0·99), being highest in mid lactation.Genetic correlations of test day milk yield with test day yields and concentrations of fat and protein throughout the lactation were similar to those for complete lactation.The high heritabilities of test day yields and their high genetic correlations with complete lactation, except for the first 1 or 2 test days, suggest that lactation performance may be predicted from test days in early and mid lactation.

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Genetic parameters for test-day milk yield in tropical Holstein Friesian cattle fitting a multiple-lactation random regression animal model

South African Journal of Animal Science ◽

10.4314/sajas.v47i3.12 ◽

1970 ◽

Vol 47 (3) ◽

pp. 352-361

Author(s):

S. Meseret ◽

E. Negussie

Keyword(s):

Animal Model ◽

Milk Yield ◽

Genetic Improvement ◽

Genetic Parameters ◽

Genetic Correlations ◽

Random Regression ◽

Likelihood Method ◽

Holstein Friesian ◽

Heritability Estimates ◽

Friesian Cattle

Accurate estimates of genetic parameters are essential for genetic improvement of milk yield in dairy cattle and for setting up breeding programmes. Estimates of genetic parameters from test-day models, particularly for Holstein Friesian cattle maintained in tropical environments, are scant in the literature. The objective of this study was therefore to estimate genetic parameters for milk yield by fitting a multiple-lactation random regression animal model (RRM) based on data from Ethiopian Holstein Friesian herds. Data were used from the first three lactations of cows that calved between 1997 and 2013. The data comprised 13 421 test-day milk yield records from 800 cows from two large dairy herds. Variance components were estimated using the average information restricted maximum likelihood method fitting an RRM. Heritability estimates for first, second, and third lactations ranged from 0.20 to 0.26, 0.15 to 0.27, and 0.17 to 0.28, respectively. Heritability estimates ranging from 0.15 to 0.28 indicate that effective genetic improvement should be accompanied by a corresponding improvement of the production environment. Across-lactation genetic correlations between first and second, second and third, and first and third lactations, expressed on a 305-day yield basis, were 0.88, 0.83, and 0.70, respectively. These genetic correlations, less than or equal to 0.88, indicate that different lactations are different traits. For an accurate evaluation of the genetic merit of animals for milk yield, lactations should be treated as different, but correlated traits in a multiple-lactation analysis.Keywords: Genetic correlation, heritability, Legendre polynomial, test-day model

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Lactation curve of Beetal goats in Pakistan

Archives Animal Breeding ◽

10.7482/0003-9438-56-089 ◽

2013 ◽

Vol 56 (1) ◽

pp. 892-898

Author(s):

A. Waheed ◽

M. S. Khan

Keyword(s):

Milk Yield ◽

Model Parameters ◽

Yield Data ◽

Lactation Length ◽

Lactation Curve ◽

Rate Of Increase ◽

The Mean ◽

Rate Of Decline ◽

Wood Model ◽

Effect Of Age

Abstract. This study was accomplished with the objective to determine parameters of lactation curves in Beetal goats using Wood’s model. Therefore, milk yield data on 127 Beetal goats maintained at five different government farms were recorded from post-kidding to drying off of does. Wood model parameters were estimated using non-linear regression and individual curves were fitted. The characteristics/parameters of lactation curve were computed. The mean initial yield »a«, rate of increase »b« and rate of decline »c« parameters in Wood’s model for Beetal were 1,214.97, 0.3690 and 0.1196, respectively with R2 value of 98.2 %. The value of percent squared bias (PSB) and the persistency were 0.13 and 60.2%, respectively with mean square error value of 38.45. Flock effect was a significant (P<0.01) source of variation for all the lactation curve parameters, PSB and persistency. Parity did not affect significantly any of the parameters. Type of birth significantly influenced parameter »a«, Time to reach peak (TPY) and lactation milk yield (LMY). Sex of kid also did not affect significantly any of the parameters. Age of doe was significant for parameters »a«, »b«, »c«. Quadratic effect of age was non-significant for all parameters and characteristics. Lactation length significantly affected parameter »a«, »b« and LMY.

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

Genetics Selection Evolution ◽

10.1186/s12711-019-0515-1 ◽

2019 ◽

Vol 51 (1) ◽

Author(s):

Motohide Nishio ◽

Aisaku Arakawa

Keyword(s):

Monte Carlo ◽

Markov Chain ◽

Markov Chain Monte Carlo ◽

Gibbs Sampling ◽

Genetic Parameters ◽

Simulated Data ◽

Animal Breeding ◽

Posterior Distributions ◽

Breeding Values ◽

Hamiltonian Monte Carlo

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.

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