scholarly journals Tunings for leapfrog integration of Hamiltonian Monte Carlo for estimating genetic parameters

2019 ◽  
Author(s):  
Aisaku Arakawa ◽  
Takeshi Hayashi ◽  
Masaaki Taniguchi ◽  
Satoshi Mikawa ◽  
Motohide Nishio
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Gibbs Sampling ◽  
Sampling Method ◽  
Monte Carlo Algorithm ◽  
Superior Performance ◽  
Pedigree Information ◽  
Hamiltonian Monte Carlo ◽  
Hamilton's Equations ◽  
Hamilton’S Equations

AbstractA Hamiltonian Monte Carlo algorithm is a Markov Chain Monte Carlo method that is considered more effective than the conventional Gibbs sampling method. 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 R language.

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

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

<p>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’s strain tensors. We infer the full moment tensor, location and centroid time of the seismic events in the study area.</p><p>To compute spatial derivatives of Green’s functions, we use a previously derived regional Earth model (Simutė et al., 2016). The model is radially anisotropic, visco-elastic, and fully heterogeneous. It was constructed using full waveforms in the period band of 15–80 s.</p><p>Green’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.</p><p>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 Simutė, 2017). We apply an L2 misfit on waveform data, and we work in the period band of 15–80 s.</p><p>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.</p>

Transdimensional seismic inversion using the reversible jump Hamiltonian Monte Carlo algorithm

Geophysics ◽  
2017 ◽  
Vol 82 (3) ◽  
pp. R119-R134 ◽  
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.

scholarly journals A GUIDED MONTE CARLO METHOD FOR OPTIMIZATION PROBLEMS

2002 ◽  
Vol 13 (10) ◽  
pp. 1365-1374 ◽  
Author(s):  
S. P. LI
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Degrees Of Freedom ◽  
State Energy ◽  
Optimization Problems ◽  
Optimal Path ◽  
Monte Carlo Algorithm ◽  
Glass Model ◽  
Speed Up ◽  
The Traveling Salesman Problem

We introduce a new Monte Carlo algorithm which incorporates a guiding function to the conventional Monte Carlo method. In this way, the efficiency of Monte Carlo methods is drastically improved. Two more ingredients, namely, the elimination of irrelevant degrees of freedom and the concept of optimal temperature are also introduced which can further speed up the search process. We use this algorithm to search for the optimal path of the traveling salesman problem and the ground state energy of the Anderson–Edwards spin glass model and demonstrate that its performance is comparable with more elaborate and heuristic methods.

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