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Elja Arjas - One of the best experts on this subject based on the ideXlab platform.
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comment on on the metropolis hastings Acceptance Probability to add or drop a quantitative trait locus in markov chain monte carlo based bayesian analyses
Genetics, 2004Co-Authors: Mikko J Sillanpaa, Dario Gasbarra, Elja ArjasAbstract:AS Jean-Luc Jannink and Rohan L. Fernando ([Jannink and Fernando 2004][1]) nicely illustrated, when applying Markov chain Monte Carlo methods in a form where the dimension [the number of quantitative trait loci (QTL)] is not fixed, it can sometimes be hard to establish the correct form of the
Rohan L Fernando - One of the best experts on this subject based on the ideXlab platform.
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on the metropolis hastings Acceptance Probability to add or drop a quantitative trait locus in markov chain monte carlo based bayesian analyses
Genetics, 2004Co-Authors: Jeanluc Jannink, Rohan L FernandoAbstract:The Metropolis-Hastings algorithm used in analyses that estimate the number of QTL segregating in a mapping population requires the calculation of an Acceptance Probability to add or drop a QTL from the model. Expressions for this Acceptance Probability need to recognize that sets of QTL are unordered such that the number of equivalent sets increases with the factorial of the QTL number. Here, we show how accounting for this fact affects the Acceptance Probability and review expressions found in the literature.
Mikko J Sillanpaa - One of the best experts on this subject based on the ideXlab platform.
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comment on on the metropolis hastings Acceptance Probability to add or drop a quantitative trait locus in markov chain monte carlo based bayesian analyses
Genetics, 2004Co-Authors: Mikko J Sillanpaa, Dario Gasbarra, Elja ArjasAbstract:AS Jean-Luc Jannink and Rohan L. Fernando ([Jannink and Fernando 2004][1]) nicely illustrated, when applying Markov chain Monte Carlo methods in a form where the dimension [the number of quantitative trait loci (QTL)] is not fixed, it can sometimes be hard to establish the correct form of the
A M Stuart - One of the best experts on this subject based on the ideXlab platform.
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optimal tuning of the hybrid monte carlo algorithm
Bernoulli, 2013Co-Authors: A Beskos, N S Pillai, G O Roberts, J M Sanzserna, A M StuartAbstract:We investigate the properties of the hybrid Monte Carlo algorithm (HMC) in high dimensions. HMC develops a Markov chain reversible with respect to a given target distribution Π using separable Hamiltonian dynamics with potential −logΠ. The additional momentum variables are chosen at random from the Boltzmann distribution, and the continuous-time Hamiltonian dynamics are then discretised using the leapfrog scheme. The induced bias is removed via a Metropolis–Hastings accept/reject rule. In the simplified scenario of independent, identically distributed components, we prove that, to obtain an O(1) Acceptance Probability as the dimension d of the state space tends to ∞, the leapfrog step size h should be scaled as h=l×d−1/4. Therefore, in high dimensions, HMC requires O(d1/4) steps to traverse the state space. We also identify analytically the asymptotically optimal Acceptance Probability, which turns out to be 0.651 (to three decimal places). This value optimally balances the cost of generating a proposal, which decreases as l increases (because fewer steps are required to reach the desired final integration time), against the cost related to the average number of proposals required to obtain Acceptance, which increases as l increases.
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optimal tuning of the hybrid monte carlo algorithm
Bernoulli, 2013Co-Authors: A Beskos, N S Pillai, G O Roberts, J M Sanzserna, A M StuartAbstract:We investigate the properties of the Hybrid Monte Carlo algorithm (HMC) in high dimensions. HMC develops a Markov chain reversible w.r.t. a given target distribution . by using separable Hamiltonian dynamics with potential -log .. The additional momentum variables are chosen at random from the Boltzmann distribution and the continuous-time Hamiltonian dynamics are then discretised using the leapfrog scheme. The induced bias is removed via a Metropolis- Hastings accept/reject rule. In the simplified scenario of independent, identically distributed components, we prove that, to obtain an O(1) Acceptance Probability as the dimension d of the state space tends to ., the leapfrog step-size h should be scaled as h=l ×d−1/ 4 . Therefore, in high dimensions, HMC requires O(d1/ 4 ) steps to traverse the state space. We also identify analytically the asymptotically optimal Acceptance Probability, which turns out to be 0.651 (to three decimal places). This is the choice which optimally balances the cost of generating a proposal, which decreases as l increases (because fewer steps are required to reach the desired final integration time), against the cost related to the average number of proposals required to obtain Acceptance, which increases as l increases
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the Acceptance Probability of the hybrid monte carlo method in high dimensional problems
ICNAAM 2010: International Conference of Numerical Analysis and Applied Mathematics 2010, 2010Co-Authors: A Beskos, N S Pillai, G O Roberts, J M Sanzserna, A M StuartAbstract:We investigate the properties of the Hybrid Monte‐Carlo algorithm in high dimensions. In the simplified scenario of independent, identically distributed components, we prove that, to obtain an G(1) Acceptance Probability as the dimension d of the state space tends to ∞, the Verlet/leap‐frog step‐size h should be scaled as h = l×d−1/4. We also identify analytically the asymptotically optimal Acceptance Probability, which turns out to be 0.651 (with three decimal places); this is the choice that optimally balances the cost of generating a proposal, which decreases as l increases, against the cost related to the average number of proposals required to obtain Acceptance, which increases as l increases.
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optimal tuning of the hybrid monte carlo algorithm
arXiv: Probability, 2010Co-Authors: A Beskos, N S Pillai, G O Roberts, J M Sanzserna, A M StuartAbstract:We investigate the properties of the Hybrid Monte-Carlo algorithm (HMC) in high dimensions. HMC develops a Markov chain reversible w.r.t. a given target distribution $\Pi$ by using separable Hamiltonian dynamics with potential $-\log\Pi$. The additional momentum variables are chosen at random from the Boltzmann distribution and the continuous-time Hamiltonian dynamics are then discretised using the leapfrog scheme. The induced bias is removed via a Metropolis-Hastings accept/reject rule. In the simplified scenario of independent, identically distributed components, we prove that, to obtain an $\mathcal{O}(1)$ Acceptance Probability as the dimension $d$ of the state space tends to $\infty$, the leapfrog step-size $h$ should be scaled as $h= l \times d^{-1/4}$. Therefore, in high dimensions, HMC requires $\mathcal{O}(d^{1/4})$ steps to traverse the state space. We also identify analytically the asymptotically optimal Acceptance Probability, which turns out to be 0.651 (to three decimal places). This is the choice which optimally balances the cost of generating a proposal, which {\em decreases} as $l$ increases, against the cost related to the average number of proposals required to obtain Acceptance, which {\em increases} as $l$ increases.
David A Kofke - One of the best experts on this subject based on the ideXlab platform.
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on the Acceptance Probability of replica exchange monte carlo trials
Journal of Chemical Physics, 2002Co-Authors: David A KofkeAbstract:An analysis is presented of the average Probability of accepting an exchange trial in the parallel-tempering Monte Carlo molecular simulation method. Arguments are given that this quantity should be related to the entropy difference between the phases, and results from simulations of a simple Lennard-Jones system are presented to support this argument qualitatively. Another analysis based on the energy distributions of a replica pair is presented, and an exact expression for the trial-move Acceptance Probability in terms of the overlap of these distributions is derived. A more detailed expression is presented using an approximation of constant heat capacity, and an asymptotic form for this result, good for large system sizes, is reported. The detailed analyses are in quantitative agreement with the simulation data. It is further shown that treatment of the energy distributions as Gaussians is an inappropriate way to analyze the Acceptance Probability.
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articles on the Acceptance Probability of replica exchange monte carlo trials
2002Co-Authors: David A KofkeAbstract:An analysis is presented of the average Probability of accepting an exchange trial in the parallel-tempering Monte Carlo molecular simulation method. Arguments are given that this quantity should be related to the entropy difference between the phases, and results from simulations of a simple Lennard-Jones system are presented to support this argument qualitatively. Another analysis based on the energy distributions of a replica pair is presented, and an exact expression for the trial-move Acceptance Probability in terms of the overlap of these distributions is derived. A more detailed expression is presented using an approximation of constant heat capacity, and an asymptotic form for this result, good for large system sizes, is reported. The detailed analyses are in quantitative agreement with the simulation data. It is further shown that treatment of the energy distributions as Gaussians is an inappropriate way to analyze the Acceptance Probability. © 2002 American Institute of Physics. @DOI: 10.1063/1.1507776#
