scholarly journals Geometric integrators and the Hamiltonian Monte Carlo method

Acta Numerica ◽  
2018 ◽  
Vol 27 ◽  
pp. 113-206 ◽  
Author(s):  
Nawaf Bou-Rabee ◽  
J. M. Sanz-Serna
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Computational Cost ◽  
Acceptance Rate ◽  
The Other ◽  
Geometric Properties ◽  
Hybrid Monte Carlo ◽  
Geometric Integrators ◽  
Numerical Integrations ◽  
Volume Preserving

This paper surveys in detail the relations between numerical integration and the Hamiltonian (or hybrid) Monte Carlo method (HMC). Since the computational cost of HMC mainly lies in the numerical integrations, these should be performed as efficiently as possible. However, HMC requires methods that have the geometric properties of being volume-preserving and reversible, and this limits the number of integrators that may be used. On the other hand, these geometric properties have important quantitative implications for the integration error, which in turn have an impact on the acceptance rate of the proposal. While at present the velocity Verlet algorithm is the method of choice for good reasons, we argue that Verlet can be improved upon. We also discuss in detail the behaviour of HMC as the dimensionality of the target distribution increases.

A simplified variable metric hybrid Monte Carlo method

2013 ◽  
Author(s):  
M. P. Calvo ◽  
I. Rodrigo ◽  
J. M. Sanz-Serna
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Hybrid Monte Carlo ◽  
Variable Metric

scholarly journals Real Estate Appraisals with Bayesian Approach and Markov Chain Hybrid Monte Carlo Method: An Application to a Central Urban Area of Naples

2017 ◽  
Vol 9 (11) ◽  
pp. 2138 ◽  
Author(s):  
Vincenzo Del Giudice ◽  
Pierfrancesco De Paola ◽  
Fabiana Forte ◽  
Benedetto Manganelli
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Monte Carlo Method ◽  
Real Estate ◽  
Urban Area ◽  
Bayesian Approach ◽  
Hybrid Monte Carlo

scholarly journals Rejection Sampling Schemes for Simulating from Arbitrary Probability Densities

2020 ◽  
Vol 68 (1) ◽  
pp. 59-64
Author(s):  
Anamul Haque Sajib
Keyword(s):  
Monte Carlo ◽  
Computational Cost ◽  
The Other ◽  
Rejection Sampling ◽  
Mcmc Method ◽  
Empirical Comparison ◽  
Sampling Schemes ◽  
Probability Densities ◽  
Better Than

Simulating random variates from arbitrary non-normalized probability densities, very often they do not have familiar forms, is an increasingly important requirement in many different fields, especially in Bayesian statistics. Accept-reject algorithm is one of the commonly used methods to simulate random variates from such densities but restriction on choosing proposal density under this framework (heavier tails than the target density) limits its applicability to a larger extent. On the other hand, Markov Chain Monte Carlo (MCMC) method can choose proposal density arbitrary which makes this method applicable to a larger class of target densities5. In addition to MCMC method, a more general widely used method known as ratio-of-uniforms (RoU) which requires only two uniform variates to simulate one variates from such densities. However, no empirical comparison among these methods for simulating random variates from such densities was seen in the literature. In this paper, we limit our study only to MCMC and RoU methods to simulate random variates from such densities. Following the generation of random variates from such densities using these two methods, we compare the performance of these two methods based on quality of the generated samples. Finally, we conclude that RoU method performs better than MCMC method as far as quality of the generated sample (randomness) and computational cost are concerned. Dhaka Univ. J. Sci. 68(1): 59-64, 2020 (January)

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