scholarly journals A separable shadow Hamiltonian hybrid Monte Carlo method

2009 ◽  
Vol 131 (17) ◽  
pp. 174106 ◽  
Author(s):  
Christopher R. Sweet ◽  
Scott S. Hampton ◽  
Robert D. Skeel ◽  
Jesús A. Izaguirre
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Hybrid Monte Carlo ◽  
Shadow Hamiltonian

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 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.

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