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1. Stochastic potential switching algorithm for Monte Carlo simulations of complex systems.

Author

Mak, C. H.

Subjects
*MONTE Carlo method, *ALGORITHMS, *PROBABILITY theory, *STATISTICAL sampling, *NUMERICAL analysis, *MATHEMATICAL models, *ESTIMATION theory
Abstract

This paper describes a new Monte Carlo method based on a novel stochastic potential switching algorithm. This algorithm enables the equilibrium properties of a system with potential V to be computed using a Monte Carlo simulation for a system with a possibly less complex stochastically altered potential V. By proper choices of the stochastic switching and transition probabilities, it is shown that detailed balance can be strictly maintained with respect to the original potential V. The validity of the method is illustrated with a simple one-dimensional example. The method is then generalized to multidimensional systems with any additive potential, providing a framework for the design of more efficient algorithms to simulate complex systems. A near-critical Lennard-Jones fluid with more than 20 000 particles is used to illustrate the method. The new algorithm produced a much smaller dynamic scaling exponent compared to the Metropolis method and improved sampling efficiency by over an order of magnitude. [ABSTRACT FROM AUTHOR]

Published
2005
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2. An importance sampling algorithm for estimating extremes of perpetuity sequences.

Author

Collamore, Jeffrey F.

Subjects
*STATISTICAL sampling, *ALGORITHMS, *PROBLEM solving, *PROBABILITY theory, *MARKOV processes, *NUMERICAL analysis, *INSURANCE
Abstract

In a wide class of problems in insurance and financial mathematics, it is of interest to study the extremal events of a perpetuity sequence. This paper addresses the problem of numerically evaluating these rare event probabilities. Specifically, an importance sampling algorithm is described which is efficient in the sense that it exhibits bounded relative error, and which is optimal in an appropriate asymptotic sense. The main idea of the algorithm is to use a 'dual' change of measure, which is employed to an associated Markov chain over a randomly-stopped time interval. The algorithm also makes use of the so-called forward sequences generated to the given stochastic recursion, together with elements of Markov chain theory. [ABSTRACT FROM AUTHOR]

Published
2012
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3. Nested Sampling’s Convergence.

Author

Skilling, John

Subjects
*STATISTICAL sampling, *ALGORITHMS, *PROBABILITY theory, *ALGEBRA
Abstract

Nested sampling is an algorithm for computing the Bayesian evidence (or prior predictive, marginal likelihood), through a probabilistic method having stated and controllable accuracy. This paper presents the method more clearly than before, and includes convergence proofs that were previously missing. [ABSTRACT FROM AUTHOR]

Published
2009
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