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This is a Quantitative Study study.

October 1, 2025Open Access

Numerical aspects of large deviations

AHAlexander K. HartmannCarl von Ossietzky Universität Oldenburg

Key Points

Direct biasing methods in large deviations can enhance sampling accuracy, especially in Bernoulli processes.
MCMC simulations, specifically the Metropolis-Hastings algorithm, provide a foundation for improving sampling techniques.
Exponential bias is a powerful tool to explore tails of distributions in various random processes.
Recent applications illustrate the versatility of these methods in studying more complex random models.

Abstract

An introduction to numerical large-deviation sampling is provided. First, direct biasing with a known distribution is explained. As simple example, the Bernoulli process is used throughout the text. Next, Markov chain Monte Carlo (MCMC) simulations are introduced. In particular, the Metropolis-Hastings algorithm is explained. As first implementation of MCMC, sampling of the plain Bernoulli model is shown. Next, an exponential bias is used for the same model, which allows one to obtain the tails of the distribution of a measurable quantity. This approach is generalized to MCMC simulations, where the states are vectors of U(0,1) U(0,1) random entries. This allows one to use the exponential or any other bias to access the large-deviation properties of rather arbitrary random processes. Finally, some recent research applications to study more complex models are discussed.

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Cite This Study

Alexander K. Hartmann (Tue,) studied this question.

synapsesocial.com/papers/68dd89defe798ba2fc497ceb https://doi.org/https://doi.org/10.21468/scipostphyslectnotes.100

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