A Modification of Neal’s Algorithm for a Continuous State Space and an Application to the Fokker-planck Equation
نویسندگان
چکیده
The Metropolis-Hastings algorithm generates correlated samples from a target distribution by constructing a Markov chain which has as its stationary distribution the desired target distribution. One property of this algorithm is that it creates reversible Markov chains. As a result, reversible chains are often used in Monte Carlo simulations. Reversible Markov chains also have the added benefit of being easier to deal with analytically. However, Neal proposes that one should not restrict to only dealing with reversible Markov chains, by proposing an algorithm for which reversible Markov chains can be made into non-reversible Markov chains in an process which will not increase the asymptotic variance. The non-reversible chains work by avoiding the ”backtracking” that causes Markov chains to remain in one position for too long. In the body of this paper, we extend Neal’s algorithm from a discrete to a continuous state space and then test the algorithm on an application to the Fokker-Planck equation. Date: 2 September, 2009.
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