{"title":"Super-efficient exact Hamiltonian Monte Carlo for the von Mises distribution","authors":"","doi":"10.1016/j.aml.2024.109284","DOIUrl":null,"url":null,"abstract":"<div><p>Markov Chain Monte Carlo algorithms, the method of choice to sample from generic high-dimensional distributions, are rarely used for continuous one-dimensional distributions, for which more effective approaches are usually available (e.g. rejection sampling). In this work we present a counter-example to this conventional wisdom for the von Mises distribution, a maximum-entropy distribution over the circle. We show that Hamiltonian Monte Carlo with Laplacian momentum has exactly solvable equations of motion and, with an appropriate travel time, the Markov chain has negative autocorrelation at odd lags for odd observables and yields a relative effective sample size bigger than one.</p></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":2.9000,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics Letters","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0893965924003045","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
Markov Chain Monte Carlo algorithms, the method of choice to sample from generic high-dimensional distributions, are rarely used for continuous one-dimensional distributions, for which more effective approaches are usually available (e.g. rejection sampling). In this work we present a counter-example to this conventional wisdom for the von Mises distribution, a maximum-entropy distribution over the circle. We show that Hamiltonian Monte Carlo with Laplacian momentum has exactly solvable equations of motion and, with an appropriate travel time, the Markov chain has negative autocorrelation at odd lags for odd observables and yields a relative effective sample size bigger than one.
期刊介绍:
The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.