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通过非可逆模拟回火实现自动再生模拟AI 解读

Simulated Tempering (ST) is an MCMC algorithm for complex target distributions that operates on a path between the target and a more amenable reference distribution. Crucially, if the reference enables i.i.d. sampling, ST is regenerative and can be parallelized across independent tours. However, the difficulty of tuning ST has hindered its widespread adoption. In this work, we develop a simple nonreversible ST (NRST) algorithm, a general theoretical analysis of ST, and an…

非可逆并行温度法：可扩展的高度并行 MCMC 方案AI 解读

Abstract Parallel tempering (PT) methods are a popular class of Markov chain Monte Carlo schemes used to sample complex high-dimensional probability distributions. They rely on a collection of N interacting auxiliary chains targeting tempered versions of the target distribution to improve the exploration of the state space. We provide here a new perspective on these highly parallel algorithms and their tuning by identifying and formalizing a sharp divide in the behaviour and…

弹跳粒子采样器的指数遍历性AI 解读

Nonreversible Markov chain Monte Carlo schemes based on piecewise deterministic Markov processes have been recently introduced in applied probability, automatic control, physics and statistics. Although these algorithms demonstrate experimentally good performance and are accordingly increasingly used in a wide range of applications, geometric ergodicity results for such schemes have only been established so far under very restrictive assumptions. We give here verifiable…

弹跳粒子采样器：非可逆、无拒绝的马尔可夫链蒙特卡洛方法AI 解读

Many Markov chain Monte Carlo techniques currently available rely on discrete-time reversible Markov processes whose transition kernels are variations of the Metropolis–Hastings algorithm. We explore and generalize an alternative scheme recently introduced in the physics literature (Peters and de With 2012) where the target distribution is explored using a continuous-time nonreversible piecewise-deterministic Markov process. In the Metropolis–Hastings algorithm, a trial move…

利用组合序贯蒙特卡洛方法进行贝叶斯系统发育推断AI 解读

The application of Bayesian methods to large-scale phylogenetics problems is increasingly limited by computational issues, motivating the development of methods that can complement existing Markov chain Monte Carlo (MCMC) schemes. Sequential Monte Carlo (SMC) methods are approximate inference algorithms that have become very popular for time series models. Such methods have been recently developed to address phylogenetic inference problems but currently available techniques…