Backward Simulation of Stochastic Process using a Time Reverse Monte Carlo method

Particle rejuvenation of Rao-Blackwellized Sequential Monte Carlo smoothers for Conditionally Linear and Gaussian models

This paper focuses on Sequential Monte Carlo approximations of smoothing distributions in conditionally linear and Gaussian state spaces. To reduce Monte Carlo variance of smoothers, it is typical in these models to use Rao-Blackwellization: particle approximation is used to sample sequences of hidden regimes while the Gaussian states are explicitly integrated conditional on the sequence of regimes and observations, using variants of the Kalman filter / smoother. The first successful attempt to use Rao-Blackwellization for smoothing extends the Bryson-Frazier smoother for Gaussian linear state…

Multiprocess parallel antithetic coupling for backward and forward Markov Chain Monte Carlo

Antithetic coupling is a general stratification strategy for reducing Monte Carlo variance without increasing the simulation size. The use of the antithetic principle in the Monte Carlo literature typically employs two strata via antithetic quantile coupling. We demonstrate here that further stratification, obtained by using k>2 (e.g., k=3-10) antithetically coupled variates, can offer substantial additional gain in Monte Carlo efficiency, in terms of both variance and bias. The reason for reduced bias is that antithetically coupled chains can provide a more dispersed search of the state space…

蒙特卡洛采样中反向扩散的新视角

A New Perspective on Reverse Diffusion for Monte Carlo Sampling

提出一种无需时间离散化和分数估计的反向扩散采样方法，通过嵌入目标密度到有限时域扩散过程的初始边际，并基于Radon-Nikodym导数推导出两类并行化MCMC算法，有效处理多模态和复杂依赖结构。

On the use of backward simulation in particle Markov chain Monte Carlo methods

Recently, Andrieu, Doucet and Holenstein (2010) introduced a general framework for using particle filters (PFs) to construct proposal kernels for Markov chain Monte Carlo (MCMC) methods. This framework, termed Particle Markov chain Monte Carlo (PMCMC), was shown to provide powerful methods for joint Bayesian state and parameter inference in nonlinear/non-Gaussian state-space models. However, the mixing of the resulting MCMC kernels can be quite sensitive, both to the number of particles used in the underlying PF and to the number of observations in the data. In the discussion following (Andrie…

薛定谔桥问题的前向-反向核回归方法

Forward Reverse Kernel Regression for the Schrödinger bridge problem

本文针对熵最优传输中的薛定谔桥问题，提出基于核回归与Picard迭代的前向-反向蒙特卡罗算法，证明其收敛性并给出势估计的最优收敛速率，还应用于桥过程分布模拟。

Metropolising forward particle filtering backward sampling and Rao-Blackwellisation of Metropolised particle smoothers

Smoothing in state-space models amounts to computing the conditional distribution of the latent state trajectory, given observations, or expectations of functionals of the state trajectory with respect to this distributions. For models that are not linear Gaussian or possess finite state space, smoothing distributions are in general infeasible to compute as they involve intergrals over a space of dimensionality at least equal to the number of observations. Recent years have seen an increased interest in Monte Carlo-based methods for smoothing, often involving particle filters. One such method …

Backward importance sampling for online estimation of state space models

This paper proposes a new Sequential Monte Carlo algorithm to perform online estimation in the context of state space models when either the transition density of the latent state or the conditional likelihood of an observation given a state is intractable. In this setting, obtaining low variance estimators of expectations under the posterior distributions of the unobserved states given the observations is a challenging task. Following recent theoretical results for pseudo-marginal sequential Monte Carlo smoothers, a pseudo-marginal backward importance sampling step is introduced to estimate s…

Comment on "Sequential Monte Carlo for Bayesian Computation" (P. Del Moral, A. Doucet, A. Jasra)

The main question concerns another recent advance in sequential Monte Carlo, the use of a mixture transition kernel that automatically adapts to the target distribution (Douc et al. 2006). Is there a class of static inference problems for which the backward-kernel approach is better suited, or is it too early to predict which method may have better performance in a particular situation?

Particle ancestor sampling for near-degenerate or intractable state transition models

We consider Bayesian inference in sequential latent variable models in general, and in nonlinear state space models in particular (i.e., state smoothing). We work with sequential Monte Carlo (SMC) algorithms, which provide a powerful inference framework for addressing this problem. However, for certain challenging and common model classes the state-of-the-art algorithms still struggle. The work is motivated in particular by two such model classes: (i) models where the state transition kernel is (nearly) degenerate, i.e. (nearly) concentrated on a low-dimensional manifold, and (ii) models where…

固定维度下通过反向扩散实现多项式查询复杂度的多模态分布采样

Sampling from multi-modal distributions with polynomial query complexity in fixed dimension via reverse diffusion

本文提出一种固定维度下基于反向扩散的多模态分布采样算法，通过自归一化蒙特卡洛估计得分函数，实现多项式查询复杂度，避免亚稳态且无需模态先验知识。

SpecSwap RMC: A novel reverse Monte Carlo approach using a discrete configuration space and pre-computed properties

We present a novel approach to reverse Monte Carlo (RMC) modeling, SpecSwap-RMC, which makes use of pre-computed property data from a discrete configuration space replacing atomistic moves with swap moves of contributions to a sample-set representing the average, or summed property. The approach is particularly suitable for disordered systems and properties which require significant computer time to compute. We demonstrate the approach by fitting jointly and separately the EXAFS signal and x-ray absorption spectrum (XAS) of ice Ih using as SpecSwap sample-set 80 configurations from a space of …