Related papers: Rao-Blackwellization in the MCMC era

Sufficient statistics are derived for the population size and parameters of commonly used closed population mark-recapture models. Rao-Blackwellization details for improving estimators that are not functions of the statistics are presented.…

Population Monte Carlo has been introduced as a sequential importance sampling technique to overcome poor fit of the importance function. In this paper, we compare the performances of the original Population Monte Carlo algorithm with a…

Exact Bayesian inference on state-space models~(SSM) is in general untractable, and unfortunately, basic Sequential Monte Carlo~(SMC) methods do not yield correct approximations for complex models. In this paper, we propose a mixed…

We study control variate methods for Markov chain Monte Carlo (MCMC) in the setting of deterministic sweep sampling using $K\geq 2$ transition kernels. New variance reduction results are provided for MCMC averages based on sweeps over…

Estimating the Kullback--Leibler (KL) divergence between language models has many applications, e.g., reinforcement learning from human feedback (RLHF), interpretability, and knowledge distillation. However, computing the exact KL…

Casella and Robert [Biometrika 83 (1996) 81--94] presented a general Rao--Blackwellization principle for accept-reject and Metropolis--Hastings schemes that leads to significant decreases in the variance of the resulting estimators, but at…

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…

We introduce a dynamic mechanism for the solution of analytically-tractable substructure in probabilistic programs, using conjugate priors and affine transformations to reduce variance in Monte Carlo estimators. For inference with…

The Rao-Blackwell theorem is utilized to analyze and improve the scalability of inference in large probabilistic models that exhibit symmetries. A novel marginal density estimator is introduced and shown both analytically and empirically to…

This paper explores a Bayesian self-organization method for state-space models, enabling simultaneous state and parameter estimation without repeated likelihood calculations. While efficient for low-dimensional models, high-dimensional…

In light transport simulation, Markov chain Monte Carlo methods are particularly effective at exploring regions with complex lighting characteristics. However, estimator variance is a central concern across Monte Carlo methods in general.…

Much research has been carried out on shrinkage methods for real-valued covariance matrices. In spectral analysis of $p$-vector-valued time series there is often a need for good shrinkage methods too, most notably when the complex-valued…

This paper uncovers and explores the close relationship between Monte Carlo Optimization of a parametrized integral (MCO), Parametric machine-Learning (PL), and `blackbox' or `oracle'-based optimization (BO). We make four contributions.…

We attempt to trace the history and development of Markov chain Monte Carlo (MCMC) from its early inception in the late 1940s through its use today. We see how the earlier stages of Monte Carlo (MC, not MCMC) research have led to the…

Majorization is a basic concept in matrix theory that has found applications in numerous settings over the past century. Power majorization is a more specialized notion that has been studied in the theory of inequalities. On the other hand,…

In the design of efficient simulation algorithms, one is often beset with a poor choice of proposal distributions. Although the performance of a given simulation kernel can clarify a posteriori how adequate this kernel is for the problem at…

Gradient estimation in models with discrete latent variables is a challenging problem, because the simplest unbiased estimators tend to have high variance. To counteract this, modern estimators either introduce bias, rely on multiple…

Markov chain Monte Carlo algorithms are used to simulate from complex statistical distributions by way of a local exploration of these distributions. This local feature avoids heavy requests on understanding the nature of the target, but it…

Markov Chain Monte Carlo (MCMC) methods have become a cornerstone of many modern scientific analyses by providing a straightforward approach to numerically estimate uncertainties in the parameters of a model using a sequence of random…

This article reviews the application of advanced Monte Carlo techniques in the context of Multilevel Monte Carlo (MLMC). MLMC is a strategy employed to compute expectations which can be biased in some sense, for instance, by using the…