Related papers: Quantile Importance Sampling
Importance sampling is a well developed method in statistics. Given a random variable $X$, the problem of estimating its expected value $\mu$ is addressed. The standard approach is to use the sample mean as an estimator $\bar x$. In…
In Bayesian optimization, accounting for the importance of the output relative to the input is a crucial yet challenging exercise, as it can considerably improve the final result but often involves inaccurate and cumbersome entropy…
Improving efficiency of importance sampler is at the center of research in Monte Carlo methods. While adaptive approach is usually difficult within the Markov Chain Monte Carlo framework, the counterpart in importance sampling can be…
Importance Sampling (IS), an effective variance reduction strategy in Monte Carlo (MC) simulation, is frequently utilized for Bayesian inference and other statistical challenges. Quasi-Monte Carlo (QMC) replaces the random samples in MC…
In the paper, we develop an ensemble-based implicit sampling method for Bayesian inverse problems. For Bayesian inference, the iterative ensemble smoother (IES) and implicit sampling are integrated to obtain importance ensemble samples,…
Approximating integrals is a fundamental task in probability theory and statistical inference, and their applied fields of signal processing, and Bayesian learning, as soon as expectations over probability distributions must be computed…
Conventional approximations to Bayesian inference rely on either approximations by statistics such as mean and covariance or by point particles. Recent advances such as the ensemble Gaussian mixture filter have generalized these notions to…
In the context of a species sampling problem we discuss a non-parametric maximum likelihood estimator for the underlying probability mass function. The estimator is known in the computer science literature as the high profile estimator. We…
We review the field of data assimilation (DA) from a Bayesian perspective and show that, in addition to its by now common application to state estimation, DA may be used for model selection. An important special case of the latter is the…
An important family of stochastic processes arising in many areas of applied probability is the class of L\'evy processes. Generally, such processes are not simulatable especially for those with infinite activity. In practice, it is common…
Nested sampling is a simulation method for approximating marginal likelihoods proposed by Skilling (2006). We establish that nested sampling has an approximation error that vanishes at the standard Monte Carlo rate and that this error is…
We propose a Monte Carlo algorithm to sample from high dimensional probability distributions that combines Markov chain Monte Carlo and importance sampling. We provide a careful theoretical analysis, including guarantees on robustness to…
The Expectation Maximisation (EM) algorithm is widely used to optimise non-convex likelihood functions with latent variables. Many authors modified its simple design to fit more specific situations. For instance, the Expectation (E) step…
In this paper, we propose an efficient importance sampling algorithm for rare event simulation under copula models. In the algorithm, the derived optimal probability measure is based on the criterion of minimizing the variance of the…
Models for which the likelihood function can be evaluated only up to a parameter-dependent unknown normalising constant, such as Markov random field models, are used widely in computer science, statistical physics, spatial statistics, and…
The basic idea of importance sampling is to use independent samples from a proposal measure in order to approximate expectations with respect to a target measure. It is key to understand how many samples are required in order to guarantee…
Monte Carlo methods represent the "de facto" standard for approximating complicated integrals involving multidimensional target distributions. In order to generate random realizations from the target distribution, Monte Carlo techniques use…
Estimation of covariance matrices or their inverses plays a central role in many statistical methods. For these methods to work reliably, estimated matrices must not only be invertible but also well-conditioned. In this paper we present an…
Given a sequence of observations from a discrete-time, finite-state hidden Markov model, we would like to estimate the sampling distribution of a statistic. The bootstrap method is employed to approximate the confidence regions of a…
The aim of this paper is to introduce a new Monte Carlo method based on importance sampling techniques for the simulation of stochastic differential equations. The main idea is to combine random walk on squares or rectangles methods with…