English
Related papers

Related papers: Vertical-likelihood Monte Carlo

200 papers

Monte Carlo method is a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. They are often used in physical and mathematical problems and are most useful when it is difficult or…

Computation · Statistics 2018-09-28 Bochao Jia

Importance sampling has been known as a powerful tool to reduce the variance of Monte Carlo estimator for rare event simulation. Based on the criterion of minimizing the variance of Monte Carlo estimator within a parametric family, we…

Methodology · Statistics 2013-02-11 Cheng-Der Fuh , Huei-Wen Teng , Ren-Her Wang

In this paper, we aim to compute numerical approximation integral by using an adaptive Monte Carlo algorithm. We propose a stratified sampling algorithm based on an iterative method which splits the strata following some quantities called…

Numerical Analysis · Mathematics 2015-07-22 Toni Sayah

The multilevel Monte Carlo (MLMC) method has been used for a wide variety of stochastic applications. In this paper we consider its use in situations in which input random variables can be replaced by similar approximate random variables…

Numerical Analysis · Mathematics 2022-04-08 Mike Giles , Oliver Sheridan-Methven

Importance sampling is a Monte Carlo technique for efficiently estimating the likelihood of rare events by biasing the sampling distribution towards the rare event of interest. By drawing weighted samples from a learned proposal…

Machine Learning · Statistics 2025-05-20 Liam A. Kruse , Marc R. Schlichting , Mykel J. Kochenderfer

We construct Monte Carlo methods for the $L^2$-approximation in Hilbert spaces of multivariate functions sampling no more than $n$ function values of the target function. Their errors catch up with the rate of convergence and the…

Numerical Analysis · Mathematics 2018-03-16 David Krieg

The performance of the Monte Carlo sampling methods relies on the crucial choice of a proposal density. The notion of optimality is fundamental to design suitable adaptive procedures of the proposal density within Monte Carlo schemes. This…

Computation · Statistics 2026-02-24 Fernando Llorente , Luca Martino

In this paper we will give a Monte Carlo algorithm by which the moments of a functions of Dirichlet probability distributions can be estimated. This algorithm is called Inner Nested Sampling and is an implementation of Skilling's general…

Methodology · Statistics 2017-04-10 H. R. N. van Erp , R. O. Linger , P. H. A. J. M. van Gelder

An importance sampling approach for sampling copula models is introduced. We propose two algorithms that improve Monte Carlo estimators when the functional of interest depends mainly on the behaviour of the underlying random vector when at…

Computation · Statistics 2015-04-08 Philipp Arbenz , Mathieu Cambou , Marius Hofert

The EM algorithm is a powerful tool for maximum likelihood estimation with missing data. In practice, the calculations required for the EM algorithm are often intractable. We review numerous methods to circumvent this intractability, all of…

Computation · Statistics 2024-01-03 William Ruth

We present two Monte Carlo sampling algorithms for probabilistic inference that guarantee polynomial-time convergence for a larger class of network than current sampling algorithms provide. These new methods are variants of the known…

Artificial Intelligence · Computer Science 2013-02-18 Malcolm Pradhan , Paul Dagum

Importance weighting is a general way to adjust Monte Carlo integration to account for draws from the wrong distribution, but the resulting estimate can be highly variable when the importance ratios have a heavy right tail. This routinely…

Computation · Statistics 2024-04-12 Aki Vehtari , Daniel Simpson , Andrew Gelman , Yuling Yao , Jonah Gabry

Sequential Monte Carlo methods, also known as particle methods, are a popular set of techniques for approximating high-dimensional probability distributions and their normalizing constants. These methods have found numerous applications in…

Computation · Statistics 2021-06-23 Jeremy Heng , Adrian N. Bishop , George Deligiannidis , Arnaud Doucet

Monte Carlo methods are used to approximate the means, $\mu$, of random variables $Y$, whose distributions are not known explicitly. The key idea is that the average of a random sample, $Y_1, ..., Y_n$, tends to $\mu$ as $n$ tends to…

Statistics Theory · Mathematics 2015-01-16 Fred J. Hickernell , Lan Jiang , Yuewei Liu , Art Owen

We introduce an efficient numerical implementation of a Markov Chain Monte Carlo method to sample a probability distribution on a manifold (introduced theoretically in Zappa, Holmes-Cerfon, Goodman (2018)), where the manifold is defined by…

Computation · Statistics 2023-08-22 Kerun Xu , Miranda Holmes-Cerfon

Computation of extreme quantiles and tail-based risk measures using standard Monte Carlo simulation can be inefficient. A method to speed up computations is provided by importance sampling. We show that importance sampling algorithms,…

Probability · Mathematics 2009-09-21 Henrik Hult , Jens Svensson

For complex latent variable models, the likelihood function is not available in closed form. In this context, a popular method to perform parameter estimation is Importance Weighted Variational Inference. It essentially maximizes the…

Statistics Theory · Mathematics 2025-01-16 Badr-Eddine Cherief-Abdellatif , Randal Douc , Arnaud Doucet , Hugo Marival

Adaptive importance sampling is a class of techniques for finding good proposal distributions for importance sampling. Often the proposal distributions are standard probability distributions whose parameters are adapted based on the…

Computation · Statistics 2021-03-10 Topi Paananen , Juho Piironen , Paul-Christian Bürkner , Aki Vehtari

In many real-world engineering systems, the performance or reliability of the system is characterised by a scalar parameter. The distribution of this performance parameter is important in many uncertainty quantification problems, ranging…

Methodology · Statistics 2022-10-03 Robert Millar , Jinglai Li , Hui Li

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…

Computation · Statistics 2019-09-18 Giacomo Zanella , Gareth Roberts