Related papers: Markov Chain Monte Carlo Estimation of Quantiles
This paper examines the precision of estimators of Quantile-Based Risk Measures (Value at Risk, Expected Shortfall, Spectral Risk Measures). It first addresses the question of how to estimate the precision of these estimators, and proposes…
Markov chain Monte Carlo (MCMC) produces a correlated sample for estimating expectations with respect to a target distribution. A fundamental question is when should sampling stop so that we have good estimates of the desired quantities?…
We present bounds for the finite sample error of sequential Monte Carlo samplers on static spaces. Our approach explicitly relates the performance of the algorithm to properties of the chosen sequence of distributions and mixing properties…
Current reporting of results based on Markov chain Monte Carlo computations could be improved. In particular, a measure of the accuracy of the resulting estimates is rarely reported. Thus we have little ability to objectively assess the…
We study the error of reversible Markov chain Monte Carlo methods for approximating the expectation of a function. Explicit error bounds with respect to different norms of the function are proven. By the estimation the well known…
Markov chain Monte Carlo (MCMC) algorithms provide a very general recipe for estimating properties of complicated distributions. While their use has become commonplace and there is a large literature on MCMC theory and practice, MCMC users…
Interest is in evaluating, by Markov chain Monte Carlo (MCMC) simulation, the expected value of a function with respect to a, possibly unnormalized, probability distribution. A general purpose variance reduction technique for the MCMC…
Recent advances in quasi-Monte Carlo integration have shown that for linearly scrambled digital net estimators, the convergence rate can be dramatically improved by taking the median rather than the mean of multiple independent replicates.…
The efficiency of a Markov chain Monte Carlo algorithm might be measured by the cost of generating one independent sample, or equivalently, the total cost divided by the effective sample size, defined in terms of the integrated…
In Monte Carlo calculations of expectation values in lattice quantum field theories, the stochastic variance of the sampling procedure that is used defines the precision of the calculation for a fixed number of samples. If the variance of…
The literature in social network analysis has largely focused on methods and models which require complete network data; however there exist many networks which can only be studied via sampling methods due to the scale or complexity of the…
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…
In this work, we consider the problem of estimating the probability distribution, the quantile or the conditional expectation above the quantile, the so called conditional-value-at-risk, of output quantities of complex random differential…
We introduce and discuss Monte Carlo methods in quantum field theories. Methods of independent Monte Carlo, such as random sampling and importance sampling, and methods of dependent Monte Carlo, such as Metropolis sampling and Hamiltonian…
Monte Carlo simulations are widely used in many areas including particle accelerators. In this lecture, after a short introduction and reviewing of some statistical backgrounds, we will discuss methods such as direct inversion, rejection…
Markov chain Monte Carlo samplers produce dependent streams of variates drawn from the limiting distribution of the Markov chain. With this as motivation, we introduce novel univariate kernel density estimators which are appropriate for the…
Statisticians often use Monte Carlo methods to approximate probability distributions, primarily with Markov chain Monte Carlo and importance sampling. Sequential Monte Carlo samplers are a class of algorithms that combine both techniques to…
Using concentration inequalities, we give non-asymptotic confidence intervals for estimates obtained by Markov chain Monte Carlo (MCMC) simulations, when using the approximation $\mathbb{E}_{\pi} f\approx (1/(N-t_0))\cdot \sum_{i=t_0+1}^N…
We consider the efficient use of an approximation within Markov chain Monte Carlo (MCMC), with subsequent importance sampling (IS) correction of the Markov chain inexact output, leading to asymptotically exact inference. We detail…
MCMC methods are used in Bayesian statistics not only to sample from posterior distributions but also to estimate expectations. Underlying functions are most often defined on a continuous state space and can be unbounded. We consider a…