Related papers: On Nesting Monte Carlo Estimators

We consider the problem of estimating expectations with respect to a target distribution with an unknown normalizing constant, and where even the unnormalized target needs to be approximated at finite resolution. This setting is ubiquitous…

In performing a Bayesian analysis, two difficult problems often emerge. First, in estimating the parameters of some model for the data, the resulting posterior distribution may be multi-modal or exhibit pronounced (curving) degeneracies.…

Nested Monte Carlo is widely used for risk estimation, but its efficiency is limited by the discontinuity of the indicator function and high computational cost. This paper proposes a nested Multilevel Monte Carlo (MLMC) method combined with…

We propose nested sequential Monte Carlo (NSMC), a methodology to sample from sequences of probability distributions, even where the random variables are high-dimensional. NSMC generalises the SMC framework by requiring only approximate,…

We investigate the problem of computing a nested expectation of the form $\mathbb{P}[\mathbb{E}[X|Y] \!\geq\!0]\!=\!\mathbb{E}[\textrm{H}(\mathbb{E}[X|Y])]$ where $\textrm{H}$ is the Heaviside function. This nested expectation appears, for…

Nested sampling is a promising tool for Bayesian statistical analysis because it simultaneously performs parameter estimation and facilitates model comparison. MultiNest is one of the most popular nested sampling implementations, and has…

This article discusses MLMC estimators with and without weights, applied to nested expectations of the form E [f (E [F (Y, Z)|Y ])]. More precisely, we are interested on the assumptions needed to comply with the MLMC framework, depending on…

For real symmetric matrices that are accessible only through matrix vector products, we present Monte Carlo estimators for computing the diagonal elements. Our probabilistic bounds for normwise absolute and relative errors apply to Monte…

This work introduces meta estimators that combine multiple multifidelity techniques based on control variates, importance sampling, and information reuse to yield a quasi-multiplicative amount of variance reduction. The proposed meta…

Multifidelity Monte Carlo methods rely on a hierarchy of possibly less accurate but statistically correlated simplified or reduced models, in order to accelerate the estimation of statistics of high-fidelity models without compromising the…

This article considers the sequential Monte Carlo (SMC) approximation of ratios of normalizing constants associated to posterior distributions which in principle rely on continuum models. Therefore, the Monte Carlo estimation error and the…

Uncertainty estimation in deep models is essential in many real-world applications and has benefited from developments over the last several years. Recent evidence suggests that existing solutions dependent on simple Gaussian formulations…

Nested sampling is a powerful approach to Bayesian inference ultimately limited by the computationally demanding task of sampling from a heavily constrained probability distribution. An effective algorithm in its own right, Hamiltonian…

Estimating the unknown density from which a given independent sample originates is more difficult than estimating the mean, in the sense that for the best popular non-parametric density estimators, the mean integrated square error converges…

This paper proposes a family of weighted batch means variance estimators, which are computationally efficient and can be conveniently applied in practice. The focus is on Markov chain Monte Carlo simulations and estimation of the asymptotic…

We study Monte Carlo estimation of the expected value of sample information (EVSI) which measures the expected benefit of gaining additional information for decision making under uncertainty. EVSI is defined as a nested expectation in which…

We introduce a new class of sequential Monte Carlo methods which reformulates the essence of the nested sampling method of Skilling (2006) in terms of sequential Monte Carlo techniques. Two new algorithms are proposed, nested sampling via…

We consider the problem of estimating a nested structure of two expectations taking the form $U_0 = E[\max\{U_1(Y), \pi(Y)\}]$, where $U_1(Y) = E[X\ |\ Y]$. Terms of this form arise in financial risk estimation and option pricing. When…

A statistical learning approach for parametric PDEs related to Uncertainty Quantification is derived. The method is based on the minimization of an empirical risk on a selected model class and it is shown to be applicable to a broad range…

Nested simulation is a natural approach to tackle nested estimation problems in operations research and financial engineering. The outer-level simulation generates outer scenarios and the inner-level simulations are run in each outer…