Related papers: Central limit theorems for multilevel Monte Carlo …
The multivariate central limit theorems (CLT) for the volumes of excursion sets of stationary quasi-associated random fields on $\mathbb{R}^d$ are proved. Special attention is paid to Gaussian and shot noise fields. Formulae for the…
The efficiency of Monte Carlo samplers is dictated not only by energetic effects, such as large barriers, but also by entropic effects that are due to the sheer volume that is sampled. The latter effects appear in the form of an entropic…
Quasi-Monte Carlo sampling can attain far better accuracy than plain Monte Carlo sampling. However, with plain Monte Carlo sampling it is much easier to estimate the attained accuracy. This article describes methods old and new to quantify…
Adaptive Monte Carlo methods are very efficient techniques designed to tune simulation estimators on-line. In this work, we present an alternative to stochastic approximation to tune the optimal change of measure in the context of…
In this paper we study uniform versions of two limit theorems in random left truncation model (RLTM). The law of large numbers (LLN) and the central limit theorem (CLT) have been obtained under the bracketing entropy conditions in this…
We investigate the properties of a sequential Monte Carlo method where the particle weight that appears in the algorithm is estimated by a positive, unbiased estimator. We present broadly-applicable convergence results, including a central…
This paper re-examines the limit theorems of Abadie and Imbens for nearest-neighbor matching estimators of average treatment effects with a fixed number of matches. We establish, for the first time, a non-normalized central limit theorem…
We prove a multivariate central limit theorem for the numbers of critical points above a level with all possible indexes of a non-necessarily isotropic Gaussian random field. In particular, we discuss the non-degeneracy of the limit…
I consider the problem of integrating a function $f$ over the $d$-dimensional unit cube. I describe a multilevel Monte Carlo method that estimates the integral with variance at most $\epsilon^{2}$ in $O(d+\ln(d)d_{t}\epsilon^{-2})$ time,…
Nested integration problems arise in various scientific and engineering applications, including Bayesian experimental design, financial risk assessment, and uncertainty quantification. These nested integrals take the form $\int f\left(\int…
The Multilevel Monte Carlo (MLMC) method has been applied successfully in a wide range of settings since its first introduction by Giles (2008). When using only two levels, the method can be viewed as a kind of control-variate approach to…
Sequential Monte Carlo (SMC) methods, also known as particle filters, constitute a class of algorithms used to approximate expectations with respect to a sequence of probability distributions as well as the normalising constants of those…
This paper investigates the central limit theorem for linear spectral statistics of high dimensional sample covariance matrices of the form $\mathbf{B}_n=n^{-1}\sum_{j=1}^{n}\mathbf{Q}\mathbf{x}_j\mathbf{x}_j^{*}\mathbf{Q}^{*}$ where…
Recent work has proposed the use of a composite hypothesis Hoeffding test for statistical anomaly detection. Setting an appropriate threshold for the test given a desired false alarm probability involves approximating the false alarm…
We propose Subsampling MCMC, a Markov Chain Monte Carlo (MCMC) framework where the likelihood function for $n$ observations is estimated from a random subset of $m$ observations. We introduce a highly efficient unbiased estimator of the…
Consider a central problem in randomized approximation schemes that use a Monte Carlo approach. Given a sequence of independent, identically distributed random variables $X_1,X_2,\ldots$ with mean $\mu$ and standard deviation at most $c…
We prove two theorems related to the Central Limit Theorem (CLT) for Martin-L\"of Random (MLR) sequences. Martin-L\"of randomness attempts to capture what it means for a sequence of bits to be "truly random". By contrast, CLTs do not make…
In this paper, we establish the central limit theorem (CLT) for linear spectral statistics (LSS) of large-dimensional sample covariance matrix when the population covariance matrices are not uniformly bounded, which is a nontrivial…
In this paper, we propose a new stochastic optimization algorithm for Bayesian inference based on multilevel Monte Carlo (MLMC) methods. In Bayesian statistics, biased estimators of the model evidence have been often used as stochastic…
We estimate linear functionals in the classical deconvolution problem by kernel estimators. We obtain a uniform central limit theorem with $\sqrt{n}$-rate on the assumption that the smoothness of the functionals is larger than the…