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There is a long-standing debate in the statistical, epidemiological and econometric fields as to whether nonparametric estimation that uses data-adaptive methods, like machine learning algorithms in model fitting, confer any meaningful…
We present general principles for the design and analysis of unbiased Monte Carlo estimators in a wide range of settings. Our estimators posses finite work-normalized variance under mild regularity conditions. We apply our estimators to…
Simulation studies are used to evaluate and compare the properties of statistical methods in controlled experimental settings. In most cases, performing a simulation study requires knowledge of the true value of the parameter, or estimand,…
This paper examines the use of Monte Carlo simulations to understand statistical concepts in A/B testing and Randomized Controlled Trials (RCTs). We discuss the applicability of simulations in understanding false positive rates and estimate…
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…
The paper presents an investigation of estimating treatment effect using different matching methods. The study proposed a new method which is computationally efficient and convenient in implication-'largest caliper matching' and compared…
Contemporary scientific studies often rely on the understanding of complex quantum systems via computer simulation. This paper initiates the statistical study of quantum simulation and proposes a Monte Carlo method for estimating…
Eliciting relevance judgments for ranking evaluation is labor-intensive and costly, motivating careful selection of which documents to judge. Unlike traditional approaches that make this selection deterministically, probabilistic sampling…
In the field of structural reliability, the Monte-Carlo estimator is considered as the reference probability estimator. However, it is still untractable for real engineering cases since it requires a high number of runs of the model. In…
We describe an embarrassingly parallel, anytime Monte Carlo method for likelihood-free models. The algorithm starts with the view that the stochasticity of the pseudo-samples generated by the simulator can be controlled externally by a…
Complex scientific models where the likelihood cannot be evaluated present a challenge for statistical inference. Over the past two decades, a wide range of algorithms have been proposed for learning parameters in computationally feasible…
We discuss techniques of estimation and inference for nonstationary nonlinear cohort panels with learning from experience, showing, inter alia, the consistency and asymptotic normality of the nonlinear least squares estimator used in…
We introduce a class of Monte Carlo estimators that aim to overcome the rapid growth of variance with dimension often observed for standard estimators by exploiting the target's independence structure. We identify the most basic…
Random sampling is an essential tool in the processing and transmission of data. It is used to summarize data too large to store or manipulate and meet resource constraints on bandwidth or battery power. Estimators that are applied to the…
Due to the potential benefits of parallelization, designing unbiased Monte Carlo estimators, primarily in the setting of randomized multilevel Monte Carlo, has recently become very popular in operations research and computational…
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…
Most reinforcement learning practitioners evaluate their policies with online Monte Carlo estimators for either hyperparameter tuning or testing different algorithmic design choices, where the policy is repeatedly executed in the…
Prior works have shown that in-context learning is brittle to presentation factors such as the order, number, and choice of selected examples. However, ablation-based guidance on selecting the number of examples may ignore the interplay…
We describe Monte Carlo methods for estimating lower envelopes of expectations of real random variables. We prove that the estimation bias is negative and that its absolute value shrinks with increasing sample size. We discuss fairly…
Consider a problem of predicting a response variable using a set of covariates in a linear regression model. If it is \emph{a priori} known or suspected that a subset of the covariates do not significantly contribute to the overall fit of…