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Protein mean and variance levels in a simple stochastic gene expression circuit are controlled using proportional integral feedback. It is shown that the protein mean level can be globally and robustly tracked to any desired value using a…

Scientific and business practices are increasingly resulting in large collections of randomized experiments. Analyzed together, these collections can tell us things that individual experiments in the collection cannot. We study how to learn…

This paper investigates estimating the variance of a temporal-difference learning agent's update target. Most reinforcement learning methods use an estimate of the value function, which captures how good it is for the agent to be in a…

We consider estimation and inference for a regression coefficient in panels with interactive fixed effects (i.e., with a factor structure). We demonstrate that existing estimators and confidence intervals (CIs) can be heavily biased and…

Mendelian randomization (MR) is widely used to uncover causal relationships in the presence of unmeasured confounders. However, most existing MR methods presuppose linear causality, risking bias when the true relationships are nonlinear,…

For many complex simulation tasks spanning areas such as healthcare, engineering, and finance, Monte Carlo (MC) methods are invaluable due to their unbiased estimates and precise error quantification. Nevertheless, Monte Carlo simulations…

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…

Given an undirected graph G, the effective resistance r(s,t) measures the dissimilarity of node pair s,t in G, which finds numerous applications in real-world problems, such as recommender systems, combinatorial optimization, molecular…

Monte Carlo estimation in plays a crucial role in stochastic reaction networks. However, reducing the statistical uncertainty of the corresponding estimators requires sampling a large number of trajectories. We propose control variates…

Control variates are variance reduction techniques for Monte Carlo estimators. They play a critical role in improving Monte Carlo estimators in scientific and machine learning applications that involve computationally expensive integrals.…

We use the technique of information relaxation to develop a duality-driven iterative approach to obtaining and improving confidence interval estimates for the true value of finite-horizon stochastic dynamic programming problems. We show…

In large scale multiple testing problems, a two-class empirical Bayes approach can be used to control the false discovery rate (Fdr) for the entire array of hypotheses under study. A sample splitting step is incorporated to modify that…

The Multilevel Monte Carlo method is an efficient variance reduction technique. It uses a sequence of coarse approximations to reduce the computational cost in uncertainty quantification applications. The method is nowadays often considered…

Multi-level normal hierarchical models, also interpreted as mixed effects models, play an important role in developing statistical theory in multi-parameter estimation for a wide range of applications. In this article, we propose a novel…

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…

Monte Carlo tests are widely used for computing valid p-values without requiring known distributions of test statistics. When performing multiple Monte Carlo tests, it is essential to maintain control of the type I error. Some techniques…

We develop new methods to integrate experimental and observational data in causal inference. While randomized controlled trials offer strong internal validity, they are often costly and therefore limited in sample size. Observational data,…

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…

In applications of linear mixed-effects models, experimenters often desire uncertainty quantification for random quantities, like predicted treatment effects for unobserved individuals or groups. For example, consider an agricultural…

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…