Related papers: Constrained-Realization Monte-Carlo Method for Hyp…

Two-sample testing is a fundamental problem in statistics. Despite its long history, there has been renewed interest in this problem with the advent of high-dimensional and complex data. Specifically, in the machine learning literature,…

Random-effects meta-analyses have been widely applied in evidence synthesis for various types of medical studies. However, standard inference methods (e.g. restricted maximum likelihood estimation) usually underestimate statistical errors…

Statistical analysis is an important tool to distinguish systematic from chance findings. Current statistical analyses rely on distributional assumptions reflecting the structure of some underlying model, which if not met lead to problems…

The steadily increasing size of scientific Monte Carlo simulations and the desire for robust, correct, and reproducible results necessitates rigorous testing procedures for scientific simulations in order to detect numerical problems and…

A common approach to synthetic data is to sample from a fitted model. We show that under general assumptions, this approach results in a sample with inefficient estimators and whose joint distribution is inconsistent with the true…

Temporal dependence and the resulting autocovariances in time series data can introduce bias into ANOVA test statistics, thereby affecting their size and power. This manuscript accounts for temporal dependence in ANOVA and develops a test…

Few-shot image classification remains challenging due to the scarcity of labeled training examples. Augmenting them with synthetic data has emerged as a promising way to alleviate this issue, but models trained on synthetic samples often…

We present two data-driven methods for estimating reachable sets with probabilistic guarantees. Both methods make use of a probabilistic formulation allowing for a formal definition of a data-driven reachable set approximation that is…

Extant "fast" algorithms for Monte Carlo confidence sets are limited to univariate shift parameters for the one-sample and two-sample problems using the sample mean as the test statistic; moreover, some do not converge reliably and most do…

Self-normalized processes are basic to many probabilistic and statistical studies. They arise naturally in the the study of stochastic integrals, martingale inequalities and limit theorems, likelihood-based methods in hypothesis testing and…

In the Monte Carlo (MC) method statistical noise is usually present. Statistical noise may become dominant in the calculation of a distribution, usually by iteration, but is less Important in calculating integrals. The subject of the…

Causal discovery is to learn cause-effect relationships among variables given observational data and is important for many applications. Existing causal discovery methods assume data sufficiency, which may not be the case in many real world…

Multiple hypothesis tests are often carried out in practice using p-value estimates obtained with bootstrap or permutation tests since the analytical p-values underlying all hypotheses are usually unknown. This article considers the…

We present a hybrid sampling-surrogate approach for reducing the computational expense of uncertainty quantification in nonlinear dynamical systems. Our motivation is to enable rapid uncertainty quantification in complex mechanical systems…

This paper clarifies a fundamental difference between causal inference and traditional statistical inference by formalizing a mathematical distinction between their respective parameters. We connect two major approaches to causal inference,…

Comparisons of different treatments or production processes are the goals of a significant fraction of applied research. Unsurprisingly, two-sample problems play a main role in Statistics through natural questions such as `Is the the new…

As increasingly complex hypothesis-testing scenarios are considered in many scientific fields, analytic derivation of null distributions is often out of reach. To the rescue comes Monte Carlo testing, which may appear deceptively simple: as…

Inference on unknown quantities in dynamical systems via observational data is essential for providing meaningful insight, furnishing accurate predictions, enabling robust control, and establishing appropriate designs for future…

Hypothesis tests calibrated by (re)sampling methods (such as permutation, rank and bootstrap tests) are useful tools for statistical analysis, at the computational cost of requiring Monte-Carlo sampling for calibration. It is common and…

Statistical model checking delivers quantitative verification results with statistical guarantees by applying Monte Carlo simulation to formal models. It scales to model sizes and model types that are out of reach for exhaustive, analytical…