Related papers: Computing p-values of LiNGAM outputs via Multiscal…

Software packages usually report the results of statistical tests using p-values. Users often interpret these by comparing them to standard thresholds, e.g. 0.1%, 1% and 5%, which is sometimes reinforced by a star rating (***, **, *). We…

This paper introduces a local optimization-based approach to test statistical hypotheses and to construct confidence intervals. This approach can be viewed as an extension of bootstrap, and yields asymptotically valid tests and confidence…

Accurate uncertainty estimates can significantly improve the performance of iterative design of experiments, as in Sequential and Reinforcement learning. For many such problems in engineering and the physical sciences, the design task…

The role played by the composite analogue of the log likelihood ratio in hypothesis testing and in setting confidence regions is not as prominent as it is in the canonical likelihood setting, since its asymptotic distribution depends on the…

Large Language Models (LLMs) are increasingly deployed in high-stakes contexts where their outputs influence real-world decisions. However, evaluating bias in LLM outputs remains methodologically challenging due to sensitivity to prompt…

We propose a general method to carry out a valid Bayesian analysis of a finite-dimensional `targeted' parameter in the presence of a finite-dimensional nuisance parameter. We apply our methods to causal inference based on estimating…

To draw scientifically meaningful conclusions and build reliable models of quantitative phenomena, cause and effect must be taken into consideration (either implicitly or explicitly). This is particularly challenging when the measurements…

The bootstrap is a popular data-driven method to quantify statistical uncertainty, but for modern high-dimensional problems, it could suffer from huge computational costs due to the need to repeatedly generate resamples and refit models. We…

There is an increasing amount of literature focused on Bayesian computational methods to address problems with intractable likelihood. One approach is a set of algorithms known as Approximate Bayesian Computational (ABC) methods. One of the…

When conducting large scale inference, such as genome-wide association studies or image analysis, nominal $p$-values are often adjusted to improve control over the family-wise error rate (FWER). When the majority of tests are null,…

Modern problems in statistics tend to include estimators of high computational complexity and with complicated distributions. Statistical inference on such estimators usually relies on asymptotic normality assumptions, however, such…

Models of stochastic processes are widely used in almost all fields of science. Theory validation, parameter estimation, and prediction all require model calibration and statistical inference using data. However, data are almost always…

Bootstrap for nonlinear statistics like U-statistics of dependent data has been studied by several authors. This is typically done by producing a bootstrap version of the sample and plugging it into the statistic. We suggest an alternative…

Reliable uncertainty quantification remains a central challenge in predictive modeling. While Bayesian methods are theoretically appealing, their predictive intervals can exhibit poor frequentist calibration, particularly with small sample…

In Change point detection task Likelihood Ratio Test (LRT) is sequentially applied in a sliding window procedure. Its high values indicate changes of parametric distribution in the data sequence. Correspondingly LRT values require…

We propose Bayesian Hierarchical Invariant Prediction (BHIP) reframing Invariant Causal Prediction (ICP) through the lens of Hierarchical Bayes. We leverage the hierarchical structure to explicitly test invariance of causal mechanisms under…

We study an optimization-based approach to construct statistically accurate confidence intervals for simulation performance measures under nonparametric input uncertainty. This approach computes confidence bounds from simulation runs driven…

One of the most commonly used methods for forming confidence intervals for statistical inference is the empirical bootstrap, which is especially expedient when the limiting distribution of the estimator is unknown. However, despite its…

Accurate statistical inference in logistic regression models remains a critical challenge when the ratio between the number of parameters and sample size is not negligible. This is because approximations based on either classical asymptotic…

A reasonable confidence interval should have a confidence coefficient no less than the given nominal level and a small expected length to reliably and accurately estimate the parameter of interest, and the bootstrap interval is considered…