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Statistical significance testing is used in natural language processing (NLP) to determine whether the results of a study or experiment are likely to be due to chance or if they reflect a genuine relationship. A key step in significance…
P-values are widely used in both the social and natural sciences to quantify the statistical significance of observed results. The recent surge of big data research has made the p-value an even more popular tool to test the significance of…
After rejecting the null hypothesis in the analysis of variance, the next step is to make the pairwise comparisons to find out differences in means. The purpose of this paper is threefold. The foremost aim is to suggest expression for…
Penalized regression models such as the Lasso have proved useful for variable selection in many fields - especially for situations with high-dimensional data where the numbers of predictors far exceeds the number of observations. These…
Computing the exact likelihood of data in large Bayesian networks consisting of thousands of vertices is often a difficult task. When these models contain many deterministic conditional probability tables and when the observed values are…
Particle physics experiments such as those run in the Large Hadron Collider result in huge quantities of data, which are boiled down to a few numbers from which it is hoped that a signal will be detected. We discuss a simple probability…
Approximate Bayesian inference is NP-hard. Dagum and Luby defined the Local Variance Bound (LVB) to measure the approximation hardness of Bayesian inference on Bayesian networks, assuming the networks model strictly positive joint…
A popular approach to significance testing proposes to decide whether the given hypothesized statistical model is likely to be true (or false). Statistical decision theory provides a basis for this approach by requiring every significance…
Restricted mean survival time (RMST) is gaining attention as a measure to quantify the treatment effect on survival outcomes in randomized clinical trials. Several methods to determine sample size based on the RMST-based tests have been…
Quantifying the usefulness of individual features in random forests learning can greatly enhance its interpretability. Existing studies have shown that some popularly used feature importance measures for random forests suffer from the bias…
Identifying genetic variants that regulate quantitative traits, or QTLs, is the primary focus of the field of statistical genetics. Most current methods are limited to identifying mean effects, or associations between genotype and the mean…
A learned generative model often produces biased statistics relative to the underlying data distribution. A standard technique to correct this bias is importance sampling, where samples from the model are weighted by the likelihood ratio…
Linear models are foundational tools in statistics and ubiquitous across the applied sciences. However, conventional statistical inference -- such as $t$-tests and $F$-tests -- are only valid at fixed sample sizes, making them unsuitable…
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,…
We study linear subset regression in the context of the high-dimensional overall model $y = \vartheta+\theta' z + \epsilon$ with univariate response $y$ and a $d$-vector of random regressors $z$, independent of $\epsilon$. Here,…
Fault detection is crucial for ensuring the safety and reliability of modern industrial systems. However, a significant scientific challenge is the lack of rigorous risk control and reliable uncertainty quantification in existing diagnostic…
Nested error regression models are useful tools for analysis of grouped data, especially in the case of small area estimation. This paper suggests a nested error regression model using uncertain random effects in which the random effect in…
While Null Hypothesis Significance Testing (NHST) remains a widely used statistical tool, it suffers from several shortcomings in its common usage, such as conflating statistical and practical significance, the formulation of inappropriate…
The difference in restricted mean survival time (RMST) is a clinically meaningful measure to quantify treatment effect in randomized controlled trials, especially when the proportional hazards assumption does not hold. Several frequentist…
Statistical inference has undergone a profound transformation over the past decade, evolving from a significance-testing paradigm toward a comprehensive, transparency-driven framework embedded within the broader open science ecosystem.…