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We first review existing sequential methods for estimating a binomial proportion. Afterward, we propose a new family of group sequential sampling schemes for estimating a binomial proportion with prescribed margin of error and confidence…
We present a novel and easy-to-use method for calibrating error-rate based confidence intervals to evidence-based support intervals. Support intervals are obtained from inverting Bayes factors based on a parameter estimate and its standard…
Algorithmic stability is a central concept in statistics and learning theory that measures how sensitive an algorithm's output is to small changes in the training data. Stability plays a crucial role in understanding generalization,…
As neural networks become more popular, the need for accompanying uncertainty estimates increases. There are currently two main approaches to test the quality of these estimates. Most methods output a density. They can be compared by…
Robust estimation is much more challenging in high dimensions than it is in one dimension: Most techniques either lead to intractable optimization problems or estimators that can tolerate only a tiny fraction of errors. Recent work in…
Machine learning algorithms have grown in sophistication over the years and are increasingly deployed for real-life applications. However, when using machine learning techniques in practical settings, particularly in high-risk applications…
Engineering risk is concerned with the likelihood of failure and the scenarios when it occurs. The sensitivity of failure probability to change in system parameters is relevant to risk-informed decision making. Computing sensitivity is at…
Interpretability is becoming increasingly important for predictive model analysis. Unfortunately, as remarked by many authors, there is still no consensus regarding this notion. The goal of this paper is to propose the definition of a score…
Prediction of future observations is an important and challenging problem. The two mainstream approaches for quantifying prediction uncertainty use prediction regions and predictive distributions, respectively, with the latter believed to…
We shall show in this paper that there are experiments which are Bernoulli trials with success probability p > 0.5, and which have the curious feature that it is possible to correctly predict the outcome with probability > p.
The flexibility and wide applicability of the Fisher randomization test (FRT) makes it an attractive tool for assessment of causal effects of interventions from modern-day randomized experiments that are increasing in size and complexity.…
In this paper, we develop invariance-based procedures for testing and inference in high-dimensional regression models. These procedures, also known as randomization tests, provide several important advantages. First, for the global null…
This paper introduces to readers the new concept and methodology of confidence distribution and the modern-day distributional inference in statistics. This discussion should be of interest to people who would like to go into the depth of…
We consider the problem of constructing confidence intervals for nonparametric functional data analysis using empirical likelihood. In this doubly infinite-dimensional context, we demonstrate the Wilks's phenomenon and propose a…
In scientific inference problems, the underlying statistical modeling assumptions have a crucial impact on the end results. There exist, however, only a few automatic means for validating these fundamental modelling assumptions. The…
This paper investigates the conceptual relationship between openness and reproducibility using a model-centric approach, heavily informed by probability theory and statistics. We first clarify the concepts of reliability, auditability,…
Throughout the last decade, random forests have established themselves as among the most accurate and popular supervised learning methods. While their black-box nature has made their mathematical analysis difficult, recent work has…
In this paper, we study the classical problem of estimating the proportion of a finite population. First, we consider a fixed sample size method and derive an explicit sample size formula which ensures a mixed criterion of absolute and…
Bayesian analysis plays a crucial role in estimating distribution of unknown parameters for given data and model. Due to the curse of dimensionality, it becomes difficult for high-dimensional problems, especially when multiple modes exist.…
Performance prediction, the task of estimating a system's performance without performing experiments, allows us to reduce the experimental burden caused by the combinatorial explosion of different datasets, languages, tasks, and models. In…