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We study sequential prediction of real-valued, arbitrary and unknown sequences under the squared error loss as well as the best parametric predictor out of a large, continuous class of predictors. Inspired by recent results from…

Risk Assessment Instruments (RAIs) are widely used to forecast adverse outcomes in domains such as healthcare and criminal justice. RAIs are commonly trained on observational data and are optimized to predict observable outcomes rather than…

The bias of the sample means of the arms in multi-armed bandits is an important issue in adaptive data analysis that has recently received considerable attention in the literature. Existing results relate in precise ways the sign and…

Most of the stochastic orders for comparing random variables, considered in the literature, are afflicted with two main drawbacks: (i) lack of connex property and (ii) lack of consideration of any dependence structure between the random…

The recent success of machine learning models, especially large-scale classifiers and language models, relies heavily on training with massive data. These data are often collected from online sources. This raises serious concerns about the…

A popular setting in medical statistics is a group sequential trial with independent and identically distributed normal outcomes, in which interim analyses of the sum of the outcomes are performed. Based on a prescribed stopping rule, one…

We study the adversarial binary hypothesis testing problem in the sequential setting. Associated with each hypothesis is a closed, convex set of distributions. Given the hypothesis, each observation is generated according to a distribution…

Models for extreme values are generally derived from limit results, which are meant to be good enough approximations when applied to finite samples. Depending on the speed of convergence of the process underlying the data, these…

The purpose of this paper is to present a mathematical theory that can be used as a foundation for statistics that include improper priors. This theory includes improper laws in the initial axioms and has in particular Bayes theorem as a…

Many measurements at collider experiments study physics candidates that are a subset of a collision event. The presence of multiple such candidates in a given event can cause raw biases which are large compared to typical statistical…

In this short paper, we study the simulation of a large system of stochastic processes subject to a common driving noise and fast mean-reverting stochastic volatilities. This model may be used to describe the firm values of a large pool of…

Independence screening is a powerful method for variable selection for `Big Data' when the number of variables is massive. Commonly used independence screening methods are based on marginal correlations or variations of it. In many…

Theoretical developments in sequential Bayesian analysis of multivariate dynamic models underlie new methodology for causal prediction. This extends the utility of existing models with computationally efficient methodology, enabling routine…

We address the problem of integrating data from multiple, possibly biased, observational and interventional studies, to eventually compute counterfactuals in structural causal models. We start from the case of a single observational dataset…

Conditioning on some set of confounders that causally affect both treatment and outcome variables can be sufficient for eliminating bias introduced by all such confounders when estimating causal effect of the treatment on the outcome from…

Machine learning can impact people with legal or ethical consequences when it is used to automate decisions in areas such as insurance, lending, hiring, and predictive policing. In many of these scenarios, previous decisions have been made…

We consider the problem of learning the causal MAG of a system from observational data in the presence of latent variables and selection bias. Constraint-based methods are one of the main approaches for solving this problem, but the…

In this article, we review selective inference, a set of techniques for inference when the statistical question asked is a function of the data. This setting often arises in contemporary scientific workflows, where hypotheses and parameters…

Shapley values, a game theoretic concept, has been one of the most popular tools for explaining Machine Learning (ML) models in recent years. Unfortunately, the two most common approaches, conditional and marginal, to calculating Shapley…

Causal interventions in language model representations have largely targeted discrete features, like grammatical number. However, language models must also make use of features that are graded. We introduce a method for causal intervention…