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The features of a logically sound approach to a theory of statistical reasoning are discussed. A particular approach that satisfies these criteria is reviewed. This is seen to involve selection of a model, model checking, elicitation of a…

It is common to conduct causal inference in matched observational studies by proceeding as though treatment assignments within matched sets are assigned uniformly at random and using this distribution as the basis for inference. This…

We propose a test of the conditional independence of random variables $X$ and~$Y$ given~$Z$ under the additional assumption that $X$ is stochastically nondecreasing in~$Z$. The well-documented hardness of testing conditional independence…

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,…

There has been a split in the statistics community about the need for taking covariates into account in the design phase of a clinical trial. There are many advocates of using stratification and covariate-adaptive randomization to promote…

This paper examines the foundational concept of random variables in probability theory and statistical inference, demonstrating that their mathematical definition requires no reference to randomization or hypothetical repeated sampling. We…

We consider the design of experiments to evaluate treatments that are administered by self-interested agents, each seeking to achieve the highest evaluation and win the experiment. For example, in an advertising experiment, a company wishes…

Randomized experiments are the "gold standard" for estimating causal effects, yet often in practice, chance imbalances exist in covariate distributions between treatment groups. If covariate data are available before units are exposed to…

We consider testing whether a set of Gaussian variables, selected from the data, is independent of the remaining variables. We assume that this set is selected via a very simple approach that is commonly used across scientific disciplines:…

In this paper, we revisit the notion of partial copula, originally introduced to test conditional independence, highlighting its capability to represent the dependence between two random variables after removing their dependence with a…

Standard statistical theory has arguably proved to be unsuitable as a basis for constructing a satisfactory completely general framework for performing statistical inference. For example, frequentist theory has never come close to providing…

We propose analyzing conditional reasoning by appeal to a notion of intervention on a simulation program, formalizing and subsuming a number of approaches to conditional thinking in the recent AI literature. Our main results include a…

Background: Adaptive interventions provide a guide for using ongoing information about individuals to decide whether and how to modify the type, amount, delivery modality, or timing of treatment, to improve intervention effectiveness while…

I study the minimax-optimal design for a two-arm controlled experiment where conditional mean outcomes may vary in a given set. When this set is permutation symmetric, the optimal design is complete randomization, and using a single…

In recent years a popular nonparametric model for coarsened data is an assumption on the coarsening mechanism called coarsening at random (CAR). It has been conjectured in several papers that this assumption cannot be tested by the data,…

Instrumental variable (IV) analyses are becoming common in health services research and epidemiology. Most IV analyses use naturally occurring instruments, such as distance to a hospital. In these analyses, investigators must assume the…

In this work, Bernoulli's Law of Large Numbers, also known as the Golden theorem, has been extended to study the relations between empirical probability and empirical randomness of an otherwise random experiment. Using the example of a coin…

This paper studies how insurers can chose which claims to investigate for fraud. Given a prediction model, typically only claims with the highest predicted propability of being fraudulent are investigated. We argue that this can lead to…

Contextuality is usually defined as absence of a joint distribution for a set of measurements (random variables) with known joint distributions of some of its subsets. However, if these subsets of measurements are not disjoint,…

It is widely believed that theory is useful in physics because it describes simple systems and that strictly empirical phenomenological approaches are necessary for complex biological and social systems. Here we prove based upon an analysis…