Related papers: On the Power of Conditional Samples in Distributio…
We consider the problem of testing whether pairs of univariate random variables are associated. Few tests of independence exist that are consistent against all dependent alternatives and are distribution free. We propose novel tests that…
In quantum physics there are well-known situations when measurements of the same property in different contexts (under different conditions) have the same probability distribution, but cannot be represented by one and the same random…
The conditionality principle $C$ plays a key role in attempts to characterize the concept of statistical evidence. The standard version of $C$ considers a model and a derived conditional model, formed by conditioning on an ancillary…
We propose a two-sample test for high-dimensional means that requires neither distributional nor correlational assumptions, besides some weak conditions on the moments and tail properties of the elements in the random vectors. This…
We propose a method for deterministic sampling of arbitrary continuous angular density functions. With deterministic sampling, good estimation results can typically be achieved with much smaller numbers of samples compared to the commonly…
We introduce a general framework for testing temporal symmetries in time series based on the distribution of ordinal patterns. While previous approaches have focused on specific forms of asymmetry, such as time reversal, our method provides…
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…
Consistent sampling is a technique for specifying, in small space, a subset $S$ of a potentially large universe $U$ such that the elements in $S$ satisfy a suitably chosen sampling condition. Given a subset $\mathcal{I}\subseteq U$ it…
We characterize the fundamental limits of high-dimensional mean testing under arbitrary truncation, where samples are drawn from the conditional distribution $P(\cdot \mid S)$ for an unknown truncation set $S$ that may hide up to an…
Formalisms for specifying statistical models, such as probabilistic-programming languages, typically consist of two components: a specification of a stochastic process (the prior), and a specification of observations that restrict the…
Out-of-distribution (OOD) generalization remains a fundamental challenge in real-world classification, where test distributions often differ substantially from training data. Most existing approaches pursue domain-invariant representations,…
We prove a new hypothesis on the conditional distribution of the sample mean of the fluctuations of an i.i.d. random potential in the Anderson model. The paper extends to uniform probability distribution some earlier work with Gaussian…
The data of a physical experiment can be represented as a presheaf of probability distributions. A striking feature of quantum theory is that those probability distributions obtained in quantum mechanical experiments do not always admit a…
We propose a sequential, anytime-valid method to test the conditional independence of a response $Y$ and a predictor $X$ given a random vector $Z$. The proposed test is based on e-statistics and test martingales, which generalize likelihood…
In combinatorics, the probabilistic method is a very powerful tool to prove the existence of combinatorial objects with interesting and useful properties. Explicit constructions of objects with such properties are often very difficult, or…
Outlier hypothesis testing is studied in a universal setting. Multiple sequences of observations are collected, a small subset of which are outliers. A sequence is considered an outlier if the observations in that sequence are distributed…
Metamorphic testing (MT) alleviates the oracle problem by checking metamorphic relations (MRs) across multiple test executions. The fault detection effectiveness of MT is influenced not only by the choice and quality of MRs, but also by how…
We prove large and moderate deviation principles for the distribution of an empirical mean conditioned by the value of the sum of discrete i.i.d. random variables. Some applications for combinatoric problems are discussed.
In a causal graphical model, an instrument for a variable X and its effect Y is a random variable that is a cause of X and independent of all the causes of Y except X. (Pearl (1995), Spirtes et al (2000)). Instrumental variables can be used…
An empirical model is a generalization of a probability space. It consists of a simplicial complex of subsets of a class X of random variables such that each simplex has an associated probability distribution. The ensuing marginalizations…