Related papers: Generic E-Variables for Exact Sequential k-Sample …

Expansion was invented at the end of the 1970s for calculating principal typings for $\lambda$-terms in type systems with intersection types. Expansion variables (E-variables) were invented at the end of the 1990s to simplify and help…

E-variables enable safe and anytime-valid inference, with log-optimal e-variables given by the likelihood ratio of the least favorable distributions (LFDs) when they exist in composite settings. While this unconstrained theory is well…

Given well-shuffled data, can we determine whether the data items are statistically (in)dependent? Formally, we consider the problem of testing whether a set of exchangeable random variables are independent. We will show that this is…

Sequential monitoring of randomized trials traditionally relies on parametric assumptions or asymptotic approximations. We discuss a family of nonparametric sequential tests - collectively called e-RT - for binary, event-only, and…

The problem of detecting changes in covariance for a single pair of features has been studied in some detail, but may be limited in importance or general applicability. In contrast, testing equality of covariance matrices of a {\it set} of…

Expansion was introduced at the end of the 1970s for calculating principal typings for $\lambda$-terms in intersection type systems. Expansion variables (E-variables) were introduced at the end of the 1990s to simplify and help mechanise…

Expectation Value Samplers (EVSs) are quantum generative models that can learn high-dimensional continuous distributions by measuring the expectation values of parameterized quantum circuits. However, these models can demand impractical…

It is often claimed that Bayesian methods, in particular Bayes factor methods for hypothesis testing, can deal with optional stopping. We first give an overview, using elementary probability theory, of three different mathematical meanings…

There is a useful counterpart of conformal prediction for e-values, called conformal e-prediction. Conformal prediction can serve as basis for testing the assumption of exchangeability, leading to conformal testing. Similarly, conformal…

In the regime of two-sample comparison, tests based on a graph constructed on observations by utilizing similarity information among them is gaining attention due to their flexibility and good performances for high-dimensional/non-Euclidean…

Consider a set of multiple, multimodal sensors capturing a complex system or a physical phenomenon of interest. Our primary goal is to distinguish the underlying sources of variability manifested in the measured data. The first step in our…

We introduce a powerful deep classifier two-sample test for high-dimensional data based on E-values, called E-value Classifier Two-Sample Test (E-C2ST). Our test combines ideas from existing work on split likelihood ratio tests and…

A standard practice in statistical hypothesis testing is to mention the p-value alongside the accept/reject decision. We show the advantages of mentioning an e-value instead. With p-values, it is not clear how to use an extreme observation…

In this paper, we derive a version of the Pontryagin maximum principle for general finite-dimensional nonlinear optimal sampled-data control problems. Our framework is actually much more general, and we treat optimal control problems for…

The problem of testing changes in covariance has received increasing attention in recent years, especially in the context of high-dimensional testing. A number of approaches have been proposed, all limited to the two-sample problem and…

This paper shows that sequential statistical analysis techniques can be generalised to the problem of selecting between alternative forecasting methods using scoring rules. A return to basic principles is necessary in order to show that…

The e-value is swiftly rising in prominence in many applications of hypothesis testing and multiple testing, yet its relationship to classical testing theory remains elusive. We unify e-values and classical testing into a single 'continuous…

Currently, statistical tests for random number generators (RNGs) are widely used in practice, and some of them are even included in information security standards. But despite the popularity of RNGs, consistent tests are known only for…

We study the problem of active nonparametric sequential two-sample testing over multiple heterogeneous data sources. In each time slot, a decision-maker adaptively selects one of $K$ data sources and receives a paired sample generated from…

We study worst-case-growth-rate-optimal (GROW) e-statistics for hypothesis testing between two group models. It is known that under a mild condition on the action of the underlying group G on the data, there exists a maximally invariant…