Related papers: Testing exchangeability in the batch mode with e-v…
Exchangeability -- in which the distribution of an infinite sequence is invariant to reorderings of its elements -- implies the existence of a simple conditional independence structure that may be leveraged in the design of statistical…
The aim of this paper is to propose a methodology for testing general hypothesis in a Markovian setting with random sampling. A discrete Markov chain X is observed at random time intervals $\tau$ k, assumed to be iid with unknown…
In inference problems involving a multi-dimensional parameter $\theta$, it is often natural to consider decision rules that have a risk which is invariant under some group $G$ of permutations of $\theta$. We show that this implies that the…
We introduce a general Bayesian framework for graph matching grounded in a new theory of exchangeable random permutations. Leveraging the cycle representation of permutations and the literature on exchangeable random partitions, we define,…
In scientific studies involving analyses of multivariate data, basic but important questions often arise for the researcher: Is the sample exchangeable, meaning that the joint distribution of the sample is invariant to the ordering of the…
We consider exchangeable Markov multi-state survival processes -- temporal processes taking values over a state-space$\mathcal{S}$ with at least one absorbing failure state $\flat \in \mathcal{S}$ that satisfy natural invariance properties…
Permutation tests are widely used in statistics, providing a finite-sample guarantee on the type I error rate whenever the distribution of the samples under the null hypothesis is invariant to some rearrangement. Despite its increasing…
Parametric Markov chains (pMC) are used to model probabilistic systems with unknown or partially known probabilities. Although (universal) pMC verification for reachability properties is known to be coETR-complete, there have been efforts…
We address the problem of testing conditional mean and conditional variance for non-stationary data. We build e-values and p-values for four types of non-parametric composite hypotheses with specified mean and variance as well as other…
E-variables are a relatively new approach for testing statistical hypotheses that has been experiencing major development during the last several years. In this paper we introduce the method of e-variable-approximability and use it to…
Permutation tests enable testing statistical hypotheses in situations when the distribution of the test statistic is complicated or not available. In some situations, the test statistic under investigation is multivariate, with the multiple…
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…
Unnormalized probability distributions are frequently used in machine learning for modeling complex data generating processes. Though Markov chain Monte Carlo (MCMC) algorithms can approximately sample from unnormalized distributions,…
We propose a general new method, the conditional permutation test, for testing the conditional independence of variables $X$ and $Y$ given a potentially high-dimensional random vector $Z$ that may contain confounding factors. The proposed…
Generalizations to the permutation test are introduced to allow for situations in which the null model is not exchangeable. It is shown that the generalized permutation tests are exact, and a partial converse: that any test function that is…
In this paper, we generalize the metric-based permutation test for the equality of covariance operators proposed by Pigoli et al. (2014) to the case of multiple samples of functional data. To this end, the non-parametric combination…
This article studies the expected occupancy probabilities on an alphabet. Unlike the standard situation, where observations are assumed to be independent and identically distributed (iid), we assume that they follow a regime switching…
This article proposes an alternative to the Hosmer-Lemeshow (HL) test for evaluating the calibration of probability forecasts for binary events. The approach is based on e-values, a new tool for hypothesis testing. An e-value is a random…
Probability forecasts for binary events play a central role in many applications. Their quality is commonly assessed with proper scoring rules, which assign forecasts a numerical score such that a correct forecast achieves a minimal…
This paper studies permutation tests for regression parameters in a time series setting, where the time series is assumed stationary but may exhibit an arbitrary (but weak) dependence structure. In such a setting, it is perhaps surprising…