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We propose a novel, succinct, and effective approach for distribution prediction to quantify uncertainty in machine learning. It incorporates adaptively flexible distribution prediction of $\mathbb{P}(\mathbf{y}|\mathbf{X}=x)$ in regression…
Multiple testing of a single hypothesis and testing multiple hypotheses are usually done in terms of p-values. In this paper we replace p-values with their natural competitor, e-values, which are closely related to betting, Bayes factors,…
Power-law distributions are essential in computational and statistical investigations of extreme events and complex systems. The usual technique to generate power-law distributed data is to first infer the scale exponent $\alpha$ using the…
Statistical tests that compare classification algorithms are univariate and use a single performance measure, e.g., misclassification error, $F$ measure, AUC, and so on. In multivariate tests, comparison is done using multiple measures…
Many scientific datasets are compositional in nature. Important biological examples include species abundances in ecology, cell-type compositions derived from single-cell sequencing data, and amplicon abundance data in microbiome research.…
Evidence-Based Climate Policy (EBCP) is an approach to policymaking that relies on evidence to make decisions about managing climate impacts, mitigation, and adaptation. A core problem for EBCP is the lack of a clear definition of evidence,…
We consider the testing and estimation of change-points, locations where the distribution abruptly changes, in a sequence of multivariate or non-Euclidean observations. We study a nonparametric framework that utilizes similarity information…
Nonparametric two sample testing is a decision theoretic problem that involves identifying differences between two random variables without making parametric assumptions about their underlying distributions. We refer to the most common…
In this paper we discuss a simple method of testing for the presence of energy-dependent dispersion in high energy data-sets. It uses the minimisation of the Kolmogorov distance between the cumulative distribution of two probability…
In this article, we present a nonparametric method for the general two-sample problem involving functional random variables modelled as elements of a separable Hilbert space ${\cal H}$. First, we present a general recipe based on linear…
A multivariate mixed-effects model seems to be the most appropriate for gene expression data collected in a crossover trial. It is, however, difficult to obtain reliable results using standard statistical inference when some responses are…
With the widespread application of causal inference, it is increasingly important to have tools which can test for the presence of causal effects in a diverse array of circumstances. In this vein we focus on the problem of testing for…
Studies that collect multi-outcome data such as tobacco and alcohol use are becoming increasingly common. In principle, multi-outcomes studies investigate the correlations between outcomes, including, causal links and/or joint…
We describe our efforts of the past few years to create a large set of more than 500 highly-accurate vertical excitation energies of various natures ($\pi \to \pi^*$, $n \to \pi^*$, double excitation, Rydberg, singlet, doublet, triplet,…
Conditional average treatment effects (CATEs) allow us to understand the effect heterogeneity across a large population of individuals. However, typical CATE learners assume all confounding variables are measured in order for the CATE to be…
In this paper, we present a novel test for determining equality in distribution of matrix distributions. Our approach is based on the integral squared difference of the empirical Laplace transforms with respect to the noncentral Wishart…
Equivalence testing for scalar data has been well addressed in the literature, however, the same cannot be said for functional data. The resultant complexity from maintaining the functional structure of the data, rather than using a scalar…
Testing the equality of two proportions is a common procedure in science, especially in medicine and public health. In these domains it is crucial to be able to quantify evidence for the absence of a treatment effect. Bayesian hypothesis…
The issue addressed in this paper is that of testing for common breaks across or within equations of a multivariate system. Our framework is very general and allows integrated regressors and trends as well as stationary regressors. The null…
The multivariate conditional probability distribution models the effects of a set of variables onto the statistical properties of another set of variables. In the study of systemic risk in a financial system, the multivariate conditional…