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The analysis of large-scale datasets, especially in biomedical contexts, frequently involves a principled screening of multiple hypotheses. The celebrated two-group model jointly models the distribution of the test statistics with mixtures…
The robust Poisson method is becoming increasingly popular when estimating the association of exposures with a binary outcome. Unlike the logistic regression model, the robust Poisson method yields results that can be interpreted as risk or…
Joint distributions over many variables are frequently modeled by decomposing them into products of simpler, lower-dimensional conditional distributions, such as in sparsely connected Bayesian networks. However, automatically learning such…
This work considers a problem of estimating a mixing probability density $f$ in the setting of discrete mixture models. The paper consists of three parts. The first part focuses on the construction of an $L_1$ consistent estimator of $f$.…
We analyse numerically the effects of small population size in the initial transient regime of a simple example population dynamics. These effects play an important role for the numerical determination of large deviation functions of…
Randomization tests have gained popularity for causal inference under network interference because they are finite-sample valid with minimal assumptions. However, existing procedures are limited as they primarily focus on the existence of…
An important functional of Poisson random measure is the negative binomial process (NBP). We use NBP to introduce a generalized Poisson-Kingman distribution and its corresponding random discrete probability measure. This random discrete…
In this work, we revisit outlier hypothesis testing and propose exponentially consistent, low-complexity fixed-length tests that achieve a better tradeoff between detection performance and computational complexity than existing…
We study how the training data distribution affects confidence and performance in image classification models. We introduce Embedding Density, a model-agnostic framework that estimates prediction confidence by measuring the distance of test…
From the distributional characterizations that lie at the heart of Stein's method we derive explicit formulae for the mass functions of discrete probability laws that identify those distributions. These identities are applied to develop…
This paper addresses the distributed convergence detection problem in asynchronous iterations. A modified recursive doubling algorithm is investigated in order to adapt to the non-power-of-two case. Some convergence detection algorithms are…
This paper investigates two fundamental descriptors of data, i.e., density distribution versus mass distribution, in the context of clustering. Density distribution has been the de facto descriptor of data distribution since the…
We offer two novel characterizations of the Zeta distribution: first, as tractable continuous mixtures of Negative Binomial distributions (with fixed shape parameter, r > 0), and second, as a tractable continuous mixture of Poisson…
It is known that, by accounting for the multiboson interferences up to a finite order, the output distribution of noisy Boson Sampling, with distinguishability of bosons serving as noise, can be approximately sampled from in a time…
Multiplicity distributions $P(N)$ measured in multiparticle production processes are most frequently described by the Negative Binomial Distribution (NBD). However, with increasing collision energy some systematic discrepancies become more…
Site occupancy models are routinely used to estimate the probability of species presence from either abundance or presence-absence data collected across sites with repeated sampling occasions. In the last two decades, a broad class of…
Codifference is a commonly used measure of dependence for stable vectors and processes for which covariance is infinite. However, we argue that it can also be used for other heavy-tail distributions and it provides useful information for…
The task of the binary classification problem is to determine which of two distributions has generated a length-$n$ test sequence. The two distributions are unknown; two training sequences of length $N$, one from each distribution, are…
A validated simulation model primarily requires performing an appropriate input analysis mainly by determining the behavior of real-world processes using probability distributions. In many practical cases, probability distributions of the…
While there is considerable work on change point analysis in univariate time series, more and more data being collected comes from high dimensional multivariate settings. This paper introduces the asymptotic concept of high dimensional…