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Many researchers have identified distribution shift as a likely contributor to the reproducibility crisis in behavioral and biomedical sciences. The idea is that if treatment effects vary across individual characteristics and experimental…
The Gibbs Mixing Paradox is a conceptual touchstone for understanding mixtures in statistical mechanics. While debates over the theoretical subtleties of particle distinguishability continue to this day, we seek to extend the discussion in…
The classical and extended occupancy distributions are useful for examining the number of occupied bins in problems involving random allocation of balls to bins. We examine the extended occupancy problem by framing it as a Markov chain and…
A predictive distribution over a sequence of $N+1$ events is said to be "frequency mimicking" whenever the probability for the final event conditioned on the outcome of the first $N$ events equals the relative frequency of successes among…
Gibbs sampling is fundamental to a wide range of computer algorithms. Such algorithms are set to be replaced by physics based processors$-$be it quantum or stochastic annealing devices$-$which embed problem instances and evolve a physical…
A new characterization of the exponential distribution is obtained. It is based on an equation involving randomly shifted (translated) order statistics. No specific distribution is assumed for the shift random variables. The proof uses a…
We study the enumeration of set partitions, according to their length, number of parts, cyclic type, and genus. We introduce genus-dependent Bell, Stirling numbers, and Fa\`a di Bruno coefficients. Besides attempting to summarize what is…
We review the experimental as well as the phenomenology status of Generalized Parton Distributions (GPDs), focusing on recent data on Deeply Virtual Compton Scattering and Deep Virtual Meson Production. We also describe the various…
Reliable knowledge of parton distributions at large x is crucial for many searches for new physics signals in the next generation of collider experiments. Although these are generally well determined in the small and medium x range, it has…
We demonstrate that statistics for several types of set partitions are described by generating functions which appear in the theory of integrable equations.
Interesting properties of the partitions of a finite field $\mathbb F_q$ induced by the combination of involutions and trace maps are studied. The special features of involutions of the form $\frac{u}{z}$, $u$ being a fixed element of…
In many growing networks, the age of the nodes plays an important role in deciding the attachment probability of the incoming nodes. For example, in a citation network, very old papers are seldom cited while recent papers are usually cited…
We study large partial sums, localized with respect to the sums of variances, of a sequence of centered random variables. An application is given to the distribution of prime factors of typical integers.
The linear semigroup associated with age-structured diffusive populations is investigated in the $L_1$-setting. A complete determination of its generator is given along with detailed spectral information that imply, in particular, an…
The distribution of differences of consecutive members of sequences of primes is investigated. A quantitative measure for oscillations among these differences is the curvature of the sequence. If the sequence is not too sparse, then sharp…
Discrete random probability measures and the exchangeable random partitions they induce are key tools for addressing a variety of estimation and prediction problems in Bayesian inference. Indeed, many popular nonparametric priors, such as…
We study a curious class of partitions, the parts of which obey an exceedingly strict congruence condition we refer to as "sequential congruence": the $m$th part is congruent to the $(m+1)$th part modulo $m$, with the smallest part…
We study a general setting of neutral evolution in which the population is of finite, constant size and can have spatial structure. Mutation leads to different genetic types ("traits"), which can be discrete or continuous. Under minimal…
Two closely related discrete probability distributions are introduced. In each case the support is a set of vectors in $\mathbb{R}^n$ obtained from the partitions of the fixed positive integer $n$. These distributions arise naturally when…
A class of probability distributions is characterized via equalities in law between two order statistics shifted by independent exponential variables. An explicit formula for the quintile function of the identified family of distributions…