Related papers: The Rescaled Polya Urn and the Wright-Fisher proce…

We study the rate of convergence to equilibrium of the solution of a Fokker--Planck type equation introduced by one of the authors in 2006 to describe opinion formation in a multi-agent system. The main feature of this Fokker--Planck…

FOLD-RM is an explainable machine learning classification algorithm that uses training data to create a set of classification rules. In this paper we introduce CON-FOLD which extends FOLD-RM in several ways. CON-FOLD assigns…

We consider a variant of the randomly reinforced urn where more balls can be simultaneously drawn out and balls of different colors can be simultaneously added. More precisely, at each time-step, the conditional distribution of the number…

In this paper, we introduce a new method of sampling from transition densities of diffusion processes including those unknown in closed forms by solving a partial differential equation satisfied by the quotient of transition densities. We…

We develop generalized approach to obtaining Edgeworth expansions for $t$-statistics of an arbitrary order using computer algebra and combinatorial algorithms. To incorporate various versions of mean-based statistics, we introduce Adjusted…

Online estimation and modelling of i.i.d. data for short sequences over large or complex "alphabets" is a ubiquitous (sub)problem in machine learning, information theory, data compression, statistical language processing, and document…

The transition distribution of a sample taken from a Wright-Fisher diffusion with general small mutation rates is found using a coalescent approach. The approximation is equivalent to having at most one mutation in the coalescent tree of…

This paper discusses the problem of adaptive estimation of a univariate object like the value of a regression function at a given point or a linear functional in a linear inverse problem. We consider an adaptive procedure originated from…

The d-dimensional Lambda-Fleming-Viot generator acting on functions g(x), with x being a vector of d allele frequencies, can be written as a Wright-Fisher generator acting on functions g with a modified random linear argument of x induced…

In populations competing for resources, it is natural to ask whether consuming fewer resources provides any selective advantage. To answer this question, we propose a Wright- Fisher model with two types of individuals: the inefficient…

We introduce a dynamic generative model, Bayesian allocation model (BAM), which establishes explicit connections between nonnegative tensor factorization (NTF), graphical models of discrete probability distributions and their Bayesian…

This paper considers the estimation and inference of the low-rank components in high-dimensional matrix-variate factor models, where each dimension of the matrix-variates ($p \times q$) is comparable to or greater than the number of…

Inferring processes or constructs from performance data is a major hallmark of cognitive psychometrics. Particularly, diffusion modeling of response times (RTs) from correct and erroneous responses using the Wiener distribution has become a…

Floating-point round-off errors are ubiquitous in numerically intensive programs arising in fields such as scientific computing and optimization. As floating-point errors potentially lead to unexpected and catastrophic program failures, one…

We study the multi-strategy stochastic evolutionary game with death-birth updating in expanding spatial populations of size $N\to \infty$. The model is a voter model perturbation. For typical populations, we require perturbation strengths…

Riemannian diffusion models draw inspiration from standard Euclidean space diffusion models to learn distributions on general manifolds. Unfortunately, the additional geometric complexity renders the diffusion transition term inexpressible…

We introduce a class of birth-and-death Polya urns, which allow for both sampling and removal of observations governed by an auxiliary inhomogeneous Bernoulli process, and investigate the asymptotic behaviour of the induced allelic…

Joint misclassification of exposure and outcome variables can lead to considerable bias in epidemiological studies of causal exposure-outcome effects. In this paper, we present a new maximum likelihood based estimator for the marginal…

Using a characterizing equation for the Beta distribution, Stein's method is applied to obtain bounds of the optimal order for the Wasserstein distance between the distribution of the scaled number of white balls drawn from a…

We consider a two-color P\'{o}lya urn in the case when a fixed number $S$ of balls is added at each step. Assume it is a large urn that is, the second eigenvalue $m$ of the replacement matrix satisfies $1/2<m/S\leq1$. After $n$ drawings,…