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The Wright-Fisher model describes a biological population containing a finite number of individuals. In this work we consider a Wright-Fisher model for a randomly mating population, where selection and mutation act at an unlinked locus. The…
Extreme value theory has constructed asymptotic properties of the sample maximum. This study concerns probability distribution estimation of the sample maximum. The traditional approach is parametric fitting to the limiting distribution --…
Predicting and anticipating future outcomes or reasoning about missing information in a sequence are critical skills for agents to be able to make intelligent decisions. This requires strong, temporally coherent generative capabilities.…
The distribution of genetic polymorphisms in a population contains information about the mutation rate and the strength of natural selection at a locus. Here, we show that the Poisson Random Field (PRF) method of population-genetic…
Many real-world systems modeled using partial differential equations (PDEs) involve unknown parameters that must be estimated from limited, noisy system observations. While typically assumed to be constants, some of these unobserved…
Understanding how stochastic and non-linear deterministic processes interact is a major challenge in population dynamics theory. After a short review, we introduce a stochastic individual-centered particle model to describe the evolution in…
Modeling the diameter distribution of trees in forest stands is a common forestry task that supports key biologically and economically relevant management decisions. The choice of model used to represent the diameter distribution and how to…
This paper introduces the R package drpop to flexibly estimate total population size from incomplete lists. Total population estimation, also called capture-recapture, is an important problem in many biological and social sciences. A…
A major challenge in the analysis of population genomics data consists of isolating signatures of natural selection from background noise caused by random drift and gene flow. Analyses of massive amounts of data from many related…
Score-based diffusion models currently constitute the state of the art in continuous generative modeling. These methods are typically formulated via overdamped or underdamped Ornstein--Uhlenbeck-type stochastic differential equations, in…
This report presents the comprehensive implementation, evaluation, and optimization of Denoising Diffusion Probabilistic Models (DDPMs) and Denoising Diffusion Implicit Models (DDIMs), which are state-of-the-art generative models. During…
Standard regression approaches assume that some finite number of the response distribution characteristics, such as location and scale, change as a (parametric or nonparametric) function of predictors. However, it is not always appropriate…
In this article, a new mathematical model of human population growth as an autonomous non-Markov queuing system with an unlimited number of servers and two types of applications is proposed. The research of this system was carried out a…
We consider an irreducible pure jump Markov process with rates Q=(q(x,y)) on \Lambda\cup\{0\} with \Lambda countable and 0 an absorbing state. A quasi-stationary distribution (qsd) is a probability measure \nu on \Lambda that satisfies:…
The stationary 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 to…
Diffusion models have demonstrated remarkable empirical success in the recent years and are considered one of the state-of-the-art generative models in modern AI. These models consist of a forward process, which gradually diffuses the data…
The filtering distribution is a time-evolving probability distribution on the state of a dynamical system, given noisy observations. We study the large-time asymptotics of this probability distribution for discrete-time, randomly…
The paper examines the Fractional Fourier Transform (FRFT) based technique as a tool for obtaining the probability density function and its derivatives, and mainly for fitting stochastic model with the fundamental probabilistic…
The aim of this paper is to provide a resampling technique that allows us to make inference on superpopulation parameters in finite population setting. Under complex sampling designs, it is often difficult to obtain explicit results about…
We explain the ubiquity and extremely slow evolution of non gaussian out-of-equilibrium distributions for the Hamiltonian Mean-Field model, by means of traditional kinetic theory. Deriving the Fokker-Planck equation for a test particle, one…