Related papers: Phase-type distributions in population genetics

In the human genomes, recombination frequency between homologous chromosomes during meiosis is highly correlated with their physical length while it differs significantly when their coding density is considered. Furthermore, it has been…

We introduce a class of continuous-time bivariate phase-type distributions for modeling dependencies from common shocks. The construction uses continuous-time Markov processes that evolve identically until an internal common-shock event,…

Recently, several methods have leveraged deep generative modeling to produce example-based explanations of image classifiers. Despite producing visually stunning results, these methods are largely disconnected from classical explainability…

By linking conceptual theories with observed data, generative models can support reasoning in complex situations. They have come to play a central role both within and beyond statistics, providing the basis for power analysis in molecular…

We reconsider the deterministic haploid mutation-selection equation with two types. This is an ordinary differential equation that describes the type distribution (forward in time) in a population of infinite size. This paper establishes…

This issue includes six articles that develop and apply statistical methods for the analysis of gene sequencing data of different types. The methods are tailored to the different data types and, in each case, lead to biological insights not…

We explore some aspects of phase transitions in cellular automata. We start recalling the standard formulation of statistical mechanics of discrete systems (Ising model), illustrating the Monte Carlo approach as Markov chains and stochastic…

Phase-type (PH) distributions are a popular tool for the analysis of univariate risks in numerous actuarial applications. Their multivariate counterparts (MPH$^\ast$), however, have not seen such a proliferation, due to lack of explicit…

What is a population? This review considers how a population may be defined in terms of understanding the structure of the underlying genetics of the individuals involved. The main approach is to consider statistically identifiable groups…

Migrations have played an important role in shaping the genetic diversity of human populations. Understanding genomic data thus requires careful modeling of historical gene flow. Here we consider the effect of relatively recent population…

Genetic data are often used to infer demographic history and changes or detect genes under selection. Inferential methods are commonly based on models making various strong assumptions: demography and population structures are supposed…

The method of 'coupling from the past' permits exact sampling from the invariant distribution of a Markov chain on a finite state space. The coupling is successful whenever the stochastic dynamics are such that there is coalescence of all…

We present a robust method which translates information on the speed of coming down from infinity of a genealogical tree into sampling formulae for the underlying population. We apply these results to population dynamics where the genealogy…

We study a density-dependent Markov jump process describing a population where each individual is characterized by a type, and reproduces at rates depending both on its type and on the population type distribution. We are interested in the…

Generative modeling, which learns joint probability distribution from data and generates samples according to it, is an important task in machine learning and artificial intelligence. Inspired by probabilistic interpretation of quantum…

In mathematical population genetics, it is well known that one can represent the genealogy of a population by a tree, which indicates how the ancestral lines of individuals in the population coalesce as they are traced back in time. As the…

We use a simplified model which is based on the same physics as inherent in most statistical models for nuclear multifragmentation. The simplified model allows exact calculations for thermodynamic properties of systems of large number of…

1) Micro-evolutionary predictions are complicated by ecological feedbacks like density dependence, while ecological predictions can be complicated by evolutionary change. A widely used approach in micro-evolution, quantitative genetics,…

Matrix-form Poisson probability distributions were recently introduced as one matrix generalization of Panjer distributions. We show in this paper that under the constraint that their representation is to be nonnegative, they have a…

We propose a model based on coupled multiplicative stochastic processes to understand the dynamics of competing species in an ecosystem. This process can be conveniently described by a Fokker-Planck equation. We provide an analytical…