Related papers: Poisson-Dirichlet Distribution with Small Mutation…
In this paper, we first study the Poisson reductions of controlled Hamiltonian (CH) system and symmetric CH system by controllability distributions. These reductions are the extension of Poisson reductions by distribution for Poisson…
We consider Markov chains on the space of (countable) partitions of the interval $[0,1]$, obtained first by size biased sampling twice (allowing repetitions) and then merging the parts with probability $\beta_m$ (if the sampled parts are…
We consider the inclusion process on the complete graph with vanishing diffusivity, which leads to condensation of particles in the thermodynamic limit. Describing particle configurations in terms of size-biased and appropriately scaled…
Natural selection explains how life has evolved over millions of years from more primitive forms. The speed at which this happens, however, has sometimes defied formal explanations when based on random (uniformly distributed) mutations.…
Evolutionary dynamics and patterns of molecular evolution are strongly influenced by selection on linked regions of the genome, but our quantitative understanding of these effects remains incomplete. Recent work has focused on predicting…
In the present paper new insights into the study of the Non-central Dirichlet distribution are provided. This latter is the analogue of the Dirichlet distribution obtained by replacing the Chi-Squared random variables involved in its…
A significant obstacle in the development of robust machine learning models is covariate shift, a form of distribution shift that occurs when the input distributions of the training and test sets differ while the conditional label…
Random models of evolution are instrumental in extracting rates of microscopic evolutionary mechanisms from empirical observations on genetic variation in genome sequences. In this context it is necessary to know the statistical properties…
We analyze a class of continuous time random walks in $\mathbb R^d,d\geq 2,$ with uniformly distributed directions. The steps performed by these processes are distributed according to a generalized Dirichlet law. Given the number of changes…
We are interested in the long-time behavior of a diploid population with sexual reproduction, characterized by its genotype composition at one bi-allelic locus. The population is modeled by a 3-dimensional birth-and-death process with…
We study conserved one-dimensional models of particle diffusion, attachment and detachment from clusters, where the detachment rates decrease with increasing cluster size as gamma(m) ~ m^{-k}, k>0. Heuristic scaling arguments based on…
Using techniques from Poisson approximation, we prove explicit error bounds on the number of permutations that avoid any pattern. Most generally, we bound the total variation distance between the joint distribution of pattern occurrences…
We describe the evolution of the quantity of parasites in a population of cells which divide in continuous-time. The quantity of parasites in a cell follows a Feller diffusion, which is splitted randomly between the two daughter cells when…
The effects of a stochastic reset, to its initial configuration, is studied in the exactly solvable one-dimensional coagulation-diffusion process. A finite resetting rate leads to a modified non-equilibrium stationary state. If in addition…
We study two problems. First, we consider the large deviation behavior of empirical measures of certain diffusion processes as, simultaneously, the time horizon becomes large and noise becomes vanishingly small. The law of large numbers…
The stationary asymptotic properties of the diffusion limit of a multi-type branching process with neutral mutations are studied. For the critical and subcritical processes the interesting limits are those of quasi-stationary distributions…
We consider a change detection problem in which the arrival rate of a Poisson process changes suddenly at some unknown and unobservable disorder time. It is assumed that the prior distribution of the disorder time is known. The objective is…
The present paper provides exact expressions for the probability distributions of linear functionals of the two-parameter Poisson--Dirichlet process $\operatorname {PD}(\alpha,\theta)$. We obtain distributional results yielding exact forms…
The study of the number of collisions in a Poisson-Dirichlet coalescent leads to the analysis of the following version of a stochastic leader-elec\-tion algorithm. Consider an infinite family of persons, labeled by $1,2,3,\ldots$, who…
Dirichlet process mixtures are flexible non-parametric models, particularly suited to density estimation and probabilistic clustering. In this work we study the posterior distribution induced by Dirichlet process mixtures as the sample size…