Related papers: The coalescent structure of uniform and Poisson sa…
We define a multi-type coalescent point process of a general branching process with finitely many types. This multi-type coalescent fully describes the genealogy of the (quasi-stationary) standing population, providing types along ancestral…
Consider a structured population consisting of $d$ colonies, with migration rates proportional to a positive parameter $K$. We sample $N_K$ individuals, distributed evenly across the $d$ colonies, and trace their ancestral lineages backward…
We provide new connections between multitype $\Lambda$-coalescents and multitype continuous state branching processes via duality and a homeomorphism on their parameter space. The approach is based on a sequential sampling procedure for the…
Multitype branching processes with immigration in one type are used to model the dynamics of stage-structured plant populations. Parametric inference is first carried out when count data of all types are observed. Statistical…
We establish a complete picture of condensation in the inclusion process in the thermodynamic limit with vanishing diffusion, covering all scaling regimes of the diffusion parameter and including large deviation results for the maximum…
We define a Markov process on the partitions of $[n]=\{1,\ldots,n\}$ by drawing a sample in $[n]$ at each time of a Poisson process, by merging blocks that contain one of these points and by leaving all other blocks unchanged. This…
Representations of branching Markov processes and their measure-valued limits in terms of countable systems of particles are constructed for models with spatially varying birth and death rates. Each particle has a location and a "level,"…
Kingman derived the Ewens sampling formula for random partitions describing the genetic variation in a neutral mutation model defined by a Poisson process of mutations along lines of descent governed by a simple coalescent process, and…
We propose a general modeling framework for marked Poisson processes observed over time or space. The modeling approach exploits the connection of the nonhomogeneous Poisson process intensity with a density function. Nonparametric Dirichlet…
Consider a multitype coalescent process in which each block has a colour in $\{1,\ldots,d\}$. Individual blocks may change colour, and some number of blocks of various colours may merge to form a new block of some colour. We show that if…
We exploit a suitable moment-based characterization of the mixture of Poisson distribution for developing Bayesian inference for the unknown size of a finite population whose units are subject to multiple occurrences during an enumeration…
Consider a continuous-state branching population constructed as a flow of nested subordinators. Inverting the subordinators and reversing time give rise to a flow of coalescing Markov processes (with negative jumps) which correspond to the…
We present a general construction for dependent random measures based on thinning Poisson processes on an augmented space. The framework is not restricted to dependent versions of a specific nonparametric model, but can be applied to all…
By decomposing the random walk path, we construct a multitype branching process with immigration in random environment for corresponding random walk with bounded jumps in random environment. Then we give two applications of the branching…
Coalescent theory combined with statistical modeling allows us to estimate effective population size fluctuations from molecular sequences of individuals sampled from a population of interest. When sequences are sampled serially through…
We consider a model of a population in which individuals are sampled from different species. The Yule-Kingman nested coalescent describes the genealogy of the sample when each species merges with another randomly chosen species with a…
In this note, we present a novel connection between a multi-type (vector) multiplicative coalescent process and a multi-type branching process with Poisson offspring distributions. More specifically, we show that the equations that govern…
A validated simulation model primarily requires performing an appropriate input analysis mainly by determining the behavior of real-world processes using probability distributions. In many practical cases, probability distributions of the…
Boson sampling is a key candidate for demonstrating quantum advantage, and has already yielded significant advances in quantum simulation, machine learning, and graph theory. In this work, a unification and extension of distinct forms of…
In this paper, we present a nonparametric method to estimate the heterogeneity of a random medium from the angular distribution of intensity transmitted through a slab of random material. Our approach is based on the modeling of forward…