Related papers: Sequential Markov coalescent algorithms for popula…
Population structure can have a significant effect on evolution. For some systems with sufficient symmetry, analytic results can be derived within the mathematical framework of evolutionary graph theory which relate to the outcome of the…
Consider the Markov process taking values in the partitions of N such that each pair of blocks merges at rate one, and each integer is eroded, i.e., becomes a singleton block, at rate d. This is a special case of exchangeable…
Specifying a full Bayesian model that integrates multiple data sources can be challenging. One natural approach is to specify each individual model separately and join them afterwards. This is the approach adopted in Markov melding.…
Consider a haploid population which has evolved through an exchangeable reproduction dynamics, and in which all individuals alive at time $t$ have a most recent common ancestor (MRCA) who lived at time $A_t$, say. As time goes on, not only…
We present a computational model to reconstruct trees of ancestors for animals with sexual reproduction. Through a recursive algorithm combined with a random number generator, it is possible to reproduce the number of ancestors for each…
We study weighted particle systems in which new generations are resampled from current particles with probabilities proportional to their weights. This covers a broad class of sequential Monte Carlo (SMC) methods, widely-used in applied…
Samples of multiple complete genome sequences contain vast amounts of information about the evolutionary history of populations, much of it in the associations among polymorphisms at different loci. Current methods that take advantage of…
We investigate real-time tracking of two correlated stochastic processes over a shared wireless channel. The joint evolution of the processes is modeled as a two-dimensional discrete-time Markov chain. Each process is observed by a…
Sequence modeling with neural networks has lead to powerful models of symbolic music data. We address the problem of exploiting these models to reach creative musical goals, by combining with human input. To this end we generalise previous…
We identify a new natural coalescent structure, which we call the seed-bank coalescent, that describes the gene genealogy of populations under the influence of a strong seed-bank effect, where "dormant forms" of individuals (such as seeds…
Filtering---estimating the state of a partially observable Markov process from a sequence of observations---is one of the most widely studied problems in control theory, AI, and computational statistics. Exact computation of the posterior…
Statisticians often use Monte Carlo methods to approximate probability distributions, primarily with Markov chain Monte Carlo and importance sampling. Sequential Monte Carlo samplers are a class of algorithms that combine both techniques to…
The multispecies coalescent process models the genealogical relationships of genes sampled from several species, enabling useful predictions about phenomena such as the discordance between the gene tree and the species phylogeny due to…
In this work we describe a new model for the evolution of a diploid structured population backwards in time that allows for large migrations and uneven offspring distributions. The model generalizes both the mean-field model of Birkner et…
Recent work has proven the existence of extreme inbreeding in a European ancestry sample taken from the contemporary UK population \cite{nature_01}. This result brings our attention again to a math problem related to inbreeding family trees…
In this paper, we establish the theory of weak convergence (toward a normal distribution) for both single-chain and population stochastic approximation MCMC algorithms. Based on the theory, we give an explicit ratio of convergence rates for…
Given $n>0$, let $S\subset [0,1]^2$ be a set of $n$ points, chosen uniformly at random. Let $R\cup B$ be a random partition, or coloring, of $S$ in which each point of $S$ is included in $R$ uniformly at random with probability $1/2$.…
We analyse the performance of a recursive Monte Carlo method for the Bayesian estimation of the static parameters of a discrete--time state--space Markov model. The algorithm employs two layers of particle filters to approximate the…
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 the genealogy of a sample of individuals taken from a spatially structured population when the variance of the offspring distribution is relatively large. The space is structured into discrete sites of a graph G. If the…