Related papers: Markov Genealogy Processes
We show that each member of a broad class of Markovian population models induces a unique stochastic process on the space of genealogies. We construct this genealogy process and derive exact expressions for the likelihood of an observed…
We define the Sampled Moran Genealogy Process, a continuous-time Markov process on the space of genealogies with the demography of the classical Moran process, sampled through time. To do so, we begin by defining the Moran Genealogy Process…
Inference for partially observed Markov process models has been a longstanding methodological challenge with many scientific and engineering applications. Iterated filtering algorithms maximize the likelihood function for partially observed…
Markov chain Monte Carlo algorithms play a key role in the Bayesian approach to phylogenetic inference. In this paper, we present the first theoretical work analyzing the rate of convergence of several Markov chains widely used in…
We present simple conditions under which the limiting genealogical process associated with a class of interacting particle systems with non-neutral selection mechanisms, as the number of particles grows, is a time-rescaled Kingman…
We consider weighted particle systems in which new generations are re-sampled from current particles with probabilities proportional to their weights. This covers a broad class of sequential Monte Carlo methods, widely used in applied…
We introduce a filtration-based framework for studying when and why adding taxa improves phylodynamic inference, by constructing a natural ordering of observed tips and applying sequential Bayesian analysis to the resulting filtration. We…
Generative diffusions are a powerful class of Monte Carlo samplers that leverage bridging Markov processes to approximate complex, high-dimensional distributions, such as those found in image processing and language models. Despite their…
We study a class of Markov processes that combine local dynamics, arising from a fixed Markov process, with regenerations arising at a state-dependent rate. We give conditions under which such processes possess a given target distribution…
Genealogical networks, also known as family trees or population pedigrees, are commonly studied by genealogists wanting to know about their ancestry, but they also provide a valuable resource for disciplines such as digital demography,…
Phylogenetics uses alignments of molecular sequence data to learn about evolutionary trees. Substitutions in sequences are modelled through a continuous-time Markov process, characterised by an instantaneous rate matrix, which standard…
State-space models are commonly used to describe different forms of ecological data. We consider the case of count data with observation errors. For such data the system process is typically multi-dimensional consisting of coupled Markov…
Monte Carlo methods to evaluate and maximize the likelihood function enable the construction of confidence intervals and hypothesis tests, facilitating scientific investigation using models for which the likelihood function is intractable.…
We present a short introduction into the framework of piecewise deterministic Markov processes. We illustrate the abstract mathematical setting with a series of examples related to dispersal of biological systems, cell cycle models, gene…
We show that evolutionary computation can be implemented as standard Markov-chain Monte-Carlo (MCMC) sampling. With some care, `genetic algorithms' can be constructed that are reversible Markov chains that satisfy detailed balance; it…
A number of algorithms have been developed to solve probabilistic inference problems on belief networks. These algorithms can be divided into two main groups: exact techniques which exploit the conditional independence revealed when the…
In simulation-based inferences for partially observed Markov process models (POMP), the by-product of the Monte Carlo filtering is an approximation of the log likelihood function. Recently, iterated filtering [14, 13] has originally been…
We give a concise self-contained presentation of known and new limit theorems for the one-type Markov branching processes with continuous time. The new streamlined proofs are based on what we call, the tail generating function approach. Our…
We survey results on the description of stochastically evolving genealogies of populations and marked genealogies of multitype populations or spatial populations via tree-valued Markov processes on (marked) ultrametric measure spaces. In…
A probabilistic reconstruction of genealogies in a polyploid population (from 2x to 4x) is investigated, by considering genetic data analyzed as the probability of allele presence in a given genotype. Based on the likelihood of all possible…