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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…
We analyze a new Monte Carlo method which uses transition matrix in the space of energy. This method gives an efficient reweighting technique. The associated artificial dynamics is a constrained random walk in energy, producing the result…
We investigate the properties of a sequential Monte Carlo method where the particle weight that appears in the algorithm is estimated by a positive, unbiased estimator. We present broadly-applicable convergence results, including a central…
The dynamics of a population exhibiting exponential growth can be modelled as a birth-death process, which naturally captures the stochastic variation in population size over time. In this article, we consider a supercritical birth-death…
We give a cross-disciplinary survey on ``population'' Monte Carlo algorithms. In these algorithms, a set of ``walkers'' or ``particles'' is used as a representation of a high-dimensional vector. The computation is carried out by a random…
Particle filters are a widely used Monte Carlo based data assimilation technique that estimates the probability distribution of a system's state conditioned on observations through a collection of weights and particles. A known problem for…
Inference of the marginal likelihood of sample allele configurations using backward algorithms yields identical results with the Kingman coalescent, the Moran model, and the diffusion model (up to a scaling of time). For inference of…
Gene tree/species tree reconciliation is a recent decisive progress in phylo-genetic methods, accounting for the possible differences between gene histories and species histories. Reconciliation consists in explaining these differences by…
We consider the evolution of populations under the joint action of mutation and differential reproduction, or selection. The population is modelled as a finite-type Markov branching process in continuous time, and the associated…
We consider Bayesian inference in sequential latent variable models in general, and in nonlinear state space models in particular (i.e., state smoothing). We work with sequential Monte Carlo (SMC) algorithms, which provide a powerful…
Bayesian Decision Trees are known for their probabilistic interpretability. However, their construction can sometimes be costly. In this article we present a general Bayesian Decision Tree algorithm applicable to both regression and…
A density-dependent branching process is a particle system in which individuals reproduce independently, but in a way that depends on the current population size. This feature can model a wide range of ecological interactions at the cost of…
We consider a general class of branching processes in discrete time, where particles have types belonging to a Polish space and reproduce independently according to their type. If the process is critical and the mean distribution of types…
Ancestral inference for branching processes in random environments involves determining the ancestor distribution parameters using the population sizes of descendant generations. In this paper, we introduce a new methodology for ancestral…
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…
Repetitions within a given genealogical tree provides some information about the degree of consanguineity of a population. They can be analyzed with techniques usually employed in statistical physics when dealing with fixed point…
It is well known that the classical recombination equation for two parent individuals is equivalent to the law of mass action of a strongly reversible chemical reaction network, and can thus be reformulated as a generalised gradient system.…
In this paper, we provide a polynomial time algorithm to calculate the probability of a {\it ranked} gene tree topology for a given species tree, where a ranked tree topology is a tree topology with the internal vertices being ordered. The…
The time evolution of the two-time conditional probability of the classical stochastic process is described in an analogous form of the quantum mechanical wave equations. By using it, we emulate the same strange behaviors as those of the…
We consider the Wright-Fisher model for a population of $N$ individuals, each identified with a sequence of a finite number of sites, and single-crossover recombination between them. We trace back the ancestry of single individuals from the…