Related papers: A piecewise deterministic model for a prey-predato…
In this paper, we study a subclass of piecewise-deterministic Markov processes with a Polish state space, involving deterministic motion punctuated by random jumps that occur at exponentially distributed time intervals. Over each of these…
We develop a theory of generalist predation showing how alternative prey species are affected by changes in both mean abundance and variability (coefficient of variation) of their predator's primary prey. The theory is motivated by the…
This document is due to appear as a chapter of the forthcoming Handbook of Approximate Bayesian Computation (ABC) by S. Sisson, L. Fan, and M. Beaumont. Here we describe some of the circumstances under which statistical ecologists might…
For a class of piecewise deterministic Markov processes, the supports of the invariant measures are characterized. This is based on the analysis of controllability properties of an associated deterministic control system. Its invariant…
We present recent results on Piecewise Deterministic Markov Processes (PDMPs), involved in biological modeling. PDMPs, first introduced in the probabilistic literature by Davis (1984), are a very general class of Markov processes and are…
Irreversible and rejection-free Monte Carlo methods, recently developed in Physics under the name Event-Chain and known in Statistics as Piecewise Deterministic Monte Carlo (PDMC), have proven to produce clear acceleration over standard…
In this paper, we develop an ensemble-based time-stepping algorithm to efficiently find numerical solutions to a group of linear, second-order parabolic partial differential equations (PDEs). Particularly, the PDE models in the group could…
Systems whose time evolutions are entirely deterministic can nevertheless be studied probabilistically, i.e. in terms of the evolution of probability distributions rather than individual trajectories. This approach is central to the…
Statistical modelling of spatial extreme events has gained increasing attention over the last few decades with max-stable processes, and more recently $r$-Pareto processes, becoming the reference tools for the statistical analysis of…
In the last years, predator-prey systems have increased their applications and have given rise to systems which represent more accurately different biological issues that appear in the context of interacting species. Our aim in this paper…
We study a density-dependent Markov jump process describing a population where each individual is characterized by a type, and reproduces at rates depending both on its type and on the population type distribution. We are interested in the…
This paper reframes approachability theory within the context of population games. Thus, whilst one player aims at driving her average payoff to a predefined set, her opponent is not malevolent but rather extracted randomly from a…
Obtaining high certainty in predictive models is crucial for making informed and trustworthy decisions in many scientific and engineering domains. However, extensive experimentation required for model accuracy can be both costly and…
We consider a population, partitioned into a set of communities, and study the problem of identifying the largest community within the population via sequential, random sampling of individuals. There are multiple sampling domains, referred…
We introduce a broad class of spatial models to describe how spatially heterogeneous populations live, die, and reproduce. Individuals are represented by points of a point measure, whose birth and death rates can depend both on spatial…
We develop a mathematical model of extinction and coexistence in a generic predator-prey ecosystem composed of two herbivores in asymmetrical competition and a hunter exerting a predatory pressure on both species. With the aim of…
Temporal point processes offer a powerful framework for sampling from discrete distributions, yet they remain underutilized in existing literature. We show how to construct, for any target multivariate count distribution with…
This paper treats a random collision model of three species, which is represented by the random time change of three standard Poisson processes. The prey-predator relation in the random collision model looks like paper-scissors-stone game,…
We give a general result concerning the rates of convergence of penalized empirical risk minimizers (PERM) in the regression model. Then, we consider the problem of agnostic learning of the regression, and give in this context an oracle…
Recently several authors have proposed stochastic evolutionary models for the growth of complex networks that give rise to power-law distributions. These models are based on the notion of preferential attachment leading to the ``rich get…