Related papers: A microscopic probabilistic description of a local…
This article attempts to offer some perspectives on Bayesian inference for finite population quantities when the units in the population are assumed to exhibit complex dependencies. Beginning with an overview of Bayesian hierarchical…
We study a multilayer SIR model with two levels of mixing, namely a global level which is uniformly mixing, and a local level with two layers distinguishing household and workplace contacts, respectively. We establish the large population…
We analyze the long-term stability of a stochastic model designed to illustrate the adaptation of a population to variation in its environment. A piecewise-deterministic process modeling adaptation is coupled to a Feller logistic diffusion…
We analyze general two-species stochastic models, of the kind generally used for the study of population dynamics. We show that the conditions for the stochastic (microscopic) model to display approximate sustained oscillatory behavior are…
The machine learning community has recently put effort into quantized or low-precision arithmetics to scale large models. This paper proposes performing probabilistic inference in the quantized, discrete parameter space created by these…
A general formalism is developed to construct a Markov chain model that converges to a one-dimensional map in the infinite population limit. Stochastic fluctuations are therefore internal to the system and not externally specified. For…
For better learning, large datasets are often split into small batches and fed sequentially to the predictive model. In this paper, we study such batch decompositions from a probabilistic perspective. We assume that data points (possibly…
Several theoretical frameworks have been proposed to explain observed biodiversity patterns, ranging from the classical niche-based theories, mainly employing a continuous formalism, to neutral theories, based on statistical mechanics of…
A model is proposed and studied describing an infinite population of point migrants arriving in and departing from $X\subseteq \mathbf{R}^d$, $d\geq 1$. Both these acts occur at random with state-dependent rates. That is, depending on their…
Evolutionary branching is analysed in a stochastic, individual-based population model under mutation and selection. In such models, the common assumption is that individual reproduction and life career are characterised by values of a…
We investigate a Poisson sampling design in the presence of unknown selection probabilities when applied to a population of unknown size for multiple sampling occasions. The fixed-population model is adopted and extended upon for inference.…
We study a stochastic linear discrete metapolulation model to understand the effect of risk spreading by dispersion. We calculate analytically the stable distribution of populations that live in different habitats. The result shows that the…
A time- and space-discrete model for the growth of a rapidly saturating local biological population $N(x,t)$ is derived from a hierarchical random deposition process previously studied in statistical physics. Two biologically relevant…
The aim of this paper is twofold. First, three theoretical principles are formalized: randomization, overrepresentation and restriction. We develop these principles and give a rationale for their use in choosing the sampling design in a…
In this paper, we investigate the asymptotic behavior of individual-based models describing the evolution of a population structured by a real trait, subject to selection and mutation. We consider two different sets of assumptions: first,…
In this paper we consider first order differential models of collective behaviors of groups of agents based on the mass conservation equation. Models are formulated taking the spatial distribution of the agents as the main unknown,…
We define a general method for finding a quasi-best approximant in sup-norm to a target density belonging to a given model, based on independent samples drawn from distributions which average to the target (which does not necessarily belong…
A general theory is developed to study individual based models which are discrete in time. We begin by constructing a Markov chain model that converges to a one-dimensional map in the infinite population limit. Stochastic fluctuations are…
For a class of processes modeling the evolution of a spatially structured population with migration and a logistic local regulation of the reproduction dynamics, we show convergence to an upper invariant measure from a suitable class of…
We consider the estimation of densities in multiple subpopulations, where the available sample size in each subpopulation greatly varies. This problem occurs in epidemiology, for example, where different diseases may share similar…