Related papers: On a representation of partially-distinguishable p…
There exists a wide variety of works on the dynamics of large populations ranging from simple heuristic modeling to those based on advanced computer supported methods. Their interconnections, however, remain mostly vague, which…
These notes provide a review of basic stochastic population models including branching processes and models of population genetics. Measure-valued population models including superprocesses and Fleming-Viot processes are also introduced…
Data represented by probability measures arise as empirical distributions, posterior distributions, and feature-based representations of complex objects. We study heterogeneity in a population of probability measures through the expected…
We are interested in modelling Darwinian evolution, resulting from the interplay of phenotypic variation and natural selection through ecological interactions. Our models are rooted in the microscopic, stochastic description of a population…
This paper deals with the derivation of a collective model of cell populations out of an individual-based description of the underlying physical particle system. By looking at the spatial distribution of cells in terms of time-evolving…
We are interested in modeling some two-level population dynamics, resulting from the interplay of ecological interactions and phenotypic variation of individuals (or hosts) and the evolution of cells (or parasites) of two types living in…
We construct a probabilistic representation of a system of fully coupled parabolic equations arising as a model describing spatial segregation of interacting population species. We derive a closed system of stochastic equations such that…
We study stochastic particle systems made up of heterogeneous units. We introduce a general framework suitable to analytically study this kind of systems and apply it to two particular models of interest in economy and epidemiology. We show…
In this paper we introduce a general stochastic representation for an important class of processes with resetting. It allows to describe any stochastic process intermittently terminated and restarted from a predefined random or non-random…
We discuss a connection between two areas of mathematics which until recently seemed to be rather distant from each other: (1) noncommutative harmonic analysis on groups and (2) some topics in probability theory related to random point…
Experimental work regularly finds that individual choices are not deterministically rationalized by well-defined preferences. Nonetheless, recent work shows that data collected from many individuals can be stochastically rationalized by a…
Many imaging techniques for biological systems -- like fixation of cells coupled with fluorescence microscopy -- provide sharp spatial resolution in reporting locations of individuals at a single moment in time but also destroy the dynamics…
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…
This paper extends the concept of informative selection, population distribution and sample distribution to a spatial process context. These notions were first defined in a context where the output of the random process of interest consists…
A stochastic representation for the solutions of the Poisson-Vlasov equation is obtained. The representation involves both an exponential and a branching process. The stochastic representation, besides providing an alternative existence…
Compartmentalization of biochemical processes underlies all biological systems, from the organelle to the tissue scale. Theoretical models to study the interplay between noisy reaction dynamics and compartmentalization are sparse, and…
Density dependent Markov population processes with countably many types can often be well approximated over finite time intervals by the solution of the differential equations that describe their average drift, provided that the total…
Human decision making can be challenging to predict because decisions are affected by a number of complex factors. Adding to this complexity, decision-making processes can differ considerably between individuals, and methods aimed at…
Heterogeneous data from multiple populations, sub-groups, or sources is often represented as a ``mixture model'' with a single latent class influencing all of the observed covariates. Heterogeneity can be resolved at multiple levels by…
Parameter identification problems are formulated in a probabilistic language, where the randomness reflects the uncertainty about the knowledge of the true values. This setting allows conceptually easily to incorporate new information, e.g.…