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Increasing effort is put into the development of methods for learning mechanistic models from data. This task entails not only the accurate estimation of parameters but also a suitable model structure. Recent work on the discovery of…
We study time continuous branching processes with exponentially distributed lifetimes, with two types of cells that proliferate according to binary fission. A range of possible system dynamics are considered, each of which is characterized…
We consider a two-dimensional time-inhomogeneous birth-death process to model the time-evolution of fake news in a population. The two components of the process represent, respectively, (i) the number of individuals (say spreaders) who know…
Consider an arbitrary large population at the present time, originated at an unspecified arbitrary large time in the past, where individuals in the same generation reproduce independently, forward in time, with the same offspring…
Spreading processes are conventionally monitored on a macroscopic level by counting the number of incidences over time. The spreading process can then be modeled either on the microscopic level, assuming an underlying interaction network,…
The Wright-Fisher model and the Moran model are both widely used in population genetics. They describe the time evolution of the frequency of an allele in a well-mixed population with fixed size. We propose a simple and tractable model…
We consider models of the population or opinion dynamics which result in the non-linear stochastic differential equations (SDEs) exhibiting the spurious long-range memory. In this context, the correspondence between the description of the…
Consider two ancestral lineages sampled from a system of two-dimensional branching random walks with logistic regulation in the stationary regime. We study the asymptotics of their coalescence time for large initial separation and find that…
Motivated by the challenge of sampling Gibbs measures with nonconvex potentials, we study a continuum birth-death dynamics. We improve results in previous works [51,57] and provide weaker hypotheses under which the probability density of…
This paper gives a holistic overview of both the design-based and model-based paradigms for sampling theory. Both methods are presented within a unified framework with a simple consistent notation, and the differences in the two paradigms…
We consider an individual-based spatially structured population for Darwinian evolution in an asexual population. The individuals move randomly on a bounded continuous space according to a reflected brownian motion. The dynamics involves…
Conditional sampling distributions (CSDs), sometimes referred to as copying models, underlie numerous practical tools in population genomic analyses. Though an important application that has received much attention is the inference of…
We present a stochastic model for the size of a taxon in paleobiology, in which we allow for the evolution of new taxon members, and both individual and catastrophic extinction events. The model uses ideas from the theory of birth and death…
We establish convergence to the Kingman coalescent for a class of age-structured population models with time-constant population size. Time is discrete with unit called a year. Offspring numbers in a year may depend on mother's age.
Stochastic models of sequential mutation acquisition are widely used to quantify cancer and bacterial evolution. Across manifold scenarios, recurrent research questions are: how many cells are there with $n$ alterations, and how long will…
In the case of informative sampling the sampling scheme explicitly or implicitly depends on the response variable. As a result, the sample distribution of response variable can- not be used for making inference about the population. In this…
We develop a Bayesian model-based approach to finite population estimation accounting for spatial dependence. Our innovation here is a framework that achieves inference for finite population quantities in spatial process settings. A key…
Natural populations often show enhanced genetic drift consistent with a strong skew in their offspring number distribution. The skew arises because the variability of family sizes is either inherently strong or amplified by population…
In studies involving lifetimes, observed survival times are frequently censored and possibly subject to biased sampling. In this paper, we model survival times under biased sampling (a.k.a., biased survival data) by a semi-parametric model,…
Many important stochastic counting models can be written as general birth-death processes (BDPs). BDPs are continuous-time Markov chains on the non-negative integers and can be used to easily parameterize a rich variety of probability…