Related papers: Galton-Watson process and bayesian inference: A tu…
Ecosystems tend to fluctuate around stable equilibria in response to internal dynamics and environmental factors. Occasionally, they enter an unstable tipping region and collapse into an alternative stable state. Our understanding of how…
This article is an essay, both expository and argumentative, on the Galton-Watson process as a tool in the domain of Branching Processes. It is at the same time the author's ways to honour two distinguished scientists in this domain, both…
Changes in population size influence genetic diversity of the population and, as a result, leave a signature of these changes in individual genomes in the population. We are interested in the inverse problem of reconstructing past…
The accurate prediction of time-changing variances is an important task in the modeling of financial data. Standard econometric models are often limited as they assume rigid functional relationships for the variances. Moreover, function…
Complex systems are sometimes subject to non Gaussian alpha stable Levy fluctuations. A new method is devised to estimate this uncertain parameter and other system parameters, using observations on either mean exit time or escape…
We introduce a Gaussian process-based model for handling of non-stationarity. The warping is achieved non-parametrically, through imposing a prior on the relative change of distance between subsequent observation inputs. The model allows…
Quantitative population modelling is an invaluable tool for identifying the cascading effects of ecosystem management and interventions. Ecosystem models are often constructed by assuming stability and coexistence in ecological communities…
In a reinforced Galton-Watson process with reproduction law $\boldsymbol{\nu}$ and memory parameter $q\in(0,1)$, the number of children of a typical individual either, with probability $q$, repeats that of one of its forebears picked…
Multispecies ecosystems modelled by generalized Lotka-Volterra equations exhibit stationary population abundances, where large number of species often coexist. Understanding the precise conditions under which this is at all feasible and…
Gaussian processes are a natural way of defining prior distributions over functions of one or more input variables. In a simple nonparametric regression problem, where such a function gives the mean of a Gaussian distribution for an…
This paper proposes a novel numerical method for computing the density of the limit random variable associated with a supercritical Galton-Watson process. This random variable captures the effect of early demographic fluctuations and…
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…
A Galton-Watson process in a varying environment is a discrete time branching process where the offspring distributions vary among generations. It is known that in the critical case, these processes have a Yaglom limit, that is, a suitable…
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 population-size-dependent branching processes (PSDBPs) which eventually become extinct with probability one. For these processes, we derive maximum likelihood estimators for the mean number of offspring born to individuals when…
The Galton-Watson process is a Markov chain modeling the population size of independently reproducing particles giving birth to $k$ offspring with probability $p_k$, $k\ge0$. In this paper we consider {\it defective} Galton-Watson processes…
A branching process in random environment $(Z_n, n \in \N)$ is a generalization of Galton Watson processes where at each generation the reproduction law is picked randomly. In this paper we give several results which belong to the class of…
The linear-fractional Galton-Watson processes is a well known case when many characteristics of a branching process can be computed explicitly. In this paper we extend the two-parameter linear-fractional family to a much richer…
Consider N particles moving independently, each one according to a subcritical continuous-time Galton-Watson process unless it hits 0, at which time it jumps instantaneously to the position of one of the other particles chosen uniformly at…
We study a generalized discrete-time multi-type Wright-Fisher population process. The mean-field dynamics of the stochastic process is induced by a general replicator difference equation. We prove several results regarding the asymptotic…