2025/04/04 by Peter Braunsteins, Braunsteins, Peter, Sophie Hautphenne +3
Mathematics · Medicine · #60J80 #COVID-19 epidemiological studies #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Probability (math.PR) #Statistics Theory (math.ST) #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2504.03389
openalex publication_date 2025/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the problem of estimating the parameters of a supercritical controlled branching process consistently from a single observed trajectory of population size counts. Our goal is to establish which parameters can and cannot be consistently estimated. When a parameter can be consistently estimated, we derive an explicit expression for the estimator. We address these questions in three scenarios: when the distribution of the control function distribution is known, when it is unknown, and when progenitor numbers are observed alongside population size counts. Our results offer a theoretical justification for the common practice in population ecology of estimating demographic and environmental stochasticity using separate observation schemes.