How old is this bird? The age distribution under some phase sampling schemes

TL;DR

This paper models individual lifetime using a phase-type distribution via a Markov chain, analyzing how different phase observation schemes affect the conditional age distribution, with application to conservation data of an endangered bird.

Contribution

It introduces a framework for calculating the conditional age distribution based on phase observation schemes within a Markov chain model.

Findings

Derived formulas for age distribution under various phase observation schemes

Applied the model to the Chatham Island black robin data during conservation efforts

Provided insights into age structure analysis in endangered species

Abstract

In this paper, we use a finite-state continuous-time Markov chain with one absorbing state to model an individual's lifetime. Under this model, the time of death follows a phase-type distribution, and the transient states of the Markov chain are known as phases. We then attempt to provide an answer to the simple question "What is the conditional age distribution of the individual, given its current phase"? We show that the answer depends on how we interpret the question, and in particular, on the phase observation scheme under consideration. We then apply our results to the computation of the age pyramid for the endangered Chatham Island black robin Petroica traversi during years of intensive conservation efforts in 1980-1989.