# Fitting Markovian binary trees using global and individual demographic data

## TL;DR

This paper introduces methods for fitting Markovian binary trees to demographic data using TMAP models, enabling detailed analysis of population dynamics with confidence intervals, demonstrated on human and bird data.

## Contribution

It develops parameter estimation techniques for Markovian binary trees with TMAP, including optimal phase selection and confidence interval computation, applied to real demographic data.

## Key findings

- Effective parameter estimation methods for TMAP-based Markovian binary trees.
- Optimal phase number selection improves model fit.
- Confidence intervals provide uncertainty quantification for model outputs.

## Abstract

We consider a class of branching processes called Markovian binary trees, in which the individuals lifetime and reproduction epochs are modeled using a transient Markovian arrival process (TMAP). We estimate the parameters of the TMAP based on population data containing information on age-specific fertility and mortality rates. Depending on the degree of detail of the available data, a weighted non-linear regression method or a maximum likelihood method is applied. We discuss the optimal choice of the number of phases in the TMAP, and we provide confidence intervals for the model outputs. The results are illustrated using real data on human and bird populations.