Inference for Partially Observed Multitype Branching Processes and Ecological Applications

TL;DR

This paper develops statistical inference methods for multitype branching processes with partial observation, focusing on ecological applications like plant populations, and analyzes estimator properties under various data limitations.

Contribution

It provides new identifiability results and estimation techniques for partially observed multitype branching processes, including non-Poisson models, with theoretical guarantees.

Findings

Identifiability holds for all parameters with full data.

Estimators are consistent and asymptotically Gaussian.

Good estimator performance even when data deviate from Poisson assumptions.

Abstract

Multitype branching processes with immigration in one type are used to model the dynamics of stage-structured plant populations. Parametric inference is first carried out when count data of all types are observed. Statistical identifiability is proved together with derivation of consistent and asymptotically Gaussian estimators for all the parameters ruling the population dynamics model. However, for many ecological data, some stages (i.e. types) cannot be observed in practice. We study which mechanisms can still be estimated given the model and the data available in this context. Parametric inference is investigated in the case of Poisson distributions. We prove that identifiability holds for only a subset of the parameter set depend- ing on the number of generations observed, together with consistent and asymptotic properties of estimators. Finally, simulations are performed to study the behaviour of the estimators when the model is no longer Poisson. Quite good results are obtained for a large class of models with distributions having mean and variance within the same order of magnitude, leading to some stability results with respect to the Poisson assumption.