Likelihood-based inference for the Gompertz model with Poisson errors
Abstract
Population dynamics models play an important role in a number of fields, such as actuarial science, demography, and ecology, as they help explain past fluctuations and predict future population. The accuracy of these models is often influenced by the uncertainty introduced by sampling error. Statistical inference for these models can be difficult when, in addition to the process' inherent stochasticity, one also needs to account for sampling error. Ignoring the latter can lead to biases in the estimation, which in turn can produce erroneous conclusions about the system's behavior. The Gompertz model is widely used to infer population size dynamics, but a full likelihood approach can be computationally prohibitive when sampling error is accounted for. We close this gap by developing efficient computational tools for statistical inference in the Gompertz model with Poisson sampling error based on the full likelihood. The approach is illustrated in both the Bayesian and frequentist paradigms. Performance is illustrated with simulations and data analysis.
Cite
@article{arxiv.2510.06787,
title = {Likelihood-based inference for the Gompertz model with Poisson errors},
author = {Paolo Onorati and Sofia Ruiz-Suarez and Radu Craiu},
journal= {arXiv preprint arXiv:2510.06787},
year = {2025}
}