Likelihood-based inference for the Gompertz model with Poisson errors

Population dynamics models play an important role in a number of fields, such as actuarial science, demography, and ecology. 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 based on the full likelihood. The approach is illustrated in both the Bayesian and frequentist paradigms. Performance is illustrated with simulations and data analysis.