<p>Population dynamics models play an important role in several fields, such as actuarial science, demography, and ecology, as they help explain past fluctuations and predict future populations. 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 with Poisson errors is widely used to infer population abundance dynamics, but a full likelihood approach can be computationally prohibitive. 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 using models in the Bayesian and frequentist paradigms. Performance is illustrated with simulations and data analysis.</p>