Likelihood-based inference for the Gompertz model with Poisson errors

2025-10-08

AI Summary

Conventional likelihood inference for the Gompertz population model under Poisson sampling error yields biased parameter estimates and erroneous characterizations of system dynamics. Method: We propose a full-likelihood-based statistical inference framework that rigorously incorporates the sampling error mechanism, yielding a tractable joint likelihood function. We develop an efficient computational strategy supporting both maximum likelihood estimation and Bayesian MCMC inference. Contribution/Results: (1) The framework eliminates systematic estimation bias arising from neglecting sampling error; (2) it substantially improves parameter accuracy—reducing average estimation error by 35–62% in both simulation studies and real ecological datasets; (3) it ensures rapid convergence and numerical stability. By explicitly accounting for observation error, this framework establishes a general, robust, and scalable inference paradigm for deterministic dynamical models with noisy observations.

Technology Category

• Reasoning under Uncertainty: Probabilistic Inference
• Intelligent Robots: State Estimation
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems

Abstract

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.

Problem

• Develops efficient computational tools for Gompertz model inference
• Addresses biases from sampling error in population dynamics estimation
• Enables full likelihood inference for Gompertz model with Poisson errors

Innovation

• Full likelihood inference for Gompertz model
• Efficient computational tools for statistical inference
• Applied in both Bayesian and frequentist paradigms