Fast Bayesian parameter estimation for stochastic logistic growth models.

Area of Science:

• Ecology
• Computational Biology
• Mathematical Biology

Background:

• Stochastic differential equation (SDE) models are used for population growth but are computationally intensive.
• Analytical solutions for the transition density of logistic growth SDEs with multiplicative noise are intractable.
• Parameter inference for these models often relies on slow numerical simulations.

Purpose of the Study:

• To develop computationally efficient approximations for stochastic logistic growth models.
• To enable fast parameter inference using analytical methods.
• To assess the accuracy and applicability of these approximations for real biological data.

Main Methods:

• Derivation of two linear noise approximation (LNA) models from a logistic growth SDE.
• Implementation of Bayesian inference with Kalman filter recursion for marginal likelihood computation.
• Comparison of LNA models against exact numerical simulations and a related approximation.

Main Results:

• Fast LNA models yield posterior distributions comparable to slow, exact models.
• Simulations from LNA models better represent stochastic logistic growth dynamics than alternative approaches.
• An LNA model with additive noise and measurement error demonstrated superior performance on microbial population data.

Conclusions:

• Linear noise approximation provides a computationally efficient and accurate method for inferring parameters of stochastic logistic growth models.
• These LNA models offer a viable alternative to slow numerical simulations for SDE model fitting.
• The developed LNA models are effective for analyzing real-world biological population data, particularly in high-throughput screening experiments.