Calibration of a bumble bee foraging model using Approximate Bayesian Computation

Abstract

1. Challenging calibration of complex models can be approached by using prior knowledge on the parameters. However, the natural choice of Bayesian inference can be computationally heavy when relying on Markov Chain Monte Carlo (MCMC) sampling. When the likelihood of the data is intractable, alternative Bayesian methods have been proposed. Approximate Bayesian Computation (ABC) only requires sampling from the data generative model, but may be problematic when the dimension of the data is high. 2. We studied alternative strategies to handle high dimensional data in ABC applied to the calibration of a spatially explicit foraging model for \textit{Bombus terrestris}. The first step consisted in building a set of summary statistics carrying enough biological meaning, i.e. as much as the original data, and then applying ABC on this set. Two ABC strategies, the use of regression adjustment leading to the production of ABC posterior samples, and the use of machine learning approaches to approximate ABC posterior quantiles, were compared with respect to coverage of model estimates and true parameter values. The comparison was made on simulated data as well as on data from two field studies. 3. Results from simulated data showed that some model parameters were easier to calibrate than others. Approaches based on random forests in general performed better on simulated data. They also performed well on field data, even though the posterior predictive distribution exhibited a higher variance. Nonlinear regression adjustment performed better than linear ones, and the classical ABC rejection algorithm performed badly. 4. ABC is an interesting and appealing approach for the calibration of complex models in biology, such as spatially explicit foraging models. However, while ABC methods are easy to implement, they require considerable tuning.