Probabilistic models of decision making under various forms of uncertainty have been applied in recent years to numerous behavioral and model-based fMRI studies. These studies were highly successful in enabling a better understanding of behavior and delineating the functional properties of brain areas involved in decision making under uncertainty. However, as different studies considered different models of decision making under uncertainty, it is unclear which of these computational models provides the best account of the observed behavioral and neuroimaging data. This is an important issue, as not performing model comparison may tempt researchers to over-interpret results based on a single model. Here we describe how in practice one can compare different behavioral models and test the accuracy of model comparison and parameter estimation of Bayesian and maximum-likelihood based methods. We focus our analysis on two well-established hierarchical probabilistic models that aim at capturing the evolution of beliefs in changing environments: Hierarchical Gaussian Filters and Change Point Models. To our knowledge, these two, well-established models have never been compared on the same data. We demonstrate, using simulated behavioral experiments, that one can accurately disambiguate between these two models, and accurately infer free model parameters and hidden belief trajectories (e.g., posterior expectations, posterior uncertainties, and prediction errors) even when using noisy and highly correlated behavioral measurements. Importantly, we found several advantages of Bayesian inference and Bayesian model comparison compared to often-used Maximum-Likelihood schemes combined with the Bayesian Information Criterion. These results stress the relevance of Bayesian data analysis for model-based neuroimaging studies that investigate human decision making under uncertainty.

Probabilistic models of decision making under various forms of uncertainty have been applied in recent years to numerous behavioral and model-based fMRI studies. These studies were highly successful in enabling a better understanding of behavior and delineating the functional properties of brain areas involved in decision making under uncertainty. However, as different studies considered different models of decision making under uncertainty, it is unclear which of these computational models provides the best account of the observed behavioral and neuroimaging data. This is an important issue, as not performing model comparison may tempt researchers to over-interpret results based on a single model. Here we describe how in practice one can compare different behavioral models and test the accuracy of model comparison and parameter estimation of Bayesian and maximum-likelihood based methods. We focus our analysis on two well-established hierarchical probabilistic models that aim at capturing the evolution of beliefs in changing environments: Hierarchical Gaussian Filters and Change Point Models. To our knowledge, these two, well-established models have never been compared on the same data. We demonstrate, using simulated behavioral experiments, that one can accurately disambiguate between these two models, and accurately infer free model parameters and hidden belief trajectories (e.g., posterior expectations, posterior uncertainties, and prediction errors) even when using noisy and highly correlated behavioral measurements. Importantly, we found several advantages of Bayesian inference and Bayesian model comparison compared to often-used Maximum-Likelihood schemes combined with the Bayesian Information Criterion. These results stress the relevance of Bayesian data analysis for model-based neuroimaging studies that investigate human decision making under uncertainty.