Hierarchical Bayesian inference for concurrent model fitting and comparison for group studies

Computational modeling plays an important role in modern neuroscience research. Much previous research has relied on statistical methods, separately, to address two problems that are actually interdependent. First, given a particular computational model, Bayesian hierarchical techniques have been used to estimate individual variation in parameters over a population of subjects, leveraging their population-level distributions. Second, candidate models are themselves compared, and individual variation in the expressed model estimated, according to the fits of the models to each subject. The interdependence between these two problems arises because the relevant population for estimating parameters of a model depends on which other subjects express the model. Here, we propose a hierarchical Bayesian inference (HBI) framework for concurrent model comparison, parameter estimation and inference at the population level, combining previous approaches. We show that this framework has important advantages for both parameter estimation and model comparison theoretically and experimentally. The parameters estimated by the HBI show smaller errors compared to other methods. Model comparison by HBI is robust against outliers and is not biased towards overly simplistic models. Furthermore, the fully Bayesian approach of our theory enables researchers to make inference on group-level parameters by performing HBI t-test. Author summary Computational modeling of brain and behavior plays an important role in modern neuroscience research. By deconstructing mechanisms of behavior and quantifying parameters of interest, computational modeling helps researchers to study brain-behavior mechanisms. In neuroscience studies, a dataset includes a number of samples, and often the question of interest is to characterize parameters of interest in a population: Do patients with attention-deficit hyperactive disorders exhibit lower learning rate than the general population? Do cognitive enhancers, such as Ritalin, enhance parameters influencing decision making? The success of these efforts heavily depends on statistical methods making inference about validity and robustness of estimated parameters, as well as generalizability of computational models. In this work, we present a novel method, hierarchical Bayesian inference, for concurrent model comparison, parameter estimation and inference at the population level. We show, both theoretically and experimentally, that our approach has important advantages over previous methods. The proposed method has implications for computational modeling research in group studies across many areas of psychology, neuroscience, and psychiatry.