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

• Published in: PLoS computational biology Vol. 15; no. 6; p. e1007043
• Main Authors: Piray, Payam, Dezfouli, Amir, Heskes, Tom, Frank, Michael J., Daw, Nathaniel D.
• Format: Journal Article
• Language: English
• Published: United States Public Library of Science 01.06.2019; Public Library of Science (PLoS)
• Subjects: Bayes Theorem; Bayesian analysis; Biology and Life Sciences; Computation; Computational Biology - methods; Computational neuroscience; Computer Simulation; Data analysis; Decision making; Decision Making - physiology; Estimates; Humans; Learning - physiology; Mathematical models; Medical imaging; Medicine and Health Sciences; Models, Neurological; Nervous system; Neurological research; Neurosciences; Normal distribution; Outliers (statistics); Parameter estimation; Parkinson's disease; Physical Sciences; Population; Population (statistical); Research and Analysis Methods; Social Sciences; Software; Statistical inference; Statistical methods; United States; United States > US; New Jersey
• ISSN: 1553-7358; 1553-734X; 1553-7358
• DOI: 10.1371/journal.pcbi.1007043

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.