Abstract
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.
Highlights
Across different areas of neuroscience, researchers increasingly employ computational models for experimental data analysis
We present a novel method, hierarchical Bayesian inference, for concurrent model comparison, parameter estimation and inference at the population level
We introduce a hierarchical and Bayesian inference method, which solves these problems by addressing both model fitting and model comparison within the same framework using variational techniques
Summary
Across different areas of neuroscience, researchers increasingly employ computational models for experimental data analysis. Decision neuroscientists use reinforcement learning (RL) and economic models of choice to analyze behavioral and brain imaging data in reward learning and decision-making tasks [1, 2]. Neuroimaging studies use models of neural interaction, such as dynamic causal modeling [7, 8], as well as abstract models to analyze brain signals [2, 9]. The success of these efforts heavily depends on statistical methods making inference about validity and robustness of estimated parameters across individuals, as well as making inference on validity and generalizability of computational models. A key theoretical and practical issue has been capturing individual variation both in a model’s parameters and in which of several candidate models a subject expresses, which may vary from subject to subject
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