A Hierarchical Bayesian Model for Inferring and Decision Making in Multi-Dimensional Volatile Binary Environments

Abstract

The ability to track the changes of the surrounding environment is critical for humans and animals to adapt their behaviors. In high-dimensional environments, the interactions between each dimension need to be estimated for better perception and decision making, for example in volatile or social cognition tasks. We develop a hierarchical Bayesian model for inferring and decision making in multi-dimensional volatile environments. The hierarchical Bayesian model is composed of a hierarchical perceptual model and a response model. Using the variational Bayes method, we derived closed-form update rules. These update rules also constitute a complete predictive coding scheme. To validate the effectiveness of the model in multi-dimensional volatile environments, we defined a probabilistic gambling task modified from a two-armed bandit. Simulation results demonstrated that an agent endowed with the proposed hierarchical Bayesian model is able to infer and to update its internal belief on the tendency and volatility of the sensory inputs. Based on the internal belief of the sensory inputs, the agent yielded near-optimal behavior following its response model. Our results pointed this model a viable framework to explain the temporal dynamics of human decision behavior in complex and high dimensional environments.

Keywords

• Bayesian inference
• filtering
• free energy
• decision making
• predictive coding
• volatility