Adaptive Bayesian Learning with Action and State-Dependent Signal Variance

This manuscript presents an advanced framework for Bayesian learning by incorporating action and state-dependent signal variances into decision-making models. This framework is pivotal in understanding complex data-feedback loops and decision-making processes in various economic systems. Through a series of examples, we demonstrate the versatility of this approach in different contexts, ranging from simple Bayesian updating in stable environments to complex models involving social learning and state-dependent uncertainties. The paper uniquely contributes to the understanding of the nuanced interplay between data, actions, outcomes, and the inherent uncertainty in economic models.