Adaptive Bayesian Learning with Action and State-Dependent Signal Variance

Bayesian learning, a fundamental concept in statistical inference and decision-making, has gained significant traction across various fields due to its ability to integrate prior knowledge with new information. As a robust methodology, Bayesian learning has been widely acknowledged for its adaptability and precision in handling uncertainty and updating beliefs (Gelman et al., 1995). This manuscript expands upon the Bayesian learning framework (Baley and Veldkamp, 2023) through uniquely addressing the action and state-dependent signal variance in the agents' information set. At the core of this framework is the concept that the precision of the signal received by an agent is contingent upon both the agent's action and the actual state, for example, based on their congruence or tracking error (Daly, 2018; du Sart and van Vuuren, 2021; Orlik and Veldkamp, 2014; Rompotis, 2011; Stone et al., 2013; Yang and Huang, 2022).