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In an ideal setting for Bayesian agents, a perfect description of the rulesof the environment (i.e., the objective observation model) is available,allowing them to reason through the Bayesian posterior to update their beliefsin an optimal way. But such an ideal setting hardly ever exists in the naturalworld, so agents have to make do with reasoning about how they should updatetheir beliefs simultaneously. This introduces a number of related challengesfor a number of research areas: (1) For Bayesian statistics, this deviation ofthe subjective model from the true data-generating mechanism is termed modelmisspecification in the literature. (2) For neuroscience, it introduces thenecessity to model how the agents' belief updates (how they use evidence toupdate their belief) and how their belief changes over time. The current paperaddresses these two challenges by (a) providing a general class ofposteriors/belief updates called cut-posteriors of Bayesian networks that havea much greater expressivity, and (b) parameterizing the space of possibleposteriors to make meta-learning (i.e., choosing the belief update from thisspace in a principled manner) possible. For (a), it is noteworthy that anycut-posterior has local computation only, making computation tractable forhuman or artificial agents. For (b), a Markov Chain Monte Carlo algorithm toperform such meta-learning will be sketched here, though it is only anillustration and but no means the only possible meta-learning procedurepossible for the space of cut-posteriors. Operationally, this work gives ageneral algorithm to take in an arbitrary Bayesian network and output allpossible cut-posteriors in the space.

A General Space of Belief Updates for Model Misspecification in Bayesian Networks