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