Open Neighborhood Seminar: Inferring the past with Bayes’ rule

SEMINARS, OPEN NEIGHBORHOOD

Speaker:

Arthur Parzygnat - MIT

We make predictions of the future by using initial conditions and the probabilities of transitioning from one state to another via some process. To make inference about the past, we can use final conditions and knowledge of the process together with Bayes’ rule, given by the formula P(y|x)P(x)=P(x|y)P(y). But can we define an intuitive, yet completely rigorous, mathematical framework for what it means to make consistent inferences about the past using only the idea of processes, without any reference to probabilities? In this talk, I will introduce ideas of categorical thinking to indicate how Bayes’ rule might be characterized in such a way.

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https://people.math.harvard.edu/~gammage/ons/