Suppose we aim to efficiently calculate the posterior distribution of certain parameters for a regression model as data arrives in a continuous stream. The sequential updating characteristic of Bayesian inference would be beneficial. However, I have observed that it is not possible to update posteriors sequentially using PyMC, and I am uncertain if any other probabilistic packages support this feature?
I am curious about the reason behind the difficulty in achieving this. Could it be because the priors, initially independent, become correlated after computations, and this correlation goes unnoticed?
I am keen to delve deeper into this issue and understand the underlying reasons. Additionally, I am interested in hearing about techniques to address this challenge.