Posterior for Gaussian Distribution with unknown Mean

[@user-or7ji5hv8y]

The TensorFlow Probability example was really helpful again. I was wondering though, if there is any intuition as to why sigma_N is substantially smaller than sigma_true and sigma_0.

[@MachineLearningSimulation]

Thanks again for your feedback :) I really appreciate it. Regarding the small sigma_N: From a mathematical perspective it seems reasonable (it always reminds me of electrical circuits, if you have two resistors in parallel, then the total resistance is smaller than the smallest resistance). But a more intuitive approach: In the prior we have prior knowledge on our parameter mu, encoded by mu_0 and sigma_0. The mu_0 describes where we expect the mu to be and the sigma_0 encodes our uncertainty about that. If we now observe data and the data is in agreement with what we expected before, our posterior sigma_N must be smaller. That is because a smaller standard deviation is associated with a more narrow Gaussian, hence in the posterior we are more certain on where the parameter mu is. I hope this made sense. Let me know if it still unclear. :)