[cgel]

Author here. The blog post contains a clear explanation of Bayesian Inference and provides careful arguments about its potential benefits and limitations. Further, Bayes rule was typed correctly when it was being used to show that the posterior q(f^*|D) \approx q(f_\theta|D).

We understand Bayes rule... just had a typo and when proof reading the article we didn't check the first equation because: Who would mess up Bayes rule?

[inciampati]

Is the posterior really an update of our prior? That doesn't make any sense to me. It's P(A|B). I can't then use it as P(A) in another inference based on different observations. What am I missing about your description of Bayesian inference?

[cgel]

Imagine you have two random variables A and B, which are 0 with prob 0.5 and 1 with prob 0.5. They just have the property that when A=1 then B is always 0 and vice versa. Thus, when you have seen the value of B, that clearly has changed the distribution of A. You should read P(A) as: the distribution of A when I know nothing about the world. And P(A|B=0) as: the distribution of A when I know that B took on value 0.