I find it prohibitively difficult to extract information from out-of-context slides. Especially if the slides are supposed to be an introduction to a new topic.
I couldn't agree more. Whenever these sorts of posts pop up, I end up wasting several minutes searching the page to see if I'm missing some kind of audio or video component, or even just a transcript of the talk.
As a rather short (9 pages) introduction to Bayesian inference, I remember greatly appreciating an extract from the book "Information Theory, Inference, and Learning Algorithms" by David MacKay.
It explains how Bayesian inference works (which is intuitive and not strange at all) and gives examples of absurdities that comes upon you when you don't do it this way.
Highlights:
• "Let me through, I’m a Bayesian" (When analysing the effectivness of a vaccine)
• "I have no problem with the idea that there is only one answer to a well-posed problem" (In response to sampling theorists wide selection of ad hoc procedures)
The notational part of this debate is definitely not agreed upon. Andrew Gelman and Christian Robert both argue for p(data|H_0) in comments on those blog posts.
>I fully agree with Andrew that, from an objective perspective, there is no misunderstanding whatsoever. Unless you get into arcane measure theory details, conditioning upon a value and taking this value as fixed amount to the same thing. Discussing about notations does not seem like an optimal use of our time (times?)…
There simply is no difference between conditioning on a value chosen before hand vs treating it as fixed. If you imagine a Venn diagram of the two scenarios, the event space under question is exactly the same. Whether your conditioning value can actually change (a rv) or whether it is universally constant, you are still only considering the space where your conditioned value is fixed.
