Do you want to become stronger in the way of Bayes? This post is intended for people whose understanding of Bayesian probability theory is currently somewhat tentative (between levels 0 and 1 to use a previous post's terms), and who are interested in developing deeper knowledge through deliberate practice.
Our intention is to form an online self-study group composed of peers, working with the assistance of a facilitator - but not necessarily of a teacher or of an expert in the topic. Some students may be somewhat more advanced along the path, and able to offer assistance to others.
Our first text will be E.T. Jaynes' Probability Theory: The Logic of Science, which can be found in PDF form (in a slightly less polished version than the book edition) here or here.
We will work through the text in sections, at a pace allowing thorough understanding: expect one new section every week, maybe every other week. A brief summary of the currently discussed section will be published as an update to this post, and simultaneously a comment will open the discussion with a few questions, or the statement of an exercise. Please use ROT13 whenever appropriate in your replies.
A first comment below collects intentions to participate. Please reply to this comment only if you are genuinely interested in gaining a better understanding of Bayesian probability and willing to commit to spend a few hours per week reading through the section assigned or doing the exercises.
As a warm-up, participants are encouraged to start in on the book:
Preface
Most of the Preface can be safely skipped. It names the giants on whose shoulders Jaynes stood ("History", "Foundations"), deals briefly with the frequentist vs Bayesian controversy ("Comparisons"), discusses his "Style of Presentation" (and incidentally his distrust of infinite sets), and contains the usual acknowledgements.
One section, "What is 'safe'?", stands out as making several strong points about the use of probability theory. Sample: "new data that we insist on analyzing in terms of old ideas (that is, models which are not questioned) cannot lead us out of the old ideas". (The emphasis is Jaynes'. This has an almost Kuhnian flavor.)
Discussion on the Preface starts with this comment.
Yes!
This reflects in the fact that great artists are invariably technical virtuosos. Mastery makes way for creativity.
This is due to limited working memory. You may be able to juggle the concepts/math of a particular field in working memory, but that takes away precious space for the combinatorial exploration of novel ideas, or even higher level concepts. Only with practice, when most of the steps in your thought processes can be carried out subconsciously, are you free to do higher-level thinking.
It's not all about working memory of course, since there is subconscious exploration going on as well. Still, things must surface to working memory to be checked that they make sense.
Also, there is also the fact that concepts are built upon concepts. To think at a higher level, you have to truly understand how concepts of the lower level work. It is simply impossible to do it all with limited working memory capacity.