Minor Review: Machine Learning Fundamentals - Probability Theory - Bayes Theorem

Minor Points

Section "Why is Bayes' Theorem of interest"

Section "Bayes Theorem"

  • From a notebook editors point of view, it would be nicer to have many small markdown cells instead of a few large ones (personal opinion). When douple clicking on a cell for editing, it jumps down to the bottom of the cell and then it's hard to locate the desired position in the markdown code.
  • Change p(A|B) to p(A \mid B) after "From the visualization it becomes clear that the following applies:"
  • Change p(A|B) to p(A \mid B) in sentence "The mathematical notation for such a question is a conditional probability p(A|B), [...]"
  • Missing period at the end of sentence "[...] divided by the cardinality of universe \Omega".

Section "Cookie Problem Example"

  • "in praxis" -> "in practice"
  • Bayes-Theorem_Cookie_Equation.png looks blurry

Major Points and General Thoughts

Please take the following points only as consideration and not as a major criticism:

  • In this notebook A and B denote sets of specific events. For example A is "Number of cases where chocolate addiction is present". Therefore p(A) is only a single probability value. When I'm reading p(A), I would usually think of A (Addicted) as a random variable that can take on several values like A=positive or A=negative. A would be a probability table.

  • The same comes to mind in the Cookie Problem example. There is no clear distinction between a random variable ("Cookie" or "Bowl") and a certain value (e.g. "Vanilla" or "1") this variable can take.

  • I don't even know if my concerns are valid here, because you are using a set notation and capital A is perfectly fine to describe a set. Also the notation is consistent throughout the notebook. I'm just concerned about later examples, like in my Cookie Problem Exercise notebook, where something like P(A) describes a probability table and P(A=positive) or P(A=negative) the possible values (subtables), which might be confusing.

  • In my notebooks I'm using P(A \mid B) with upper case P instead of p(A \mid B). Is there a special meaning in lower case P over upper case P. If not, we should agree on one of these notations.

Section "Why is Bayes' Theorem of interest"

  • I think the "Disease" example is incomplete because the prevalence (probability of disease occurring in population) is missing.

Final Thoughts

Overall the notebook provides a very good explanation and the visual approach gave me a new understanding of this topic, although I was already familiar with Bayes' Theorem.

The art style is great and we should use it in other notebooks as well.

Edited by Christoph