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

# Minor Points

## Section "Why is Bayes' Theorem of interest"

- Change "interest" to "Interest" in section title. Tested with Headline Capitalization Website.

## 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.