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)
top(A \mid B)
after "From the visualization it becomes clear that the following applies:" - Change
p(A|B)
top(A \mid B)
in sentence "The mathematical notation for such a question is a conditional probabilityp(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 ofp(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.