[ExI] A guide to Bayes Theorem

[BillK]

John Horgan has written a basic guide to Bayes Theorem.

Bayes’ theorem, touted as a powerful method for generating knowledge,
can also be used to promote superstition and pseudoscience.
By John Horgan on January 4, 2016
<http://blogs.scientificamerican.com/cross-check/bayes-theorem-what-s-the-big-deal/>

Quotes:

Consider the cancer-testing case: Bayes’ theorem says your probability
of having cancer if you test positive is the probability of a true
positive test divided by the probability of all positive tests, false
and true. In short, beware of false positives.

Here is my more general statement of that principle: The plausibility
of your belief depends on the degree to which your belief--and only
your belief--explains the evidence for it. The more alternative
explanations there are for the evidence, the less plausible your
belief is. That, to me, is the essence of Bayes’ theorem.

“Alternative explanations” can encompass many things. Your evidence
might be erroneous, skewed by a malfunctioning instrument, faulty
analysis, confirmation bias, even fraud. Your evidence might be sound
but explicable by many beliefs, or hypotheses, other than yours.

In other words, there’s nothing magical about Bayes’ theorem. It boils
down to the truism that your belief is only as valid as its evidence.
If you have good evidence, Bayes’ theorem can yield good results. If
your evidence is flimsy, Bayes’ theorem won’t be of much use. Garbage
in, garbage out.
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BillK