Your friends and colleagues are talking about something called “Bayes’s
Theorem” or “Bayes’s Rule,” or something called Bayesian reasoning. They
sound really enthusiastic about it, too, so you google and find a web page
about Bayes’s Theorem and... It’s this equation. That’s all. Just one
equation. The page you found gives a definition of it, but it doesn’t say
what it is, or why it’s useful, or why your friends would be interested in
it. It looks like this random statistics thing. Why does a mathematical
concept generate this strange enthusiasm in its students? What is the
so-called Bayesian Revolution now sweeping through the sciences, which
claims to subsume even the experimental method itself as a special case?
What is the secret that the adherents of Bayes know? What is the light
that they have seen? Soon you will know. Soon you will be one of us.
While there are a few existing online explanations of Bayes’s Theorem, my
experience with trying to introduce people to Bayesian reasoning is that
the existing online explanations are too abstract. Bayesian reasoning is
very counterintuitive. People do not employ Bayesian reasoning
intuitively, find it very difficult to learn Bayesian reasoning when
tutored, and rapidly forget Bayesian methods once the tutoring is over.
This holds equally true for novice students and highly trained
professionals in a field. Bayesian reasoning is apparently one of those
things which, like quantum mechanics or the Wason Selection Test, is
inherently difficult for humans to grasp with our built-in mental
faculties. Or so they claim. Here you will find an attempt to offer an
intuitive explanation of Bayesian reasoning—an excruciatingly gentle
introduction that invokes all the human ways of grasping numbers, from
natural frequencies to spatial visualization. The intent is to convey, not
abstract rules for manipulating numbers, but what the numbers mean, and
why the rules are what they are (and cannot possibly be anything else).
When you are finished reading this, you will see Bayesian problems in your