An introduction to Bayesian analysis and why you might care. The
subject of statistics is about how to learn. Given that it is
about the unknown, it shouldn’t be surprising that there are
deep differences of opinion on how to go about doing it (in
spite of the stereotype that statisticians are accountants minus
the personality). A slightly simplistic division of statistical
philosophies is: - frequentist estimator - frequentist tester
We’ll explore that division with the coin in my pocket. Flip a
coin What’s the probability — sight unseen — that a flip of my
coin will be heads? The frequentist estimator will say that
without data there is no way to tell — it could be anything.
We’re in complete ignorance. The frequentist tester will
probably hypothesize that the probability is one-half, then say
there is no evidence to reject that hypothesis. A Bayesian will
say that the probability has a distribution centered on one-half
and is close to it. Something like the distribution in Figure 1.
A smarter Bayesian will