The Mathematics of Teaching Pigs

The old saying goes:

"Never try to teach a pig to sing. You make the pig mad. You make yourself mad. You still don't end up with a pig that can sing."

But what do Bayesian Statistics have to say about all this?

From Wikipedia


"....Bayesian statisticians argue that even when people have very different prior subjective probabilities, new evidence from repeated observations will tend to bring their posterior subjective probabilities closer together. However, others argue that when people hold widely different prior subjective probabilities their posterior subjective probabilities may never converge even with repeated collection of evidence. These critics argue that worldviews which are completely different initially can remain completely different over time despite a large accumulation of evidence......"

Lindley's paradox describes a counterintuitive situation in statistics in which the Bayesian and frequentist approaches to a hypothesis testing problem give opposite results for certain choices of the prior distribution.

The Net

If a person places a high probability of truth on their initial belief, they may never change their mind no matter what new information arrives.

That Pig Won't Sing! You will make yourself and the pig mad! Run Away!