Bayes' theorem looks innocent enough, but from it emerges an entire school of statistical reasoning, Bayesian statistics. We have a hypothesis $A$, which might be true or false. A priori we think it is true with probability $p$. We collect some data and then want to update our belief that $A$ is true, that is find $P(A\mid\text{data})$. We can find the answer using $P(\text{data}\mid A)$ and Bayes' theorem.
Here is a YouTube video of students in a sing-a-long of George Box's "There's no theorem like Bayes' theorem", sung to the tune of "There's no business like show business".
There's no theorem like Bayes' theorem
Like no theorem we know
Everything about it is appealing
Everything about it is a wow
Let out all that a priori feeling
You've been concealing right up to now!
Here is a YouTube video of students in a sing-a-long of George Box's "There's no theorem like Bayes' theorem", sung to the tune of "There's no business like show business".
There's no theorem like Bayes' theorem
Like no theorem we know
Everything about it is appealing
Everything about it is a wow
Let out all that a priori feeling
You've been concealing right up to now!
Further words are here.
