Re:Bayes's Theorem: What's the Big Deal?
by skybrian on Tuesday January 05, 2016 @12:20PM
(#10844487)
How does that work? It doesn't sound like a well-defined distribution since the area under the curve needs to be 1.
It has to do with calculus. If the probability of a given result approaches zero as the result itself approaches positive or negative infinity, then the area under the curve approaches 1.
Imagine 1/2 + 1/4 + 1/8 ... to infinity. The sum approaches 1 as the denominator approaches infinity. With calculus, we can determine that with mathematical methods.
I think he was referring specifically to an unbounded uniform distribution, which is indeed not well-defined.
It's more of a philosophical statement than an actual implementation. Mainly that frequentist analysis begins with the prior "I dunno, could be anything..."
See also: The calculus answer.
It turns out that priors don't actually need to be distributions all the time. This often occurs when seeking maximally "uninformative" priors.
Re:Bayes's Theorem: What's the Big Deal?
by jsprogrammer on Tuesday January 05, 2016 @01:46PM
(#10845098)
Bayesian analysis comes directly from the probability axioms, which are 'frequentist'.
Re:Bayes's Theorem: What's the Big Deal?
by XFrequentist on Tuesday January 05, 2016 @04:14PM
(#10846105)
Huh? You mean the Kolmogorov axioms? In what sense are these 'frequentist'?
Re:Bayes's Theorem: What's the Big Deal?
by jsprogrammer on Tuesday January 05, 2016 @06:30PM
(#10847021)
The third axiom just counts the event space.
It's been argued that frequentist analysis is essentially a Bayesian analysis with a prior distribution centered on zero with bounds from positive to negative infinity.