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In my field (Epidemiology), when doing Bayesian analysis, it is very common to set one's priors to be a distribution. Sometimes the point estimate and spread of
by Fomite 11y ago
In my field (Epidemiology), when doing Bayesian analysis, it is very common to set one's priors to be a distribution. Sometimes the point estimate and spread of a previously conducted study or meta-analysis, sometimes merely a uniform distribution with upper and lower bounds ("It is extremely unlikely that the relative risk of disease for this exposure is below 0.01 or above 100...")
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.
- skybrian 11y agoHow does that work? It doesn't sound like a well-defined distribution since the area under the curve needs to be 1.
- Fomite 11y agoIt'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.
- bmh100 11y agoIt 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.
- gipp 11y agoI think he was referring specifically to an unbounded uniform distribution, which is indeed not well-defined.
- tel 11y agoIt turns out that priors don't actually need to be distributions all the time. This often occurs when seeking maximally "uninformative" priors.
- jsprogrammer 11y agoBayesian analysis comes directly from the probability axioms, which are 'frequentist'.
- XFrequentist 11y agoHuh? You mean the Kolmogorov axioms? In what sense are these 'frequentist'?
- jsprogrammer 11y agoThe third axiom just counts the event space.
- cwhy 11y agoThat's the right bottom part of the Bayes' rule?