An example of how an improper prior leads to an improper posterior

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Provides an illustration of how choosing a prior probability distribution which is not valid can lead to an improper posterior distribution.

  1. Ben Lambert
  2. econometrics
  3. statistics
  4. bayesian
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I've come across this several times, 'the posterior is proportional to the numerator.' I'm a little lost; don't we need an exact result? Or is there a simpler method to account for the denominator in some desired output?

jacobmoore
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If a prior is for example that P(theta = theta*) = 1; i.e. the person is without looking at the data certain that theta is equal to theta*, e.g. 0.5 (fair coin). would the posterior distribution then always be equal to the prior and there is never any updating?

luupio
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How do you divide by 0? When theta is equals to 1 or 0

batyr