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Questions tagged [improper-prior]

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12
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1answer
308 views

When should I be worried about the Jeffreys-Lindley paradox in Bayesian model choice?

I am considering a large (but finite) space of models of varying complexity which I explore using RJMCMC. The prior on the parameter vector for each model is fairly informative. In what cases (if any)...
14
votes
2answers
1k views

Sampling from an Improper Distribution (using MCMC and otherwise)

My basic question is: how would you sample from an improper distribution? Does it even make sense to sample from an improper distribution? Xi'an's comment here kind of addresses the question, but I ...
1
vote
2answers
794 views

Haldane's prior Beta(0,0) - Part 1

This article$^1$ on p.16 specifies Haldane's prior as: $$p(\theta) = \frac{1}{θ(1−θ)}$$. However, other$^2$ source on p.6 specifies Haldane's prior as proportional to $\frac{1}{θ(1−θ)}$, i.e. $$p(\...
3
votes
2answers
966 views

Does “improper” posterior or prior refer to a density function that does not integrate to 1 or to one that does not integrate to a finite value?

I am a bit confused about improper priors and posteriors. I have seen references that classify a prior or posterior probability density function as "improper" if the integral over infinite support ...
2
votes
1answer
138 views

How to choose a importance density for Jeffreys prior?

I want to draw Bayesian inference via importance sampling and I do not come up with a good idea of an importance density for $$p(\sigma)\sim\frac{1}{\sigma}.$$ Is there a way to sample from this ...