# Questions tagged [improper-prior]

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### 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 ...
1answer
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### 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)...
2answers
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### Difference between non-informative and improper Priors

I wonder what is the difference between these two kind of priors: Non-informative Improper
3answers
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### verifying a posterior is proper

There's a homework problem in a textbook that asks to verify propriety of a certain posterior distribution, and I'm having a little trouble with it. The setup is you have a logistic regression model ...
2answers
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### 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 ...
2answers
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### Gaussian mixture model - does an improper uniform prior give a proper posterior?

We draw $n$ i.i.d. points $x_1 , x_2 , ..., x_n$ from the following Gaussian mixture: $$p(x|\mu_1,\mu_2) = \frac{1}{2} \text{N} (x|\mu_1,1) + \frac{1}{2} \text{N} (x|\mu_2,1).$$ The prior is the ...
1answer
147 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 ...
1answer
72 views

### Compute $\pi(H_0|x)$ with Jeffreys prior for a family $N(\theta,1)$

Given a random sample $x = (x_1,\ldots,x_n)$ taken from a family $\{N(x|\theta,1):\theta \in \mathbb{R}\}$. And consider the hypothesis test: $H_0: \theta = 0$ vs $H_1: \theta \in \mathbb{R}$ (this ...
2answers
144 views

### How are does software compute posterior distributions from improper (flat) priors?

In Bayesian statistics, how do software packages compute the posterior distribution when the prior is improper (flat)? If I understand correctly, this can't be done analytically so how is it done ...
1answer
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0answers
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### Objective Bayesianism: Jeffreys priors vs reference priors vs principle of transformation groups

According to this answer, José Bernardo has produced an original theory of reference priors where he chooses the prior in order to maximise the information brought by the data by maximising the ...
1answer
119 views

### Bayesian Biased Prior Formula

I know that for a Bayesian uniform/flat prior, the formula is 1/n (and n=1), as each value has an equal chance of being chosen. However, is there an equation for when the prior is biased/informative? ...
0answers
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