# Questions tagged [improper-prior]

The tag has no usage guidance.

16 questions
Filter by
Sorted by
Tagged with
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 ...
323 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)...
2k views

### Difference between non-informative and improper Priors

I wonder what is the difference between these two kind of priors: Non-informative Improper
354 views

### 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 ...
1k 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 ...
368 views

### 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 ...
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 ...
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 ...
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 ...
72 views

42 views

### 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 ...