# Questions tagged [improper-prior]

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### Is there any strong argument about objective/non-informative improper prior?

Decades ago improper objective priors - e.g. $\pi(\sigma) \propto \sigma^{-1}, \sigma > 0,$ for a scale parameter - were considered problematic because some authors thought they were leading to the ...
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### Bayesian statistics

Assuming I have that $Y_i\mid \mu$ is an iid ~ $N(\mu,\sigma^2)$, for $i \in (1,\dotsc,n)$ with $\sigma_i$ known and improper prior $\pi(\mu)=1$ for all $\mu$. i. How can I derive a formula for the ...
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### What is a non-informative choice of parameters for a Dirichlet distribution?

Dirichlet distribution is a conjugate prior for multinomial distribution. I want to impose a non-informative prior over sampling weights $\pi$ for a draw $x=(x_1,…,x_N)$ from a multinomial ...
681 views

### Why is this an example of a noninformative prior?

From Bayesian Data Analysis 3rd Edition [Gelman et. al], they give this as an example when introducing non-informative priors: "We return to the problem of estimating the mean θ of a normal ...
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### Can an improper prior distribution be informative?

I have just worked through an example where, with an improper prior, the bayesian estimator equals the maximum likelihood estimator, leading me to believe that improper priors are uninformative. But ...
1 vote
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### Finding the posterior distribution given an improper prior

Let $X \sim N(\theta, \sigma^2)$ where $\sigma^2$ is known. Let the prior density $\pi(\theta) =1, \theta \in \mathbb{R}$ to be the improper uniform density over the real line. Find the posterior ...
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### 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 ...
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### 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 ...
1 vote
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### 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? ...
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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
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### Understanding my posterior with an uninformative prior with a poisson likelihood. Am I thinking about this correctly?

I have a problem to which I am trying to apply a Bayesian model. My data is generated as follows \begin{align} N_i \mid \mu &\sim \text{Poisson}(\mu) \\ Y_i \mid N_i, \theta_i &\sim \text{...
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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 ...
2k 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 ...
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 ...