Questions tagged [uninformative-prior]

A prior that express lack of detailed information or lack of any information at all.

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15
votes
1answer
4k views

Choosing between uninformative beta priors

I am looking for uninformative priors for beta distribution to work with a binomial process (Hit/Miss). At first I thought about using $\alpha=1, \beta=1$ that generate an uniform PDF, or Jeffrey ...
3
votes
1answer
441 views

Why there is no uniform prior for Box-Cox Power Transformed Normal Models

I am trying to get intuition why uniform prior like below will not work for the box-cox model. Box-cox model: $y^{(\phi)}_i \sim N(\mu, \sigma^{2})$ where $y^{(\phi)}_i = (y^{\phi}_i-1)/\phi $ if ...
12
votes
1answer
11k views

What is the point of non-informative priors?

Why even have non-informative priors? They don't provide information about $\theta$. So why use them? Why not only use informative priors? For example, suppose $ \theta \in [0,1]$. Then is $\theta \...
6
votes
1answer
2k views

Why is uniform prior on log(x) equal to 1/x prior on x?

I'm trying to understand Jeffreys prior. One application is for 'scale' variables like the standard deviation $\sigma$ (or its square, the variance $\sigma^2$) of Gaussian distributions. It is often ...
8
votes
1answer
588 views

Choosing non-informative priors

I am working on a model relying on an ugly parametrized function acting as a calibration function on a part of the model. Using a Bayesian setting, I need to get non-informative priors for the ...
9
votes
3answers
7k views

Estimating the parameter of a uniform distribution: improper prior?

We have N samples, $X_i$, from a uniform distribution $[0,\theta]$ where $\theta$ is unknown. Estimate $\theta$ from the data. So, Bayes' rule... $f(\theta | {X_i}) = \frac{f({X_i}|\theta)f(\theta)}...
1
vote
2answers
889 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(\...
0
votes
0answers
167 views

Posterior distribution of a multi parameter model

Suppose I have a sample of observations $y = (y_1,y_2, ... ,y_n)$ is drawn from a normal distribution $N(\mu,\sigma^2)$. We are assuming a non-informative prior on $(\mu,\log\sigma)$ i.e; $f(\mu,\...
4
votes
1answer
132 views

Understanding definition of informative and uninformative prior distribution

When using the "non-informative" prior $\pi(\mu,\sigma)\propto\frac{1}{\sigma^2}$ where $\pi(\mu)\propto1$ and $\pi(\sigma^2)\propto\frac{1}{\sigma^2}$ Where is the no information for the ...
1
vote
0answers
74 views

Information about parameters using priors distributions [duplicate]

When using the "non-informative" prior $\pi(\mu,\sigma)\propto\frac{1}{\sigma^2}$ where $\pi(\mu)\propto1$ and $\pi(\sigma^2)\propto\frac{1}{\sigma^2}$ Where is the no information for the ...