# 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 $\theta \sim \mathcal{U}(0,1)$ a non-informative prior for $\theta$?

• A recent related discussion: stats.stackexchange.com/questions/27589/… – jthetzel May 5 '12 at 2:31
• Well, if you have no basis for specifying a prior, why would you want to bias your estimates by arbitrarily assigning one? – Macro May 5 '12 at 2:51
• Moreover the uniform distribution is not a non-informative prior. For instance it forces $\theta^2$ to be more probably close to $0$ than $1$. – Stéphane Laurent May 5 '12 at 8:14

This vision is best represented by Jeffreys' distributions, where the information matrix of the sampling model, $I(\theta)$, is turned into a prior distribution $$\pi(\theta) \propto |I(\theta)|^{1/2}$$ which is most often improper, i.e. does not integrate to a finite value. The label "non-informative" associated with Jeffreys' priors is rather unfortunate, as they represent an input from the statistician, hence are informative about something! Similarly, "objective" has an authoritative weight I dislike... I thus prefer the label "reference prior", used for instance by José Bernado.