The Bayes theorem is:
$P(\theta | x)=\displaystyle \frac{p(\theta)L_x(\theta)}{\int_{\theta \in A}p(\theta)L_x(\theta)d\theta}$
It's pretty clear that $\theta's$ support will not change as bayes theorem update its distribution given some data, if $\theta's$ support is $(a,b)$ so it's easy to define a uninformative prior ( I'd just use $U(a,b)$) but when the support is either:
- $A=(-\infty,\infty)$
- $A=(0,\infty)$
- $A=(-\infty,0)$
it becomes trouble to get a non-informative prior like $U(a,b)$ so Is there any alternative for a uninformative prior distribution to get through this?
