Currently in the known pulsar searches we have been using a uniform prior distribution between zero and some arbitrary, but large, upper value e.g.

\begin{equation} p(h_{0}|I)=\begin{cases}\frac{1}{h_{\mathrm{max}}}&\text{if }0\leq h_{0}<h_{\mathrm{max}}\\ 0&\text{otherwise}.\end{cases}\\ \end{equation}However, this type of prior place a lot of probability at large values of \(h_{0}\) where in fact there is very little prior probability. As \(h_{0}\) is a scale factor, the general least informative prior is the Jeffreys prior of the form

\begin{equation} \label{eq:jeffreys}p(h_{0}|I)\propto\frac{1}{h_{0}},\\ \end{equation}but this suffers from being improper (unnormalisable) and in the presence of no signal it will often overwhelm the likelihood when setting upper limits.

Maximiliano Isiover 1 year ago · Publicthese are two separate issue right? Also, Alan brought up the point that whether the prior dominates over the likelihood or not shouldn’t matter (you shouldn’t in principle just pick the prior that gives you the result you want a priori) and that we should justify this more strongly…