Joint reference prior for normal distribution

#1
Hello, hoping for some help understanding Bayesian reference priors. This is the first time I have had to resort to Bayesian methods so please be gentle :).

My basic problem is I have a single measurement drawn from a normal distribution of unknown mean and variance. I am interested in both parameters. I know nothing about the mean and variance except that they could be non-zero. So, it seems I should try to use the reference prior as in Bernado (1979). However, they provide a "joint reference prior to make inferences about mu", and another one to make inferences about sigma. In fact most literature always seems to look at one parameter at a time and treat all the other ones as nuisance parameters. Granted I can get a marginal posterior for mu and one for sigma, but I'm really interested in the shape of the joint posterior. Is there such a thing as a joint reference posterior or am I barking up the wrong tree??

thanks