What priors are typically used for the correlation parameter in a bivariate normal? The Bivariate normal distribution contains a correlation parameter. I want to implement an MCMC sampler to sample from the posterior distribution of the parameters of the bivariate normal distribution. I have already selected the priors for the mean and variance parameters. However, I was not sure how to choose the prior for $\rho\in(-1,1)$, the correlation parameter.
Are there any standard choices such as the Jeffreys prior or other noninformative priors? If so, what are they?

The Wishart distribution is the conjugate prior to the inverse of the covariance matrix of a multivariate normal distribution (it as a distribution over positive semi-definite matrices).
So instead of using separate priors for the variance and correlation, you can use it as a prior for the entire (inverse of) covariance matrix.
