*beta*and the covariance with parameters

*alph*a. Under certain regularity conditions, GEE2 can provide consistent estimators for both

*beta*and

*alpha*without having to specify any likelihood. I think the main benefit of GEE2 is that it does not rely on any strong parametric assumptions. For example, if you have a continuous response of interest that is not really normally distirubted, GEE2 may be more robust than fitting a normal model with MLE.

I know that fundamentally bayesian statistics requires a likelihood. Nontheless, I'm wondering if there is any bayesian analog to GEE2 that can let me estimate mean and covariance parameters for a continuous response without having to assume the response is normally distributed (for example). I.e. I want to obtain more robust estimates of mean and covariance parameters (

*beta*and

*alpha*) that do not rely on strong parametric assumptions of the data.

The reason I'd prefer to do something like GEE2 within a Bayesian context is because I want to use MCMC to do the estimation (if possible), since I trust MCMC a lot more than the modified newton-raphson algorithm proposed for GEE2 (too sensitive to initial starting values IMO).