I have data for many time series. Each time series can be modeled by a particular nonlinear function of several parameters and, though I want point estimates of the model parameters for each of the many time series, I am more interested in the uncertainty associated with the parameter estimates (i.e., in the strength of the data). I have good prior information that I'd ideally like to include. I have tried MCMC, but am not confident that reasonable quality posterior samples can be obtained for the many time series (I can tweak the parameters of the MCMC algorithm for specific time series, but I'm not convinced my settings generalize well for other time series); additionally, CPU time is an issue.
Rather than use MCMC, I'm wondering about using conjugate priors (a multivariate normal is a good model of my log-transformed parameters). However, I'm having trouble finding examples of Bayesian nonlinear regression with conjugate priors. Is it possible?
Your assistance is much appreciated.