Efficient multivariate conditional autoregressive priors

Hi all,

I am a post graduate student at QUT and love using Stan for spatial modelling! I’ve recently starting looking more deeply at multivariate conditional autoregressive priors, which to my knowledge are yet to be implemented in Stan. These models allow one to jointly model the spatial dependence of multiple factors using a separable covariance matrix.

Leveraging the strides taken by @cmcd in this space, I want to share that I have begun developing efficient implementations for the multivariate proper CAR and Leroux CAR models, which offer significant efficiency gains. In my examples (with 1500 areas and 3 factors) it takes about 8.5 seconds to evaluate the 4500 dimensional multivariate normal using multi_normal_prec_lpdf, while under 0.04 seconds with my implementation. When fitting a model, my implementation takes a little over 3 minutes to fit a multivariate PCAR with 2000 areas and 5 factors.

The work is very early days, but exciting nonetheless. I am posting today to see if anyone would like to collaborate with me on this work. The goal would be to publish a short vignette. With inspiration from the fantastic CAR vignettes by @mitzimorris and @mbjoseph, I’ve started drafting this using the common Scottish lip cancer data.

If this work interests you, please do not hesitate to get in contact!