Estimating von Mises Parameters for Angular Data

Question

I want to model some angular data.

Any input on how to incorporate the von Mises distribution and suggestions on appropriate priors in RJAGS for von Mises mean and concentration would be greatly appreciated.

Answer 1

The von Mises distribution has two parameters, a mean direction $\mu$ and a concentration parameter $\kappa$. A basic way to go about it is to specify a von Mises prior for the mean direction (the distribution of the mean is $VM(\mu, R\kappa)$, so a VM prior for it makes sense). An uninformative prior has $\kappa = 0$, and is the circular uniform distribution. You could consider something like an exponential distribution as a prior for $\kappa$.

What is probably a better way to go about it is to employ a conjugate prior. We can imagine a prior as a dataset with $c$ observations with mean direction $\mu_0$ and resultant length $R_0$. A non-informative prior has $c=0$. Then, we can combine these into a sample size, mean direction and resultant length for a posterior, which will be von Mises.

This conjugate prior was first used in Guttorp & Lockhart (1988). More details are given in the first part of Damien & Walker (1999).