Include half normal priors on the rates (SIR model)

[maxbiostat]

We have three choices for priors on the rates beta and gamma:

• Gamma priors -> Gamma ratio distribution on R_0
• Log-normal priors -> log-normal prior on R_0
• Half-normal priors -> Weird distribution R_0

I have derived the density for the ratio of half normals. It ain't pretty, but it's closed-form. What would be nice here would be to implement the Boarding School example also with halfnormal priors as done here

[maxbiostat]

Distribution of R_0 under three different choices for the priors on beta and gamma.