Experiment 1: simple SIR

[maxbiostat]

The goal of this experiment is to understand two things:

• a) How do the priors on gamma and beta affect inferences for R0?

To answer a) we could:

• Run the two ODE model parametrised in terms of gamma and beta:

  • Informative log-normal priors;
  • "Uninformative" Gamma(1, 1) priors;
  • "Uninformative" half-normal(0, 1) priors;
  • "Uninformative" log-normal priors: mu = 0 and sd =1, 10, 100

• Run the two ODE model parametrised in terms of gamma and R0 with

  • Informative Gamma priors on both gamma and R0;
  • Informative half-normal priors on both gamma and R0;
  • Informative log-normal priors on both gamma and R0;
  • An informative Gamma prior on R_0 and an uninformative Gamma prior on gamma.
  • An informative Gamma prior on R_0 and an uninformative half-normal prior on gamma.
  • An informative log-normal prior on R_0 and an uninformative log-normal prior on gamma.
  • An informative log-normal prior on R_0 truncated at 1 (epidemic prior) and an uninformative prior on gamma.

Quantities to track

• mean, median and BCI;
• Divergences;
• ESS;
• Run time.

Q: Why use different prior families? A: to assess tail effects.
Obs: we should try to make all of the "informative" priors be moment-matching. E.g.: if we pick a Gamma(2, 1) prior for R0, then the informative half-normal prior would have to be a half-normal(m0, s0), with m0and s0 chosen so as to have the same first two moments.