Gaussian Prior vs Gamma Prior

[Kyle Thompson]

Instead of modelling $R_t$, could we model $\lambda_t$ over time? The idea is that since $k|\lambda ~ Poisson(\lambda)$ we could use the natural Gamma distribution as the prior to the Poisson distribution to quickly update the $lambda_t$'s over time. We could then back out $R_t$ using your relationship of $lambda_t = k_t-1 exp(-1/GAMMA (R_t - 1))$.

This also raises the question of whether or not the Guassian distribution is the natural choice of the prior for $R_t | R_t-1$. It seems like some transformed along the lines of the relationship between $lambda_t$ and $R_t$ of a Gamma distribution would be more reasonable. What do you think?

[Kyle Thompson]

Oh, I see. I misunderstand the role of the Gaussian. It isn't playing the role of a prior. It's used allow for drift over time in Rt.