Inference for the Poisson rate parameter

Again, recall the likelihood structure for your Bayesian Poisson regression model of volume \(Y\)_i by weekday status \(X\)_i and temperature \(Z\)_i:

\(Y\)_i \(\sim Pois(l\)_i) where \(l\)_i\( \; = exp(a + b \; X\)_i \(+ c \; Z\)_i\()\)

Your 10,000 iteration RJAGS simulation of the model posterior, poisson_sim, is in your workspace along with a data frame of the Markov chain output:

> head(poisson_chains, 2)
         a b.1.       b.2.          c
1 5.019807    0 -0.1222143 0.01405269
2 5.018642    0 -0.1217608 0.01407691

Using these 10,000 unique sets of posterior plausible values for parameters \(a\), \(b\), and \(c\) you will make inferences about the typical trail volume on 80 degree days.

From each set of poisson_chains parameter values, calculate the typical trail volumes \(l\) on an 80 degree weekend day. Store these trends as a new variable, l_weekend, in poisson_chains.
Similarly, calculate the typical trail volumes on an 80 degree weekday. Store these as a new variable, l_weekday.
Calculate 95% posterior credible intervals for the typical volume on an 80 degree weekend day and the typical volume on an 80 degree weekday.

Take Hint (-30 XP)

Exercise

Inference for the Poisson rate parameter

Instructions