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.

This exercise is part of the course

Bayesian Modeling with RJAGS

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Exercise instructions

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.

Hands-on interactive exercise

Have a go at this exercise by completing this sample code.

# Calculate the typical volume on 80 degree weekends & 80 degree weekdays
poisson_chains <- poisson_chains %>% 
    mutate(l_weekend = exp(___ + ___ * 80)) %>% 
    mutate(l_weekday = exp(___ + ___ + ___ * 80))

# Construct a 95% CI for typical volume on 80 degree weekend


# Construct a 95% CI for typical volume on 80 degree weekday

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