Exercise

# Poisson posterior prediction

Your `l_weekday`

variable reflects the *trend* in volume on 80 degree weekdays:

```
> head(poisson_chains, 2)
a b.1. b.2. c l_weekend l_weekday
1 5.0198 0 -0.1222 0.0141 465.924 412.324
2 5.0186 0 -0.1218 0.0141 466.284 412.829
```

Now that you understand the *trend*, let's make some predictions! Specifically, let's *predict* trail volumes on the next 80 degree weekday. To do so, you must take into account individual variability from the trend, modeled by the likelihood \(Y\)_{i} \(\sim Pois(l\)_{i}).

Using `rpois(n, lambda)`

for sample size `n`

and rate parameter `lambda`

, you will simulate Poisson predictions of volume under each value of the posterior plausible trend in `poisson_chains`

.

Instructions

**100 XP**

- From each of the 10,000
`l_weekday`

values in`poisson_chains`

, use`rpois()`

to predict volume on an 80 degree weekday. Store these as`Y_weekday`

in`poisson_chains`

. - Use
`ggplot()`

to construct a density plot of your`Y_weekday`

predictions. - Approximate the posterior probability that the volume on an 80 degree weekday is less than 400 users.