Prior predictive plots allow you to visualize the implications of a set of priors

To better illustrate uncertainty in posterior estimates, we will use a random subsample of 400 counter–days.

For any given mean temperature, is the value of log ridership that is “expected” by the model on a day with that temperature.

The posterior distribution of describes our uncertainty about the value of after seeing the data.

This distribution takes into account the model coefficients and , but not the model standard deviation .

The 80% posterior interval of should get narrower as more data is added.

For any given mean temperature, the posterior predictive distribution describes the range of riderships we would expect for any day with that temperature.

The posterior predictive distribution describes our uncertainty about the value of after seeing the data.

This distribution takes into account all the model parameters: , , and .

The 80% posterior predictive interval should contain about 80% of the data, and should not get appreciably narrower as more data is added.