This makes a tidy data frame of stuff, and also changes things back to factors, if the levels are provided.
tidy_pi_traces(input, pname, car_tib, interval)
The output to tidy (i.e.. out$trace$pi)
the name that you want the parameter to be called in the output
a tibble with repunit and collection in the order they appear in the output
the thinning interval that was used