Looking at differences

Let’s look at the differences between some parameters in a fake posterior distribution.

Here’s an areas plot of 4 parameters.

FakePosterior %>% select(matches("a|b")) %>% precis()

##    mean       sd      5.5%    94.5% histogram
## a    10 1.999922  6.805612 13.19439  ▁▁▂▇▇▂▁▁
## b1   17 3.999844 10.611224 23.38878   ▁▁▃▇▃▁▁
## b2   17 3.999844 10.611224 23.38878   ▁▁▃▇▃▁▁
## b3   17 3.999844 10.611224 23.38878   ▁▁▃▇▃▁▁

FakePosterior %>% mcmc_areas( regex_pars = "a|b")

We are interested in the differences between the a parameter and the b parameters. Fortunately, we have heard enough times that we should compute those differences in the posterior and not just look at the plot above.

FakePosterior <-
  FakePosterior %>% 
  mutate(
    d1 = b1 - a,
    d2 = b2 - a,
    d3 = b3 - a
  )

FakePosterior %>% mcmc_areas( regex_pars = "a|b1|d")

Can you figure out why this is happening? How do you think I created the fake posterior to make this happen? What plot might you make to see if that’s what I did?

FakePosterior %>% mcmc_pairs( regex_pars = "a|b")

## Warning: Only one chain in 'x'. This plot is more useful with multiple chains.

FakePosterior <-
  FakePosterior %>%
  mutate(
    e12 = b1 - b2,
    e23 = b2 - b3,
    e31 = b3 - b1
  )
  
FakePosterior %>% mcmc_areas( regex_pars = "b|e")