How to compute expected value of the posterior predictive distribution (epred)

[JLC]

I’m trying to calculate it myself, but can’t find anything that comes close.

@andrewheiss 's write up has this for epred:

epred_manual <- model_normal |> 
  spread_draws(b_Intercept, b_flipper_length_mm, sigma) |> 
  mutate(mu = b_Intercept + 
           (b_flipper_length_mm * 
              penguins_avg_flipper$flipper_length_mm),  # This is posterior_linpred()
         y_new = rnorm(n(), mean = mu, sd = sigma))  # This is posterior_predict()

# This is posterior_epred()
epred_manual |> 
  summarize(epred = mean(y_new))

Calling mean averages over the draws, so there is a only single estimate/draw rather than draws of ndraws() per row.

What does brms do to get multiple epreds per observation?

This post:

Reproduce posterior_predict from posterior_linpred for a neg binom spline model

Hi Angelo, here’s a brief explanation of the difference. Suppose you have a negative binomial regression with a log link: \eta_i = a + bx_i \\ \lambda_i = \exp(\eta_i) \\ y_i \sim {\rm NegBinom}(\lambda_i, \phi) posterior_linpred() gives you posterior draws of \eta. posterior_linpred(transform=TRUE), or equivalently posterior_epred(), gives you posterior draws of \lambda, that is, it does the inverse link transformation for you. posterior_predict() gives you draws from {\rm NegBinom}(\l…

Suggests posterior_epred() would be mu for a Student model.