Trouble using loo::psis for importance sampling

[avehtari]

@anon75146577

My expectation for the following code is that it takes the log ratios log_r and produces the smoothed log weights log_w . If I ask for unnormalized weights, I expect all of these weights to be the same except for the last attr(out,"tail_len") (which is 300 in this case) which should be the modified weights according to the fitted pareto distribution.

To make computations more stable we subtract the maximum log_r before exponentiating required by Pareto fit. In this case

> max(log_r)  #[1] 5.217747

We don’t add that back, but you can get what you want by

log_w = weights(out,log=TRUE,normalize=FALSE)  + max(log_r)
lm(log_w~log_r)
mean(exp(log_r)) #[1] 0.9603866
mean(exp(log_w)) #[1] 0.9625504

@anon75146577

If I ask for normalized weights I get an intercept of -9.17, which also doesn’t make sense.

Normalized weights sum to 1.

log_w = weights(out,log=TRUE,normalize=TRUE)  
sum(exp(log_r)) #[1] 9603.866
sum(exp(log_w)) #[1] 1