I’m having some trouble making the `loo::psis`

function do what I think it’s supposed to do when using it to build an importance sampler. (NB: Yes. I know this is not the intended use case, but I can’t see from the code why it wouldn’t work, so I’m clearly missing something.)

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.

Hence if I fit a regression of the log-weights vs the log-ratios, I expect to get an intercept of around zero and a slope of around 1.This did not happen. Instead if I run `lm`

on the samples I get

```
Call:
lm(formula = log_w ~ log_r)
Coefficients:
(Intercept) log_r
-5.2179 0.9997
```

I’m clearly missing something here, but that -5.21 doesn’t make sense to me. If I ask for normalized weights I get an intercept of -9.17, which also doesn’t make sense.

Any idea what’s going on? (Specifically @avehtari but someone else may know)

Reproducible code and session info below:

```
library(loo)
set.seed(9183)
S = 10000
x = rexp(S,rate=3)
log_r = dexp(x = x,rate=1,log=TRUE) - dexp(x=x,rate=3,log=TRUE)
out = loo::psis(log_r,r_eff=1)
log_w = weights(out,log=TRUE,normalize=FALSE)
lm(log_w~log_r)
mean(exp(log_r)) #[1] 0.9603866
mean(exp(log_w)) #[1] 0.005216566
```

```
> sessionInfo()
R version 3.5.1 (2018-07-02)
Platform: x86_64-apple-darwin15.6.0 (64-bit)
Running under: macOS High Sierra 10.13.6
Matrix products: default
BLAS: /System/Library/Frameworks/Accelerate.framework/Versions/A/Frameworks/vecLib.framework/Versions/A/libBLAS.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/3.5/Resources/lib/libRlapack.dylib
locale:
[1] en_CA.UTF-8/en_CA.UTF-8/en_CA.UTF-8/C/en_CA.UTF-8/en_CA.UTF-8
attached base packages:
[1] stats graphics grDevices utils datasets
[6] methods base
other attached packages:
[1] loo_2.1.0
loaded via a namespace (and not attached):
[1] compiler_3.5.1 parallel_3.5.1 tools_3.5.1
[4] yaml_2.1.19 matrixStats_0.54.0
```