# LOOCV for GEV in Stan

Hey y’all,
How can I calculate LOO and WAIC for GEV distribution in Stan?

1. In the functions block, write a function to evaluate the GEV log-density
2. In the generated quantities block, call it on each observation and put the result in the n-th element of `log_lik`, which is declared as a real array
3. Call `loo` on the object produced by `stan`
4. Forget about WAIC.

ArviZ on a Python side has implementation of loo and waic.

(loo is the way to go).

Please double check the scaling if you need to compare models against some paper etc.

Thank you so much Prof Goodri for your help.
You find my r code bellow.
How can I write the function of GEV log-density in the generated quantities block?

#### R code for GEV in Stan

functions{
real gev_log (real y, real loc, real scale, real shape){
real z;
real inv_shape;
inv_shape = 1.0/shape;
z = 1 + (y - loc) * shape / scale;
return -log(scale) - (1 + inv_shape)log(z) - pow(z,-inv_shape);
}
// GEV log pdf
real gev_v_lpdf(vector y, vector mu, real sigma, real xi){
vector[rows(y)] z;
vector[rows(y)] logp;
vector[rows(y)] zi;
z = 1 + xi
(y - mu)/sigma;
for(i in 1:rows(y)){
zi[i] = z[i]^(-1/xi);
}
logp = log(sigma) + (1 + 1/xi)*log(z) + zi;
return -sum(logp);
}
}
data {
int<lower=0> ns;
int<lower=0> ns_c;
int<lower=0> ns_m;
int<lower=0> nt;
int<lower=0> np;
matrix [nt,ns] y; //matrix containing data
matrix [nt,np] x;//matrix containing predictors
}
}
parameters {
vector <lower=0, upper=100> [ns] mu;
vector <lower=0, upper=15> [ns] sigma;
vector <lower=-0.5, upper=0.5> [ns] xi;
}

model {
// Priors
// mu ~ normal(0,10);
// sigma ~ normal(0,10);
// xi ~ uniform(0,0.3);

// Complete stations
for (i in 1:(ns_c+ns_m)){
if(i <= ns_c){
y[,i] ~ gev_v(mu[i],sigma[i],xi[i]);
}else{
// Incomplete stations
for(t in 1:nt)
if(y[t,i] != -99)
y[t,i] ~ gev(mu[i],sigma[i],xi[i]);
}
}
}

It is explained in the vignette
http://mc-stan.org/loo/articles/loo2-with-rstan.html

Thank you so much

Thank you so much