LOOCV for GEV in Stan

Modeling
1

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

2
  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.
3

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.

4

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]);
}
}
}

5

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

6

Thank you so much

7

Thank you so much