# Log(0) error, when defining shape parameter with normal distribution containing regression parameters in non-stationary GEV

**URL:** <https://discourse.mc-stan.org/t/log-0-error-when-defining-shape-parameter-with-normal-distribution-containing-regression-parameters-in-non-stationary-gev/30312>\
**Category:** Modeling\
**Tags:** reparametrization, rstan\
**Created:** [February 8, 2023, 4:41pm UTC](https://discourse.mc-stan.org/t/log-0-error-when-defining-shape-parameter-with-normal-distribution-containing-regression-parameters-in-non-stationary-gev/30312 "2023-02-08T16:41:34Z")\
**Posts on this page:** 6\
**Page:** 1

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**Author:** ![Alex\_Lee](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/alex_lee/32/13479_2.png) [@Alex\_Lee](https://discourse.mc-stan.org/u/Alex_Lee)\
**Post date:** [February 8, 2023, 4:41pm UTC](https://discourse.mc-stan.org/t/log-0-error-when-defining-shape-parameter-with-normal-distribution-containing-regression-parameters-in-non-stationary-gev/30312/1 "2023-02-08T16:41:34Z")

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I have define a hierarchical GEV with a non-stationary shape parameter.

I have defined some samples `y` with a changing shape parameter `shvec[i]` and the covariates `COV` for the shape parameter are simply `1+(3*shvec)`.

```plaintext
library(rstan)
library(extRemes)

set.seed(10)

shvec = seq(-0.3,0.2,length.out=20)
y = array(0,dim=c(40,20))

for (i in 1:20) {
  y[,i] = revd(40,loc=20,scale=0.5,shape=shvec[i])
}

# Bayesian hierarchical model
library(rstan)
N = 40
J = 20
COV = 1 + (3*shvec)

model = stan_model("GEV.stan")
fit = sampling(model,list(N=N,J=J,y=y,COV=COV),iter=2000,chains=1,seed=10)

```

The model `GEV.stan` is below:

```plaintext
functions {
    real gev_lpdf(vector y, real mu, real sigma, real xi) {
        vector[rows(y)] z;
        vector[rows(y)] lp;
        real loglike;
        int N;
         
        N = rows(y);
         
        if (fabs(xi) > 1e-10) {
            for(i in 1:N){
                z[i] = 1 + xi * (y[i] - mu) / sigma;
                lp[i] = (1 + 1 / xi) * log(z[i]) + pow(z[i], -1 / xi);
            }
        loglike = - sum(lp) - N * log(sigma);
        } else {
            for (i in 1:N){
                z[i] = (y[i] - mu) / sigma;
                lp[i] = z[i] + exp(-z[i]);
            }
            loglike = - sum(lp) - N * log(sigma);
        }
        return(loglike);
    }
}

data {
  int<lower=1> N;      
  int<lower=1> J;      
  vector[J] y[N];
  vector[J] COV;
}

parameters {
  real xi[J];
  real mu[J];
  real<lower=0> sigma[J];
  
  real alpha;
  real delta;
}

model {
  for (jj in 1:J) {
    xi[jj] ~ normal(alpha + delta*COV[jj],10);
    y[jj] ~ gev(mu[jj], sigma[jj], xi[jj]);
  }
}

```

Unfortunaly I get `Log probability evaluates to log(0), i.e. negative infinity` for this. Anybody know what I’m doing wrong here?

I think it may have something to do with shape parameter `xi[jj] ~ normal(alpha + delta*COV[jj],10)`.

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<div class="post-metadata">

**Author:** ![caesoma](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/caesoma/32/19767_2.png) [@caesoma](https://discourse.mc-stan.org/u/caesoma)\
**Post date:** [February 12, 2023, 5:41pm UTC](https://discourse.mc-stan.org/t/log-0-error-when-defining-shape-parameter-with-normal-distribution-containing-regression-parameters-in-non-stationary-gev/30312/2 "2023-02-12T17:41:46Z")

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Doesn’t it tell you exactly which parameter the error refers to? It can be something that is wrongly (intentionally or unintentionally) set to zero than used to compute the likelihood, or something that is randomly initialized to a very low probability that ends up underflowing to zero. The latter is common when the parameter space is large, but can be easily solved by setting the initial parameter values to values known to have nonzero likelihood.

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<div class="post-metadata">

**Author:** ![bgeorgios](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/bgeorgios/32/15151_2.png) [@bgeorgios](https://discourse.mc-stan.org/u/bgeorgios)\
**Post date:** [February 13, 2023, 3:30am UTC](https://discourse.mc-stan.org/t/log-0-error-when-defining-shape-parameter-with-normal-distribution-containing-regression-parameters-in-non-stationary-gev/30312/3 "2023-02-13T03:30:07Z")

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Do not force the sigma parameter to be positive but rather model **log(sigma)**, i.e., replace sigma with **exp(sigma)** in your likelihood function. See if that fixes the issue…

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<div class="post-metadata">

**Author:** ![Alex\_Lee](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/alex_lee/32/13479_2.png) [@Alex\_Lee](https://discourse.mc-stan.org/u/Alex_Lee)\
**Post date:** [February 13, 2023, 10:13am UTC](https://discourse.mc-stan.org/t/log-0-error-when-defining-shape-parameter-with-normal-distribution-containing-regression-parameters-in-non-stationary-gev/30312/4 "2023-02-13T10:13:40Z")

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I found my problem.

Obviously, the shape parameter also needs to be constrained:

1 + \xi \left( \frac{y-\mu}{\sigma} \right) \> 0

So the code for that:

```plaintext
transformed data {
  vector[J] ymin;
  for (j in 1:J) {
    ymin[j] = min(y[j]);
  }
}

parameters {
  real mu[J];
  real<lower=0> sigma[J];
  real<lower=-sigma[J]/(ymin[J] - mu[J])> xi[J];
  
  real alpha;
  real delta;
}

```

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<div class="post-metadata">

**Author:** ![bgeorgios](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/bgeorgios/32/15151_2.png) [@bgeorgios](https://discourse.mc-stan.org/u/bgeorgios)\
**Post date:** [February 13, 2023, 4:59pm UTC](https://discourse.mc-stan.org/t/log-0-error-when-defining-shape-parameter-with-normal-distribution-containing-regression-parameters-in-non-stationary-gev/30312/5 "2023-02-13T16:59:01Z")

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Nice! I wonder why you need to model shape as a function of covariates… Usually, this is not a good idea (see Coles et al. 2001).

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<div class="post-metadata">

**Author:** ![Alex\_Lee](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/alex_lee/32/13479_2.png) [@Alex\_Lee](https://discourse.mc-stan.org/u/Alex_Lee)\
**Post date:** [February 14, 2023, 3:33pm UTC](https://discourse.mc-stan.org/t/log-0-error-when-defining-shape-parameter-with-normal-distribution-containing-regression-parameters-in-non-stationary-gev/30312/6 "2023-02-14T15:33:06Z")

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Yes, it’s probably better to keep the covariates in the location or, if needed, the scale parameter.