Problem using integrate

Modeling
1

Hi, my name is Jose Alejandro ordoñez, I´m writing because I have problems with the function integrate_1d. The code below shows what i´m triying to do.

scode= "
functions{
   real dplogisstan (real x, real mu, real sigma, real alpha){
     real dens = alpha*pow(logistic_cdf(x,mu,sigma),alpha-1)*exp(logistic_lpdf(x|mu,sigma));
     return dens;
}

real eapp_integrand (real x, real xc, real[] theta, real[] x_r,int[] x_i){
  real alpha = theta[1];
  real a = theta[2];
  real ez = digamma(alpha)-digamma(a);
  real vz = trigamma(alpha)+trigamma(a);
  real sigmaalpha = sqrt(1/vz);
  real sigma1 = sqrt(0.5/trigamma(a));
  real mualpha = -sigmaalpha*(digamma(alpha)-digamma(a));
  real integrand = log (1+ exp(-x/sigma1))*dplogisstan(x,mualpha,sigmaalpha,alpha);
  return integrand;
 }
 
 real eapp_integral(real alpha){
  real x_r[0];
  int x_i[0]; 
  real integral=integrate_1d(eapp_integrand, negative_infinity(),positive_infinity(), {alpha, 1.0}, x_r, x_i);
  return integral;
}
}
"

After this code, I used the function expose_stan_functions(stanc(model_code = scode)) to verify that my sintaxis is correct, nevertheless, the last function which uses integrate_1d shows me this error.

``stan
SYNTAX ERROR, MESSAGE(S) FROM PARSER:
error in ‘model7adc79c87c32_scode’ at line 24, column 108

22:   real x_r[0];
23:   int x_i[0]; 
24:   real integral=integrate_1d(eapp_integrand, negative_infinity(),positive_infinity(), {alpha, 1.0}, x_r, x_i);
                                                                                                               ^
25:   return integral;

PARSER EXPECTED: “,”
Error in stanc(model_code = scode) :
failed to parse Stan model ‘scode’ due to the above error.
``
After that, as in the website of stan, I decided to include the argument relative_tolerance with a similar result but in this case the error was PARSER EXPECTED= “)”.

Thanks for the attention, I would be grateful with any suggestion.

2

Hi Jose,

There are two issues here, first (as you’ve already figured out), you need to specify the relative tolerance. After that, the issue is that the x_i and x_r parameters have to be declared in the data or transformed data blocks. What you can do in your case, is just specify that they’ll be passed to the eapp_integral function:

scode= "
functions{
   real dplogisstan (real x, real mu, real sigma, real alpha){
     real dens = alpha*pow(logistic_cdf(x,mu,sigma),alpha-1)*exp(logistic_lpdf(x|mu,sigma));
     return dens;
}

real eapp_integrand (real x, real xc, real[] theta, real[] x_r,int[] x_i){
  real alpha = theta[1];
  real a = theta[2];
  real ez = digamma(alpha)-digamma(a);
  real vz = trigamma(alpha)+trigamma(a);
  real sigmaalpha = sqrt(1/vz);
  real sigma1 = sqrt(0.5/trigamma(a));
  real mualpha = -sigmaalpha*(digamma(alpha)-digamma(a));
  real integrand = log (1+ exp(-x/sigma1))*dplogisstan(x,mualpha,sigmaalpha,alpha);
  return integrand;
 }
 
 real eapp_integral(real alpha, data real[] x_r, data int[] x_i){
  real integral=integrate_1d(eapp_integrand, negative_infinity(),positive_infinity(), {alpha, 1.0}, x_r, x_i, 0.001);
  return integral;
}
}
"

Note that the relative tolerance I’ve specified (0.001) is completely arbitrary and should be updated

3

Thank you andrjohns, you helped me a lot!