Binomial simulated based calibration (SBC)

Modeling
1

I want to develop a binomial SBC by applying this code followed the instructions of Stan’s manual.
But the error i am getting is “Ill-typed arguments to ‘~’ statement. No distribution ‘bernoulli_logit’ was found with the correct signature.”

transformed data {
  real mu_sim = normal_rng(1.5, 1);
  real<lower=0> sigma_sim = lognormal_rng(0, 1);
  int<lower=0> J = 10;
  vector<lower=0, upper=1>[J] y_sim;
  vector<lower=-2, upper=4>[J] theta_sim;
  for (j in 1:J) {
    theta_sim[j] = lognormal_rng(mu_sim, sigma_sim);
    y_sim[j] = bernoulli_logit_rng(theta_sim[j]);
  }
}
parameters {
  real mu;
  real<lower=0> sigma;
  re<lower=-2, upper=4> theta;
}
model {
  mu ~ normal(1.5, 1);
  sigma ~ lognormal(0, 1);
  theta ~ lognormal(mu,sigma);
  y_sim ~ bernoulli_logit(theta);
}

I tried to vectorise the model by replacing the model section with

model {
  mu ~ normal(1.5, 1);
  sigma ~ lognormal(0, 1);
  for (j in 1:10) {
    theta[j] ~ lognormal(mu, sigma);
    y_sim[j] ~ bernoulli(inv_logit(theta[j]));
  }
}

But i am getting the same error "“Ill-typed arguments to ‘~’ statement. No distribution ‘bernoulli_logit’ was found with the correct signature”.
Can you help??
Thank you

1 Like
2

Hi, @nicksc79 and welcome to the Stan forums.

I’m afraid Stan’s deficient in not having a bernoulli_logit_rng. We will get around to adding it eventually.

For now, you can replace calls bernoulli_logit_rng(x) with bernoulli_rng(inv_logit(x)). The _logit in bernoulli_logit indicates the argument is on the logit scale, so applying inv_logit takes it back to the probability scale.

There are a few other issues with your model. First, interval constraints, like those on theta can be problematic both computationally and statistically when probabability mass accumulates near the boundaries. So we usually recommend softer constraints. Here, there’s a bigger problem. The lognormal distribution is only defined for positive values, but you let theta go down to -2. Any values of theta below zero will just cause rejections during sampling. Did you intend normal distribution rather than a lognormal here?

Given that theta is univariate, the stacked lognormal priors are just going to add extra diffusion and not really do anything for you in the model and should probably just be replaced with a simpler prior on theta.

2 Likes
3

Thank you a lot for your response.
Following your guidelines, I changed the code to

transformed data {
  int<lower=0> J = 10;
  vector<lower=0, upper=100>[J] theta_sim;
  vector<lower=0, upper=1>[J] y_sim;
  for (j in 1:J) {
    theta_sim[j] = lognormal_rng(1, 1);
    y_sim[j] = bernoulli_rng(inv_logit(theta_sim[j]));
  }
}
parameters {
  real<lower = 0, upper=100> theta;
}
model {
  theta ~ lognormal(1,1);
  y_sim ~ bernoulli_logit(theta);
}

but now the error message I am getting is 
Semantic error in 'string', line 15, column 2 to column 33:
   -------------------------------------------------
    13:  model {
    14:    theta ~ lognormal(1,1);
    15:    y_sim ~ bernoulli_logit(theta);
           ^
    16:  }
   -------------------------------------------------

Ill-typed arguments supplied to function 'bernoulli_logit':
(vector, real)
Available signatures:
(array[] int, row_vector) => real
  The first argument must be array[] int but got vector
(array[] int, vector) => real
  The first argument must be array[] int but got vector
(array[] int, array[] real) => real
  The first argument must be array[] int but got vector
(array[] int, real) => real
  The first argument must be array[] int but got vector
(int, row_vector) => real
  The first argument must be int but got vector
(Additional signatures omitted)

I wonder why since the theta value is a real.
Apologies for, I suppose my naive questions

4

bernoulli_logit is defined only over intergers, but you have declared y_sim to be a vector (of reals). Change your declaration of y_sim to be an array of integers.

1 Like