Chain 1: Log probability evaluates to log(0), i.e. negative infinity. What is causing this error?

Modeling
1

Hello,

I am running the following model:

// generated with brms 2.17.0
functions {
  /* hurdle lognormal log-PDF of a single response
   * logit parameterization of the hurdle part
   * Args:
   *   y: the response value
   *   mu: mean parameter of the lognormal distribution
   *   sigma: sd parameter of the lognormal distribution
   *   hu: linear predictor for the hurdle part
   * Returns:
   *   a scalar to be added to the log posterior
   */
  real hurdle_lognormal_logit_lpdf(real y_true, real y_obs, real mu, real y_err, real hu) {
    if (y_true == 0) {
      return bernoulli_logit_lpmf(1 | hu);
    } else {
      return bernoulli_logit_lpmf(0 | hu) +
             lognormal_lpdf(y_obs | mu, y_err);
    }
  }
}
data {
  int<lower=1> N;  // total number of observations
  vector[N] Y_obs;  // response variable (MBH)
  int<lower=1> K;  // number of population-level effects
  matrix[N, K] X;  // population-level design matrix
  int<lower=1> K_hu;  // number of population-level effects
  matrix[N, K_hu] X_hu;  // population-level design matrix
  int prior_only;  // should the likelihood be ignored?
  vector[N] Y_err;
}
transformed data {
  int Kc = K - 1;
  matrix[N, Kc] Xc;  // centered version of X without an intercept
  vector[Kc] means_X;  // column means of X before centering
  int Kc_hu = K_hu - 1;
  matrix[N, Kc_hu] Xc_hu;  // centered version of X_hu without an intercept
  vector[Kc_hu] means_X_hu;  // column means of X_hu before centering
  vector[N] Y_true;
  for (i in 2:K) {
    means_X[i - 1] = mean(X[, i]);
    Xc[, i - 1] = X[, i] - means_X[i - 1];
  }
  for (i in 2:K_hu) {
    means_X_hu[i - 1] = mean(X_hu[, i]);
    Xc_hu[, i - 1] = X_hu[, i] - means_X_hu[i - 1];
  }
  for (n in 1:N) {
    Y_true[n] = normal_rng(Y_obs[n], Y_err[n]);
    if (Y_true[n] < 0) {
      Y_true[n] = 0;
    }
  }
}
parameters {
  vector[Kc] b;  // population-level effects
  real Intercept;  // temporary intercept for centered predictors
  real<lower=0> sigma;  // dispersion parameter
  vector[Kc_hu] b_hu;  // population-level effects
  real Intercept_hu;  // temporary intercept for centered predictors
}
transformed parameters {
  real lprior = 0;  // prior contributions to the log posterior
  lprior += student_t_lpdf(Intercept | 3, 2, 2.5);
  lprior += student_t_lpdf(sigma | 3, 0, 2.5)
    - 1 * student_t_lccdf(0 | 3, 0, 2.5);
  lprior += logistic_lpdf(Intercept_hu | 0, 1);
}
model {
  // likelihood including constants
  if (!prior_only) {
    // initialize linear predictor term
    vector[N] mu = Intercept + Xc * b;
    // initialize linear predictor term
    vector[N] hu = Intercept_hu + Xc_hu * b_hu;
    for (n in 1:N) {
      target += hurdle_lognormal_logit_lpdf(Y_true[n] | Y_obs[n], mu[n], Y_err[n], hu[n]); // modify sigma for Y_err[n]
    }
  }
  // priors including constants
  target += lprior;
}
generated quantities {
  // actual population-level intercept
  real b_Intercept = Intercept - dot_product(means_X, b);
  // actual population-level intercept
  real b_hu_Intercept = Intercept_hu - dot_product(means_X_hu, b_hu);
}

And for some reason, I keep obtaining this error:

Chain 1: Rejecting initial value:
Chain 1: Log probability evaluates to log(0), i.e. negative infinity.
Chain 1: Stan can’t start sampling from this initial value.
Chain 1:
Chain 1: Initialization between (-2, 2) failed after 100 attempts.
Chain 1: Try specifying initial values, reducing ranges of constrained values, or reparameterizing the model.
[1] “Error in sampler$call_sampler(args_list[[i]]) : Initialization failed.”
[1] “error occurred during calling the sampler; sampling not done”

It has only started happening since I introduced the Y_true vector in the transformed data block. I don’t understand what is causing this as my parameters to be sampled haven’t changed?

2

The usual reason for this error is a variable violating its constraints, like providing a negative scale parameter in a multivariate normal. For instance, you have an unconstrained data variable Y_err that’s used as a scale variable, so if any of the values are 0 or negative, this is going to cause the problem you’re seeing. You should add a lower=0 constraint to the declaration, so you’ll catch that error on data load.

Are there no other error messages that happen as the sampler proceeds? So the best thing to do is start printing values after assignments to make sure everything satisfies its constraints. You can print target() to track how the log density is evolving and detect when things get bad.

You don’t need that -1 * student_t_lccdf(...) term because it’s constant. In general, rather than multiplying by -1, use negation.

You’re missing a prior on b.

P.S. The standard way to get “prior only” inference is to use the same code and provide an empty data set.

P.P.S. The program will be faster if you just use sampling statements instead of the lprior += pattern you’re using.