use safe negative binomial rng

inst/stan/functions/observation_model.stan

@@ -189,6 +189,29 @@ vector report_log_lik(array[] int cases, vector reports,
   return(log_lik);
 }
 
+
+/**
+ * Custom safe version of the negative binomial sampler
+ *
+ * This function generates random samples of the negative binomial distribution
+ * whilst avoiding numerical overflows.
+ *
+ * @param mu Real value ofr mean mu.
+ * @param phi Real value for phi.
+ *
+ * @return A random sample from the negative binomial distribution.
+ */
+int neg_binomial_2_safe_rng(real mu, real phi) {
+  if (mu < 1e-8) {
+    return(0);
+  } else if (phi > 1e4) {
+    return(poisson_rng(mu > 1e8 ? 1e8 : mu));
+  } else {
+    real gamma_rate = gamma_rng(phi, phi / mu);
+    return(poisson_rng(gamma_rate > 1e8 ? 1e8 : gamma_rate));
+  }
+}
+
 /**
  * Generate random samples of reported cases
  *
@@ -209,16 +232,7 @@ array[] int report_rng(vector reports, real rep_phi, int model_type) {
   }
 
   for (s in 1:t) {
-    if (reports[s] < 1e-8) {
-      sampled_reports[s] = 0;
-    } else {
-      // defer to poisson if phi is large, to avoid overflow
-      if (dispersion > 1e4) {
-        sampled_reports[s] = poisson_rng(reports[s] > 1e8 ? 1e8 : reports[s]);
-      } else {
-        sampled_reports[s] = neg_binomial_2_rng(reports[s] > 1e8 ? 1e8 : reports[s], dispersion);
-      }
-    }
+    sampled_reports[s] = neg_binomial_2_safe_rng(reports[s], dispersion);
   }
   return(sampled_reports);
 }