primarycensored.stan

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real primarycensored_log_normalizer(real log_cdf_D, real log_cdf_L, real L) {
  if (L > 0) {
    return log_diff_exp(log_cdf_D, log_cdf_L);
  } else {
    return log_cdf_D;
  }
}
 
real primarycensored_apply_truncation(real log_cdf, real log_cdf_L,
                                      real log_normalizer, real L) {
  if (L > 0) {
    return log_diff_exp(log_cdf, log_cdf_L) - log_normalizer;
  } else {
    return log_cdf - log_normalizer;
  }
}
 
vector primarycensored_truncation_bounds(
  data real L, data real D,
  int dist_id, array[] real params, data real pwindow,
  int primary_id, array[] real primary_params
) {
  vector[2] result;
 
  // Get CDF at lower truncation point L
  if (L <= 0) {
    result[1] = negative_infinity();
  } else {
    result[1] = primarycensored_lcdf(
      L | dist_id, params, pwindow, 0, positive_infinity(),
      primary_id, primary_params
    );
  }
 
  // Get CDF at upper truncation point D
  if (is_inf(D)) {
    result[2] = 0;
  } else {
    result[2] = primarycensored_lcdf(
      D | dist_id, params, pwindow, 0, positive_infinity(),
      primary_id, primary_params
    );
  }
 
  return result;
}
 
real primarycensored_cdf(data real d, int dist_id, array[] real params,
                               data real pwindow, data real L, data real D,
                               int primary_id,
                               array[] real primary_params) {
  real result;
  if (d <= L) {
    return 0;
  }
 
  if (d >= D) {
    return 1;
  }
 
  // Check if an analytical solution exists
  if (check_for_analytical(dist_id, primary_id)) {
    // Use analytical solution
    result = primarycensored_analytical_cdf(
      d | dist_id, params, pwindow, L, D, primary_id, primary_params
    );
  } else {
    // Use numerical integration for other cases
    real lower_bound = max({d - pwindow, 1e-6});
    int n_params = num_elements(params);
    int n_primary_params = num_elements(primary_params);
    array[n_params + n_primary_params] real theta = append_array(params, primary_params);
    array[4] int ids = {dist_id, primary_id, n_params, n_primary_params};
 
    vector[1] y0 = rep_vector(0.0, 1);
    result = ode_rk45(primarycensored_ode, y0, lower_bound, {d}, theta, {d, pwindow}, ids)[1, 1];
 
    // Apply truncation normalization on log scale for numerical stability
    if (!is_inf(D) || L > 0) {
      real log_result = log(result);
      vector[2] bounds = primarycensored_truncation_bounds(
        L, D, dist_id, params, pwindow, primary_id, primary_params
      );
      real log_cdf_L = bounds[1];
      real log_cdf_D = bounds[2];
 
      real log_normalizer = primarycensored_log_normalizer(log_cdf_D, log_cdf_L, L);
      log_result = primarycensored_apply_truncation(
        log_result, log_cdf_L, log_normalizer, L
      );
      result = exp(log_result);
    }
  }
 
  return result;
}
 
real primarycensored_lcdf(data real d, int dist_id, array[] real params,
                                data real pwindow, data real L, data real D,
                                int primary_id,
                                array[] real primary_params) {
  real result;
 
  if (d <= L) {
    return negative_infinity();
  }
 
  if (d >= D) {
    return 0;
  }
 
  // Check if an analytical solution exists
  if (check_for_analytical(dist_id, primary_id)) {
    result = primarycensored_analytical_lcdf(
      d | dist_id, params, pwindow, 0, positive_infinity(), primary_id, primary_params
    );
  } else {
    // Use numerical integration
    result = log(primarycensored_cdf(
      d | dist_id, params, pwindow, 0, positive_infinity(), primary_id, primary_params
    ));
  }
 
  // Handle truncation normalization
  if (!is_inf(D) || L > 0) {
    vector[2] bounds = primarycensored_truncation_bounds(
      L, D, dist_id, params, pwindow, primary_id, primary_params
    );
    real log_cdf_L = bounds[1];
    real log_cdf_D = bounds[2];
 
    real log_normalizer = primarycensored_log_normalizer(log_cdf_D, log_cdf_L, L);
    result = primarycensored_apply_truncation(result, log_cdf_L, log_normalizer, L);
  }
 
  return result;
}
 
real primarycensored_lpmf(data int d, int dist_id, array[] real params,
                                data real pwindow, data real d_upper,
                                data real L, data real D, int primary_id,
                                array[] real primary_params) {
  if (d_upper > D) {
    reject("Upper truncation point is greater than D. It is ", d_upper,
           " and D is ", D, ". Resolve this by increasing D to be greater or equal to d + swindow or decreasing swindow.");
  }
  if (d_upper <= d) {
    reject("Upper truncation point is less than or equal to d. It is ", d_upper,
           " and d is ", d, ". Resolve this by increasing d to be less than d_upper.");
  }
  if (d < L) {
    return negative_infinity();
  }
  real log_cdf_upper = primarycensored_lcdf(
    d_upper | dist_id, params, pwindow, 0, positive_infinity(), primary_id, primary_params
  );
  real log_cdf_lower = primarycensored_lcdf(
    d | dist_id, params, pwindow, 0, positive_infinity(), primary_id, primary_params
  );
 
  // Apply truncation normalization: log((F(d_upper) - F(d)) / (F(D) - F(L)))
  if (!is_inf(D) || L > 0) {
    real log_cdf_D;
    real log_cdf_L;
 
    // Get CDF at lower truncation point L
    if (L <= 0) {
      // No left truncation
      log_cdf_L = negative_infinity();
    } else if (d == L) {
      // Reuse already computed CDF at d
      log_cdf_L = log_cdf_lower;
    } else {
      // Compute CDF at L directly
      log_cdf_L = primarycensored_lcdf(
        L | dist_id, params, pwindow, 0, positive_infinity(),
        primary_id, primary_params
      );
    }
 
    // Get CDF at upper truncation point D
    if (d_upper == D) {
      log_cdf_D = log_cdf_upper;
    } else if (is_inf(D)) {
      log_cdf_D = 0;
    } else {
      log_cdf_D = primarycensored_lcdf(
        D | dist_id, params, pwindow, 0, positive_infinity(),
        primary_id, primary_params
      );
    }
 
    real log_normalizer = primarycensored_log_normalizer(log_cdf_D, log_cdf_L, L);
    return log_diff_exp(log_cdf_upper, log_cdf_lower) - log_normalizer;
  } else {
    return log_diff_exp(log_cdf_upper, log_cdf_lower);
  }
}
 
real primarycensored_pmf(data int d, int dist_id, array[] real params,
                               data real pwindow, data real d_upper,
                               data real L, data real D, int primary_id,
                               array[] real primary_params) {
  return exp(
    primarycensored_lpmf(
      d | dist_id, params, pwindow, d_upper, L, D, primary_id, primary_params
    )
  );
}
 
vector primarycensored_sone_lpmf_vectorized(
  int max_delay, data real L, data real D, int dist_id,
  array[] real params, data real pwindow,
  int primary_id, array[] real primary_params
) {
 
  int upper_interval = max_delay + 1;
  vector[upper_interval] log_pmfs;
  vector[upper_interval] log_cdfs;
  real log_normalizer;
 
  // Check if D is at least max_delay + 1
  if (D < upper_interval) {
    reject("D must be at least max_delay + 1");
  }
 
  // Compute log CDFs (without truncation normalization)
  // Start from max(1, floor(L)) to avoid computing unused CDFs when L > 0
  int start_idx = L > 0 ? max(1, to_int(floor(L))) : 1;
  for (d in start_idx:upper_interval) {
    log_cdfs[d] = primarycensored_lcdf(
      d | dist_id, params, pwindow, 0, positive_infinity(), primary_id,
      primary_params
    );
  }
 
  // Get CDF at lower truncation point L
  real log_cdf_L;
  if (L <= 0) {
    // No left truncation
    log_cdf_L = negative_infinity();
  } else if (L <= upper_interval && floor(L) == L) {
    // L is an integer within computed range, reuse cached value
    log_cdf_L = log_cdfs[to_int(L)];
  } else {
    // L is outside computed range or non-integer, compute directly
    log_cdf_L = primarycensored_lcdf(
      L | dist_id, params, pwindow, 0, positive_infinity(),
      primary_id, primary_params
    );
  }
 
  // Compute log normalizer: log(F(D) - F(L))
  real log_cdf_D;
  if (D > upper_interval) {
    if (is_inf(D)) {
      log_cdf_D = 0; // log(1) = 0 for infinite D
    } else {
      log_cdf_D = primarycensored_lcdf(
        D | dist_id, params, pwindow, 0, positive_infinity(),
        primary_id, primary_params
      );
    }
  } else {
    log_cdf_D = log_cdfs[upper_interval];
  }
 
  log_normalizer = primarycensored_log_normalizer(log_cdf_D, log_cdf_L, L);
 
  // Compute log PMFs: log((F(d) - F(d-1)) / (F(D) - F(L)))
  for (d in 1:upper_interval) {
    if (d <= L) {
      // Delay interval [d-1, d) is entirely at or below L
      log_pmfs[d] = negative_infinity();
    } else if (d - 1 < L) {
      // L falls within interval [d-1, d), so compute mass in [L, d)
      log_pmfs[d] = log_diff_exp(log_cdfs[d], log_cdf_L) - log_normalizer;
    } else if (d == 1) {
      // First interval [0, 1) with L <= 0: F(0) = 0, so PMF = F(1) / normalizer
      log_pmfs[d] = log_cdfs[d] - log_normalizer;
    } else {
      // Standard case: PMF = (F(d) - F(d-1)) / normalizer
      log_pmfs[d] = log_diff_exp(log_cdfs[d], log_cdfs[d-1]) - log_normalizer;
    }
  }
 
  return log_pmfs;
}
 
vector primarycensored_sone_pmf_vectorized(
  int max_delay, data real L, data real D, int dist_id,
  array[] real params, data real pwindow,
  int primary_id,
  array[] real primary_params
) {
  return exp(
    primarycensored_sone_lpmf_vectorized(
      max_delay, L, D, dist_id, params, pwindow, primary_id, primary_params
    )
  );
}