beta_binomial_cdf.hpp

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#ifndef STAN_MATH_PRIM_PROB_BETA_BINOMIAL_CDF_HPP
#define STAN_MATH_PRIM_PROB_BETA_BINOMIAL_CDF_HPP
 
#include <stan/math/prim/meta.hpp>
#include <stan/math/prim/err.hpp>
#include <stan/math/prim/fun/beta.hpp>
#include <stan/math/prim/fun/constants.hpp>
#include <stan/math/prim/fun/digamma.hpp>
#include <stan/math/prim/fun/exp.hpp>
#include <stan/math/prim/fun/hypergeometric_3F2.hpp>
#include <stan/math/prim/fun/grad_F32.hpp>
#include <stan/math/prim/fun/lbeta.hpp>
#include <stan/math/prim/fun/max_size.hpp>
#include <stan/math/prim/fun/scalar_seq_view.hpp>
#include <stan/math/prim/fun/size.hpp>
#include <stan/math/prim/fun/size_zero.hpp>
#include <stan/math/prim/fun/value_of.hpp>
#include <stan/math/prim/functor/partials_propagator.hpp>
#include <cmath>
 
namespace stan {
namespace math {
 
template <typename T_n, typename T_N, typename T_size1, typename T_size2>
return_type_t<T_size1, T_size2> beta_binomial_cdf(const T_n& n, const T_N& N,
                                                  const T_size1& alpha,
                                                  const T_size2& beta) {
  using T_partials_return = partials_return_t<T_n, T_N, T_size1, T_size2>;
  using std::exp;
  using T_N_ref = ref_type_t<T_N>;
  using T_alpha_ref = ref_type_t<T_size1>;
  using T_beta_ref = ref_type_t<T_size2>;
  static constexpr const char* function = "beta_binomial_cdf";
  check_consistent_sizes(function, "Successes variable", n,
                         "Population size parameter", N,
                         "First prior sample size parameter", alpha,
                         "Second prior sample size parameter", beta);
  if (size_zero(n, N, alpha, beta)) {
    return 1.0;
  }
 
  T_N_ref N_ref = N;
  T_alpha_ref alpha_ref = alpha;
  T_beta_ref beta_ref = beta;
  check_nonnegative(function, "Population size parameter", N_ref);
  check_positive_finite(function, "First prior sample size parameter",
                        alpha_ref);
  check_positive_finite(function, "Second prior sample size parameter",
                        beta_ref);
 
  T_partials_return P(1.0);
  auto ops_partials = make_partials_propagator(alpha_ref, beta_ref);
 
  scalar_seq_view<T_n> n_vec(n);
  scalar_seq_view<T_N_ref> N_vec(N_ref);
  scalar_seq_view<T_alpha_ref> alpha_vec(alpha_ref);
  scalar_seq_view<T_beta_ref> beta_vec(beta_ref);
  size_t max_size_seq_view = max_size(n, N, alpha, beta);
 
  // Explicit return for extreme values
  // The gradients are technically ill-defined, but treated as zero
  for (size_t i = 0; i < stan::math::size(n); i++) {
    if (n_vec.val(i) < 0) {
      return ops_partials.build(0.0);
    }
  }
 
  for (size_t i = 0; i < max_size_seq_view; i++) {
    // Explicit results for extreme values
    // The gradients are technically ill-defined, but treated as zero
    if (n_vec.val(i) >= N_vec.val(i)) {
      continue;
    }
 
    const T_partials_return n_dbl = n_vec.val(i);
    const T_partials_return N_dbl = N_vec.val(i);
    const T_partials_return alpha_dbl = alpha_vec.val(i);
    const T_partials_return beta_dbl = beta_vec.val(i);
    const T_partials_return N_minus_n = N_dbl - n_dbl;
    const T_partials_return mu = alpha_dbl + n_dbl + 1;
    const T_partials_return nu = beta_dbl + N_minus_n - 1;
    const T_partials_return one = 1;
 
    const T_partials_return F = hypergeometric_3F2({one, mu, 1 - N_minus_n},
                                                   {n_dbl + 2, 1 - nu}, one);
 
    T_partials_return C = lbeta(nu, mu) - lbeta(alpha_dbl, beta_dbl)
                          - lbeta(N_minus_n, n_dbl + 2);
    C = F * exp(C) / (N_dbl + 1);
 
    const T_partials_return Pi = 1 - C;
 
    P *= Pi;
 
    T_partials_return digammaDiff
        = is_constant_all<T_size1, T_size2>::value
              ? 0
              : digamma(alpha_dbl + beta_dbl) - digamma(mu + nu);
 
    T_partials_return dF[6];
    if (!is_constant_all<T_size1, T_size2>::value) {
      grad_F32(dF, one, mu, 1 - N_minus_n, n_dbl + 2, 1 - nu, one);
    }
    if (!is_constant_all<T_size1>::value) {
      const T_partials_return g
          = -C * (digamma(mu) - digamma(alpha_dbl) + digammaDiff + dF[1] / F);
      partials<0>(ops_partials)[i] += g / Pi;
    }
    if (!is_constant_all<T_size2>::value) {
      const T_partials_return g
          = -C * (digamma(nu) - digamma(beta_dbl) + digammaDiff - dF[4] / F);
      partials<1>(ops_partials)[i] += g / Pi;
    }
  }
 
  if (!is_constant_all<T_size1>::value) {
    for (size_t i = 0; i < stan::math::size(alpha); ++i) {
      partials<0>(ops_partials)[i] *= P;
    }
  }
  if (!is_constant_all<T_size2>::value) {
    for (size_t i = 0; i < stan::math::size(beta); ++i) {
      partials<1>(ops_partials)[i] *= P;
    }
  }
 
  return ops_partials.build(P);
}
 
}  // namespace math
}  // namespace stan
#endif