beta_binomial_lpmf.hpp

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#ifndef STAN_MATH_PRIM_PROB_BETA_BINOMIAL_LPMF_HPP
#define STAN_MATH_PRIM_PROB_BETA_BINOMIAL_LPMF_HPP
 
#include <stan/math/prim/meta.hpp>
#include <stan/math/prim/err.hpp>
#include <stan/math/prim/fun/binomial_coefficient_log.hpp>
#include <stan/math/prim/fun/constants.hpp>
#include <stan/math/prim/fun/digamma.hpp>
#include <stan/math/prim/fun/grad_F32.hpp>
#include <stan/math/prim/fun/lbeta.hpp>
#include <stan/math/prim/fun/lgamma.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>
 
namespace stan {
namespace math {
 
template <bool propto, typename T_n, typename T_N, typename T_size1,
          typename T_size2,
          require_all_not_nonscalar_prim_or_rev_kernel_expression_t<
              T_n, T_N, T_size1, T_size2>* = nullptr>
return_type_t<T_size1, T_size2> beta_binomial_lpmf(const T_n& n, const T_N& N,
                                                   const T_size1& alpha,
                                                   const T_size2& beta) {
  using T_partials_return = partials_return_t<T_size1, T_size2>;
  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_lpmf";
  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 0.0;
  }
 
  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);
 
  if (!include_summand<propto, T_size1, T_size2>::value) {
    return 0.0;
  }
 
  T_partials_return logp(0.0);
  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 size_alpha = stan::math::size(alpha);
  size_t size_beta = stan::math::size(beta);
  size_t size_n_N = max_size(n, N);
  size_t size_alpha_beta = max_size(alpha, beta);
  size_t max_size_seq_view = max_size(n, N, alpha, beta);
 
  for (size_t i = 0; i < max_size_seq_view; i++) {
    if (n_vec[i] < 0 || n_vec[i] > N_vec[i]) {
      return ops_partials.build(LOG_ZERO);
    }
  }
 
  VectorBuilder<include_summand<propto>::value, T_partials_return, T_n, T_N>
      normalizing_constant(size_n_N);
  for (size_t i = 0; i < size_n_N; i++)
    if (include_summand<propto>::value)
      normalizing_constant[i] = binomial_coefficient_log(N_vec[i], n_vec[i]);
 
  VectorBuilder<true, T_partials_return, T_size1, T_size2> lbeta_denominator(
      size_alpha_beta);
  for (size_t i = 0; i < size_alpha_beta; i++) {
    lbeta_denominator[i] = lbeta(alpha_vec.val(i), beta_vec.val(i));
  }
 
  VectorBuilder<true, T_partials_return, T_n, T_N, T_size1, T_size2> lbeta_diff(
      max_size_seq_view);
  for (size_t i = 0; i < max_size_seq_view; i++) {
    lbeta_diff[i] = lbeta(n_vec[i] + alpha_vec.val(i),
                          N_vec[i] - n_vec[i] + beta_vec.val(i))
                    - lbeta_denominator[i];
  }
 
  VectorBuilder<!is_constant_all<T_size1>::value, T_partials_return, T_n,
                T_size1>
      digamma_n_plus_alpha(max_size(n, alpha));
  if (!is_constant_all<T_size1>::value) {
    for (size_t i = 0; i < max_size(n, alpha); i++) {
      digamma_n_plus_alpha[i] = digamma(n_vec.val(i) + alpha_vec.val(i));
    }
  }
 
  VectorBuilder<!is_constant_all<T_size1, T_size2>::value, T_partials_return,
                T_size1, T_size2>
      digamma_alpha_plus_beta(size_alpha_beta);
  if (!is_constant_all<T_size1, T_size2>::value) {
    for (size_t i = 0; i < size_alpha_beta; i++) {
      digamma_alpha_plus_beta[i] = digamma(alpha_vec.val(i) + beta_vec.val(i));
    }
  }
 
  VectorBuilder<!is_constant_all<T_size1, T_size2>::value, T_partials_return,
                T_N, T_size1, T_size2>
      digamma_diff(max_size(N, alpha, beta));
  if (!is_constant_all<T_size1, T_size2>::value) {
    for (size_t i = 0; i < max_size(N, alpha, beta); i++) {
      digamma_diff[i]
          = digamma_alpha_plus_beta[i]
            - digamma(N_vec.val(i) + alpha_vec.val(i) + beta_vec.val(i));
    }
  }
 
  VectorBuilder<!is_constant_all<T_size1>::value, T_partials_return, T_size1>
      digamma_alpha(size_alpha);
  for (size_t i = 0; i < size_alpha; i++)
    if (!is_constant_all<T_size1>::value)
      digamma_alpha[i] = digamma(alpha_vec.val(i));
 
  VectorBuilder<!is_constant_all<T_size2>::value, T_partials_return, T_size2>
      digamma_beta(size_beta);
  for (size_t i = 0; i < size_beta; i++)
    if (!is_constant_all<T_size2>::value)
      digamma_beta[i] = digamma(beta_vec.val(i));
 
  for (size_t i = 0; i < max_size_seq_view; i++) {
    if (include_summand<propto>::value)
      logp += normalizing_constant[i];
    logp += lbeta_diff[i];
 
    if (!is_constant_all<T_size1>::value)
      partials<0>(ops_partials)[i]
          += digamma_n_plus_alpha[i] + digamma_diff[i] - digamma_alpha[i];
    if (!is_constant_all<T_size2>::value)
      partials<1>(ops_partials)[i]
          += digamma(N_vec.val(i) - n_vec.val(i) + beta_vec.val(i))
             + digamma_diff[i] - digamma_beta[i];
  }
  return ops_partials.build(logp);
}
 
template <typename T_n, typename T_N, typename T_size1, typename T_size2>
return_type_t<T_size1, T_size2> beta_binomial_lpmf(const T_n& n, const T_N& N,
                                                   const T_size1& alpha,
                                                   const T_size2& beta) {
  return beta_binomial_lpmf<false>(n, N, alpha, beta);
}
 
}  // namespace math
}  // namespace stan
#endif