beta_proportion_lpdf.hpp

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#ifndef STAN_MATH_PRIM_PROB_BETA_PROPORTION_LPDF_HPP
#define STAN_MATH_PRIM_PROB_BETA_PROPORTION_LPDF_HPP
 
#include <stan/math/prim/meta.hpp>
#include <stan/math/prim/err.hpp>
#include <stan/math/prim/fun/as_column_vector_or_scalar.hpp>
#include <stan/math/prim/fun/as_array_or_scalar.hpp>
#include <stan/math/prim/fun/as_value_column_array_or_scalar.hpp>
#include <stan/math/prim/fun/constants.hpp>
#include <stan/math/prim/fun/digamma.hpp>
#include <stan/math/prim/fun/lgamma.hpp>
#include <stan/math/prim/fun/log.hpp>
#include <stan/math/prim/fun/log1m.hpp>
#include <stan/math/prim/fun/max_size.hpp>
#include <stan/math/prim/fun/promote_scalar.hpp>
#include <stan/math/prim/fun/size.hpp>
#include <stan/math/prim/fun/size_zero.hpp>
#include <stan/math/prim/fun/to_ref.hpp>
#include <stan/math/prim/fun/value_of.hpp>
#include <stan/math/prim/functor/partials_propagator.hpp>
#include <cmath>
 
namespace stan {
namespace math {
 
template <bool propto, typename T_y, typename T_loc, typename T_prec,
          require_all_not_nonscalar_prim_or_rev_kernel_expression_t<
              T_y, T_loc, T_prec>* = nullptr>
inline return_type_t<T_y, T_loc, T_prec> beta_proportion_lpdf(
    const T_y& y, const T_loc& mu, const T_prec& kappa) {
  using T_partials_return = partials_return_t<T_y, T_loc, T_prec>;
  using std::log;
  using T_y_ref = ref_type_if_not_constant_t<T_y>;
  using T_mu_ref = ref_type_if_not_constant_t<T_loc>;
  using T_kappa_ref = ref_type_if_not_constant_t<T_prec>;
  static constexpr const char* function = "beta_proportion_lpdf";
  check_consistent_sizes(function, "Random variable", y, "Location parameter",
                         mu, "Precision parameter", kappa);
  if (size_zero(y, mu, kappa)) {
    return 0;
  }
 
  T_y_ref y_ref = y;
  T_mu_ref mu_ref = mu;
  T_kappa_ref kappa_ref = kappa;
 
  decltype(auto) y_val = to_ref(as_value_column_array_or_scalar(y_ref));
  decltype(auto) mu_val = to_ref(as_value_column_array_or_scalar(mu_ref));
  decltype(auto) kappa_val = to_ref(as_value_column_array_or_scalar(kappa_ref));
 
  check_positive(function, "Location parameter", mu_val);
  check_less(function, "Location parameter", mu_val, 1.0);
  check_positive_finite(function, "Precision parameter", kappa_val);
  check_bounded(function, "Random variable", value_of(y_val), 0, 1);
 
  if constexpr (!include_summand<propto, T_y, T_loc, T_prec>::value) {
    return 0;
  }
 
  const auto& log_y = to_ref_if<is_any_autodiff_v<T_loc, T_prec>>(log(y_val));
  const auto& log1m_y
      = to_ref_if<is_any_autodiff_v<T_loc, T_prec>>(log1m(y_val));
  const auto& mukappa = to_ref(mu_val * kappa_val);
 
  size_t N = max_size(y, mu, kappa);
  T_partials_return logp(0);
  if constexpr (include_summand<propto, T_prec>::value) {
    logp += sum(lgamma(kappa_val)) * N / math::size(kappa);
  }
  if constexpr (include_summand<propto, T_loc, T_prec>::value) {
    logp -= sum(lgamma(mukappa) + lgamma(kappa_val - mukappa)) * N
            / max_size(mu, kappa_val);
  }
  logp += sum((mukappa - 1) * log_y + (kappa_val - mukappa - 1) * log1m_y);
 
  auto ops_partials = make_partials_propagator(y_ref, mu_ref, kappa_ref);
  if constexpr (is_autodiff_v<T_y>) {
    edge<0>(ops_partials).partials_
        = (mukappa - 1) / y_val + (kappa_val - mukappa - 1) / (y_val - 1);
  }
  if constexpr (is_any_autodiff_v<T_loc, T_prec>) {
    auto digamma_mukappa
        = to_ref_if<(is_autodiff_v<T_loc> && is_autodiff_v<T_prec>)>(
            digamma(mukappa));
    auto digamma_kappa_mukappa
        = to_ref_if<(is_autodiff_v<T_loc> && is_autodiff_v<T_prec>)>(
            digamma(kappa_val - mukappa));
    if constexpr (is_autodiff_v<T_loc>) {
      edge<1>(ops_partials).partials_
          = kappa_val
            * (digamma_kappa_mukappa - digamma_mukappa + log_y - log1m_y);
    }
    if constexpr (is_autodiff_v<T_prec>) {
      edge<2>(ops_partials).partials_
          = digamma(kappa_val) + mu_val * (log_y - digamma_mukappa)
            + (1 - mu_val) * (log1m_y - digamma_kappa_mukappa);
    }
  }
  return ops_partials.build(logp);
}
 
template <typename T_y, typename T_loc, typename T_prec>
inline return_type_t<T_y, T_loc, T_prec> beta_proportion_lpdf(
    const T_y& y, const T_loc& mu, const T_prec& kappa) {
  return beta_proportion_lpdf<false>(y, mu, kappa);
}
 
}  // namespace math
}  // namespace stan
#endif