inv_gamma_lpdf.hpp

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#ifndef STAN_MATH_PRIM_PROB_INV_GAMMA_LPDF_HPP
#define STAN_MATH_PRIM_PROB_INV_GAMMA_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/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_shape, typename T_scale,
          require_all_not_nonscalar_prim_or_rev_kernel_expression_t<
              T_y, T_shape, T_scale>* = nullptr>
inline return_type_t<T_y, T_shape, T_scale> inv_gamma_lpdf(
    const T_y& y, const T_shape& alpha, const T_scale& beta) {
  using T_partials_return = partials_return_t<T_y, T_shape, T_scale>;
  using T_y_ref = ref_type_if_not_constant_t<T_y>;
  using T_alpha_ref = ref_type_if_not_constant_t<T_shape>;
  using T_beta_ref = ref_type_if_not_constant_t<T_scale>;
  static constexpr const char* function = "inv_gamma_lpdf";
  check_consistent_sizes(function, "Random variable", y, "Shape parameter",
                         alpha, "Scale parameter", beta);
 
  T_y_ref y_ref = y;
  T_alpha_ref alpha_ref = alpha;
  T_beta_ref beta_ref = beta;
 
  decltype(auto) y_val = to_ref(as_value_column_array_or_scalar(y_ref));
  decltype(auto) alpha_val = to_ref(as_value_column_array_or_scalar(alpha_ref));
  decltype(auto) beta_val = to_ref(as_value_column_array_or_scalar(beta_ref));
 
  check_not_nan(function, "Random variable", y_val);
  check_positive_finite(function, "Shape parameter", alpha_val);
  check_positive_finite(function, "Scale parameter", beta_val);
 
  if (size_zero(y, alpha, beta)) {
    return 0;
  }
  if constexpr (!include_summand<propto, T_y, T_shape, T_scale>::value) {
    return 0;
  }
  if (sum(promote_scalar<int>(y_val <= 0))) {
    return LOG_ZERO;
  }
 
  T_partials_return logp(0);
  auto ops_partials = make_partials_propagator(y_ref, alpha_ref, beta_ref);
 
  const auto& log_y
      = to_ref_if<include_summand<propto, T_y, T_shape>::value>(log(y_val));
 
  size_t N = max_size(y, alpha, beta);
  if constexpr (include_summand<propto, T_shape>::value) {
    logp -= sum(lgamma(alpha_val)) * N / math::size(alpha);
  }
  if constexpr (include_summand<propto, T_shape, T_scale>::value) {
    const auto& log_beta = to_ref_if<is_autodiff_v<T_shape>>(log(beta_val));
    logp += sum(alpha_val * log_beta) * N / max_size(alpha, beta);
    if constexpr (is_autodiff_v<T_shape>) {
      partials<1>(ops_partials) = log_beta - digamma(alpha_val) - log_y;
    }
  }
  if constexpr (include_summand<propto, T_y, T_shape>::value) {
    logp -= sum((alpha_val + 1.0) * log_y) * N / max_size(y, alpha);
  }
  if constexpr (include_summand<propto, T_y, T_scale>::value) {
    const auto& inv_y
        = to_ref_if<(is_autodiff_v<T_y> || is_autodiff_v<T_scale>)>(inv(y_val));
    logp -= sum(beta_val * inv_y) * N / max_size(y, beta);
    if constexpr (is_autodiff_v<T_y>) {
      edge<0>(ops_partials).partials_
          = (beta_val * inv_y - alpha_val - 1) * inv_y;
    }
    if constexpr (is_autodiff_v<T_scale>) {
      partials<2>(ops_partials) = alpha_val / beta_val - inv_y;
    }
  }
  return ops_partials.build(logp);
}
 
template <typename T_y, typename T_shape, typename T_scale>
inline return_type_t<T_y, T_shape, T_scale> inv_gamma_lpdf(
    const T_y& y, const T_shape& alpha, const T_scale& beta) {
  return inv_gamma_lpdf<false>(y, alpha, beta);
}
 
}  // namespace math
}  // namespace stan
#endif