beta_binomial.hpp

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#ifndef __STAN__PROB__DISTRIBUTIONS__UNIVARIATE__DISCRETE__BETA_BINOMIAL_HPP__
#define __STAN__PROB__DISTRIBUTIONS__UNIVARIATE__DISCRETE__BETA_BINOMIAL_HPP__

#include <stan/agrad.hpp>
#include <stan/math/error_handling.hpp>
#include <stan/math/special_functions.hpp>
#include <stan/meta/traits.hpp>
#include <stan/prob/traits.hpp>
#include <stan/prob/constants.hpp>

namespace stan {
  
  namespace prob {

    // BetaBinomial(n|alpha,beta) [alpha > 0;  beta > 0;  n >= 0]
    template <bool propto,
              typename T_n,
              typename T_N,
              typename T_size1, 
              typename T_size2, 
              class Policy>
    typename return_type<T_size1,T_size2>::type
    beta_binomial_log(const T_n& n, 
                      const T_N& N, 
                      const T_size1& alpha, 
                      const T_size2& beta, 
                      const Policy&) {
      static const char* function = "stan::prob::beta_binomial_log(%1%)";

      using stan::math::check_finite;
      using stan::math::check_nonnegative;
      using stan::math::check_positive;
      using stan::math::value_of;
      using stan::math::check_consistent_sizes;
      using stan::prob::include_summand;

      // check if any vectors are zero length
      if (!(stan::length(n)
            && stan::length(N)
            && stan::length(alpha)
            && stan::length(beta)))
        return 0.0;
      
      typename return_type<T_size1,T_size2>::type logp(0.0);
      if (!check_nonnegative(function, N, "Population size parameter", &logp, Policy()))
        return logp;
      if (!check_finite(function, alpha, "First prior sample size parameter", &logp, 
                        Policy()))
        return logp;
      if (!check_positive(function, alpha, "First prior sample size parameter", 
                          &logp, Policy()))
        return logp;
      if (!check_finite(function, beta, "Second prior sample size parameter",
                        &logp, Policy()))
        return logp;
      if (!check_positive(function, beta, "Second prior sample size parameter", 
                          &logp, Policy()))
        return logp;
      if (!(check_consistent_sizes(function,
                                   n,N,alpha,beta,
                                   "Successes variable","Population size parameter","First prior sample size parameter","Second prior sample size parameter",
                                   &logp, Policy())))
        return logp;

      // check if no variables are involved and prop-to
      if (!include_summand<propto,T_size1,T_size2>::value)
        return 0.0;

      VectorView<const T_n> n_vec(n);
      VectorView<const T_N> N_vec(N);
      VectorView<const T_size1> alpha_vec(alpha);
      VectorView<const T_size2> beta_vec(beta);
      size_t size = max_size(n, N, alpha, beta);
      
      for (size_t i = 0; i < size; i++) {
        if (n_vec[i] < 0 || n_vec[i] > N_vec[i])
          return LOG_ZERO;
      }

      using stan::math::lbeta;
      using stan::math::binomial_coefficient_log;

      for (size_t i = 0; i < size; i++) {
        if (include_summand<propto>::value)
          logp += binomial_coefficient_log(N_vec[i],n_vec[i]);
        if (include_summand<propto,T_size1,T_size2>::value)
          logp += lbeta(n_vec[i] + alpha_vec[i], N_vec[i] - n_vec[i] + beta_vec[i]) 
            - lbeta(alpha_vec[i],beta_vec[i]);
      }
      return logp;
    }

    template <bool propto,
              typename T_n,
              typename T_N,
              typename T_size1,
              typename T_size2>
    typename return_type<T_size1,T_size2>::type
    beta_binomial_log(const T_n& n, const T_N& N, 
                      const T_size1& alpha, const T_size2& beta) {
      return beta_binomial_log<propto>(n,N,alpha,beta,
                                       stan::math::default_policy());
    }

    template <typename T_n,
              typename T_N,
              typename T_size1,
              typename T_size2, 
              class Policy>
    typename return_type<T_size1,T_size2>::type
    inline
    beta_binomial_log(const T_n& n, const T_N& N, 
                      const T_size1& alpha, const T_size2& beta, 
                      const Policy&) {
      return beta_binomial_log<false>(n,N,alpha,beta,Policy());
    }

    template <typename T_n,
              typename T_N,
              typename T_size1,
              typename T_size2>
    typename return_type<T_size1,T_size2>::type
    beta_binomial_log(const T_n& n, const T_N& N, 
                      const T_size1& alpha, const T_size2& beta) {
      return beta_binomial_log<false>(n,N,alpha,beta,
                                      stan::math::default_policy());
    }

  }
}
#endif