beta_binomial_cdf.hpp
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#ifndef STAN_MATH_PRIM_SCAL_PROB_BETA_BINOMIAL_CDF_HPP
#define STAN_MATH_PRIM_SCAL_PROB_BETA_BINOMIAL_CDF_HPP
#include <stan/math/prim/scal/meta/is_constant_struct.hpp>
#include <stan/math/prim/scal/meta/partials_return_type.hpp>
#include <stan/math/prim/scal/meta/OperandsAndPartials.hpp>
#include <stan/math/prim/scal/err/check_consistent_sizes.hpp>
#include <stan/math/prim/scal/err/check_nonnegative.hpp>
#include <stan/math/prim/scal/err/check_positive_finite.hpp>
#include <stan/math/prim/scal/fun/constants.hpp>
#include <stan/math/prim/scal/fun/lbeta.hpp>
#include <stan/math/prim/scal/fun/digamma.hpp>
#include <stan/math/prim/scal/fun/lgamma.hpp>
#include <stan/math/prim/scal/fun/binomial_coefficient_log.hpp>
#include <stan/math/prim/scal/fun/value_of.hpp>
#include <stan/math/prim/scal/meta/contains_nonconstant_struct.hpp>
#include <stan/math/prim/scal/meta/include_summand.hpp>
#include <stan/math/prim/scal/prob/beta_rng.hpp>
#include <stan/math/prim/scal/fun/F32.hpp>
#include <stan/math/prim/scal/fun/grad_F32.hpp>
#include <cmath>
namespace stan {
namespace math {
// Beta-Binomial CDF
template <typename T_n, typename T_N,
typename T_size1, typename T_size2>
typename return_type<T_size1, T_size2>::type
beta_binomial_cdf(const T_n& n, const T_N& N, const T_size1& alpha,
const T_size2& beta) {
static const char* function("beta_binomial_cdf");
typedef typename stan::partials_return_type<T_n, T_N, T_size1,
T_size2>::type
T_partials_return;
if (!(stan::length(n) && stan::length(N) && stan::length(alpha)
&& stan::length(beta)))
return 1.0;
T_partials_return P(1.0);
check_nonnegative(function, "Population size parameter", N);
check_positive_finite(function,
"First prior sample size parameter", alpha);
check_positive_finite(function,
"Second prior sample size parameter", beta);
check_consistent_sizes(function,
"Successes variable", n,
"Population size parameter", N,
"First prior sample size parameter", alpha,
"Second prior sample size parameter", beta);
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);
using std::exp;
using std::exp;
OperandsAndPartials<T_size1, T_size2>
operands_and_partials(alpha, beta);
// Explicit return for extreme values
// The gradients are technically ill-defined, but treated as zero
for (size_t i = 0; i < stan::length(n); i++) {
if (value_of(n_vec[i]) <= 0)
return operands_and_partials.value(0.0);
}
for (size_t i = 0; i < size; i++) {
// Explicit results for extreme values
// The gradients are technically ill-defined, but treated as zero
if (value_of(n_vec[i]) >= value_of(N_vec[i])) {
continue;
}
const T_partials_return n_dbl = value_of(n_vec[i]);
const T_partials_return N_dbl = value_of(N_vec[i]);
const T_partials_return alpha_dbl = value_of(alpha_vec[i]);
const T_partials_return beta_dbl = value_of(beta_vec[i]);
const T_partials_return mu = alpha_dbl + n_dbl + 1;
const T_partials_return nu = beta_dbl + N_dbl - n_dbl - 1;
const T_partials_return F = F32((T_partials_return)1, mu,
-N_dbl + n_dbl + 1,
n_dbl + 2, 1 - nu,
(T_partials_return)1);
T_partials_return C = lgamma(nu) - lgamma(N_dbl - n_dbl);
C += lgamma(mu) - lgamma(n_dbl + 2);
C += lgamma(N_dbl + 2) - lgamma(N_dbl + alpha_dbl + beta_dbl);
C = exp(C);
C *= F / exp(lbeta(alpha_dbl, beta_dbl));
C /= N_dbl + 1;
const T_partials_return Pi = 1 - C;
P *= Pi;
T_partials_return dF[6];
T_partials_return digammaOne = 0;
T_partials_return digammaTwo = 0;
if (contains_nonconstant_struct<T_size1, T_size2>::value) {
digammaOne = digamma(mu + nu);
digammaTwo = digamma(alpha_dbl + beta_dbl);
grad_F32(dF, (T_partials_return)1, mu, -N_dbl + n_dbl + 1,
n_dbl + 2,
1 - nu, (T_partials_return)1);
}
if (!is_constant_struct<T_size1>::value) {
const T_partials_return g
= - C * (digamma(mu) - digammaOne + dF[1] / F
- digamma(alpha_dbl) + digammaTwo);
operands_and_partials.d_x1[i]
+= g / Pi;
}
if (!is_constant_struct<T_size2>::value) {
const T_partials_return g
= - C * (digamma(nu) - digammaOne - dF[4] / F - digamma(beta_dbl)
+ digammaTwo);
operands_and_partials.d_x2[i]
+= g / Pi;
}
}
if (!is_constant_struct<T_size1>::value) {
for (size_t i = 0; i < stan::length(alpha); ++i)
operands_and_partials.d_x1[i] *= P;
}
if (!is_constant_struct<T_size2>::value) {
for (size_t i = 0; i < stan::length(beta); ++i)
operands_and_partials.d_x2[i] *= P;
}
return operands_and_partials.value(P);
}
}
}
#endif
stan::math::OperandsAndPartials::d_x2
VectorView< T_return_type, false, true > d_x2
Definition: OperandsAndPartials.hpp:39
lgamma.hpp
stan::math::lgamma
fvar< T > lgamma(const fvar< T > &x)
Return the natural logarithm of the gamma function applied to the specified argument.
Definition: lgamma.hpp:20
check_positive_finite.hpp
stan
Definition: log_sum_exp.hpp:8
stan::math::value_of
T value_of(const fvar< T > &v)
Return the value of the specified variable.
Definition: value_of.hpp:16
stan::math::lbeta
fvar< T > lbeta(const fvar< T > &x1, const fvar< T > &x2)
Definition: lbeta.hpp:15
digamma.hpp
stan::math::OperandsAndPartials::value
T_return_type value(double value)
Returns a T_return_type with the value specified with the partial derivatves.
Definition: OperandsAndPartials.hpp:67
contains_nonconstant_struct.hpp
stan::length
size_t length(const std::vector< T > &x)
Definition: length.hpp:10
binomial_coefficient_log.hpp
is_constant_struct.hpp
F32.hpp
stan::math::check_nonnegative
void check_nonnegative(const char *function, const char *name, const T_y &y)
Check if y is non-negative.
Definition: check_nonnegative.hpp:61
stan::return_type::type
boost::math::tools::promote_args< typename scalar_type< T1 >::type, typename scalar_type< T2 >::type, typename scalar_type< T3 >::type, typename scalar_type< T4 >::type, typename scalar_type< T5 >::type, typename scalar_type< T6 >::type >::type type
Definition: return_type.hpp:27
include_summand.hpp
check_nonnegative.hpp
stan::is_constant_struct
Metaprogram to determine if a type has a base scalar type that can be assigned to type double...
Definition: is_constant_struct.hpp:13
stan::math::beta_binomial_cdf
return_type< T_size1, T_size2 >::type beta_binomial_cdf(const T_n &n, const T_N &N, const T_size1 &alpha, const T_size2 &beta)
Definition: beta_binomial_cdf.hpp:30
stan::math::check_positive_finite
void check_positive_finite(const char *function, const char *name, const T_y &y)
Check if y is positive and finite.
Definition: check_positive_finite.hpp:26
stan::partials_return_type
Definition: partials_return_type.hpp:16
stan::math::exp
fvar< T > exp(const fvar< T > &x)
Definition: exp.hpp:10
beta_rng.hpp
stan::math::OperandsAndPartials
This class builds partial derivatives with respect to a set of operands.
Definition: OperandsAndPartials.hpp:37
stan::max_size
size_t max_size(const T1 &x1, const T2 &x2)
Definition: max_size.hpp:9
partials_return_type.hpp
OperandsAndPartials.hpp
stan::contains_nonconstant_struct
Definition: contains_nonconstant_struct.hpp:14
grad_F32.hpp
stan::math::grad_F32
void grad_F32(T *g, T a, T b, T c, T d, T e, T z, T precision=1e-6)
Definition: grad_F32.hpp:10
constants.hpp
stan::math::size
int size(const std::vector< T > &x)
Return the size of the specified standard vector.
Definition: size.hpp:17
lbeta.hpp
stan::math::F32
T F32(T a, T b, T c, T d, T e, T z, T precision=1e-6)
Definition: F32.hpp:10
value_of.hpp
stan::VectorView
VectorView is a template expression that is constructed with a container or scalar, which it then allows to be used as an array using operator[].
Definition: VectorView.hpp:48
stan::math::check_consistent_sizes
void check_consistent_sizes(const char *function, const char *name1, const T1 &x1, const char *name2, const T2 &x2)
Check if the dimension of x1 is consistent with x2.
Definition: check_consistent_sizes.hpp:30
check_consistent_sizes.hpp
stan::math::OperandsAndPartials::d_x1
VectorView< T_return_type, false, true > d_x1
Definition: OperandsAndPartials.hpp:38
stan::math::digamma
fvar< T > digamma(const fvar< T > &x)
Return the derivative of the log gamma function at the specified argument.
Definition: digamma.hpp:22

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