student_t_lcdf.hpp
Go to the documentation of this file.
#ifndef STAN_MATH_PRIM_SCAL_PROB_STUDENT_T_LCDF_HPP
#define STAN_MATH_PRIM_SCAL_PROB_STUDENT_T_LCDF_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_finite.hpp>
#include <stan/math/prim/scal/err/check_not_nan.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/square.hpp>
#include <stan/math/prim/scal/fun/value_of.hpp>
#include <stan/math/prim/scal/fun/lbeta.hpp>
#include <stan/math/prim/scal/fun/lgamma.hpp>
#include <stan/math/prim/scal/fun/digamma.hpp>
#include <stan/math/prim/scal/meta/length.hpp>
#include <stan/math/prim/scal/fun/grad_reg_inc_beta.hpp>
#include <stan/math/prim/scal/fun/inc_beta.hpp>
#include <stan/math/prim/scal/meta/include_summand.hpp>
#include <stan/math/prim/scal/meta/VectorBuilder.hpp>
#include <boost/random/student_t_distribution.hpp>
#include <boost/random/variate_generator.hpp>
#include <limits>
#include <cmath>
namespace stan {
namespace math {
template <typename T_y, typename T_dof, typename T_loc, typename T_scale>
typename return_type<T_y, T_dof, T_loc, T_scale>::type
student_t_lcdf(const T_y& y, const T_dof& nu, const T_loc& mu,
const T_scale& sigma) {
typedef typename
stan::partials_return_type<T_y, T_dof, T_loc, T_scale>::type
T_partials_return;
if (!(stan::length(y) && stan::length(nu) && stan::length(mu)
&& stan::length(sigma)))
return 0.0;
static const char* function("student_t_lcdf");
using std::exp;
T_partials_return P(0.0);
check_not_nan(function, "Random variable", y);
check_positive_finite(function, "Degrees of freedom parameter", nu);
check_finite(function, "Location parameter", mu);
check_positive_finite(function, "Scale parameter", sigma);
VectorView<const T_y> y_vec(y);
VectorView<const T_dof> nu_vec(nu);
VectorView<const T_loc> mu_vec(mu);
VectorView<const T_scale> sigma_vec(sigma);
size_t N = max_size(y, nu, mu, sigma);
OperandsAndPartials<T_y, T_dof, T_loc, T_scale>
operands_and_partials(y, nu, mu, sigma);
// Explicit return for extreme values
// The gradients are technically ill-defined, but treated as zero
for (size_t i = 0; i < stan::length(y); i++) {
if (value_of(y_vec[i]) == -std::numeric_limits<double>::infinity())
return operands_and_partials.value(negative_infinity());
}
using std::pow;
using std::exp;
using std::log;
T_partials_return digammaHalf = 0;
VectorBuilder<!is_constant_struct<T_dof>::value,
T_partials_return, T_dof>
digamma_vec(stan::length(nu));
VectorBuilder<!is_constant_struct<T_dof>::value,
T_partials_return, T_dof>
digammaNu_vec(stan::length(nu));
VectorBuilder<!is_constant_struct<T_dof>::value,
T_partials_return, T_dof>
digammaNuPlusHalf_vec(stan::length(nu));
if (!is_constant_struct<T_dof>::value) {
digammaHalf = digamma(0.5);
for (size_t i = 0; i < stan::length(nu); i++) {
const T_partials_return nu_dbl = value_of(nu_vec[i]);
digammaNu_vec[i] = digamma(0.5 * nu_dbl);
digammaNuPlusHalf_vec[i] = digamma(0.5 + 0.5 * nu_dbl);
}
}
for (size_t n = 0; n < N; n++) {
// Explicit results for extreme values
// The gradients are technically ill-defined, but treated as zero
if (value_of(y_vec[n]) == std::numeric_limits<double>::infinity()) {
continue;
}
const T_partials_return sigma_inv = 1.0 / value_of(sigma_vec[n]);
const T_partials_return t = (value_of(y_vec[n]) - value_of(mu_vec[n]))
* sigma_inv;
const T_partials_return nu_dbl = value_of(nu_vec[n]);
const T_partials_return q = nu_dbl / (t * t);
const T_partials_return r = 1.0 / (1.0 + q);
const T_partials_return J = 2 * r * r * q / t;
const T_partials_return betaNuHalf = exp(lbeta(0.5, 0.5 * nu_dbl));
T_partials_return zJacobian = t > 0 ? - 0.5 : 0.5;
if (q < 2) {
T_partials_return z
= inc_beta(0.5 * nu_dbl, (T_partials_return)0.5, 1.0 - r);
const T_partials_return Pn = t > 0 ? 1.0 - 0.5 * z : 0.5 * z;
const T_partials_return d_ibeta = pow(r, -0.5)
* pow(1.0 - r, 0.5*nu_dbl - 1) / betaNuHalf;
P += log(Pn);
if (!is_constant_struct<T_y>::value)
operands_and_partials.d_x1[n]
+= - zJacobian * d_ibeta * J * sigma_inv / Pn;
if (!is_constant_struct<T_dof>::value) {
T_partials_return g1 = 0;
T_partials_return g2 = 0;
grad_reg_inc_beta(g1, g2, 0.5 * nu_dbl,
(T_partials_return)0.5, 1.0 - r,
digammaNu_vec[n], digammaHalf,
digammaNuPlusHalf_vec[n],
betaNuHalf);
operands_and_partials.d_x2[n]
+= zJacobian * (d_ibeta * (r / t) * (r / t) + 0.5 * g1) / Pn;
}
if (!is_constant_struct<T_loc>::value)
operands_and_partials.d_x3[n]
+= zJacobian * d_ibeta * J * sigma_inv / Pn;
if (!is_constant_struct<T_scale>::value)
operands_and_partials.d_x4[n]
+= zJacobian * d_ibeta * J * sigma_inv * t / Pn;
} else {
T_partials_return z = 1.0 - inc_beta((T_partials_return)0.5,
0.5*nu_dbl, r);
zJacobian *= -1;
const T_partials_return Pn = t > 0 ? 1.0 - 0.5 * z : 0.5 * z;
T_partials_return d_ibeta = pow(1.0-r, 0.5*nu_dbl-1) * pow(r, -0.5)
/ betaNuHalf;
P += log(Pn);
if (!is_constant_struct<T_y>::value)
operands_and_partials.d_x1[n]
+= zJacobian * d_ibeta * J * sigma_inv / Pn;
if (!is_constant_struct<T_dof>::value) {
T_partials_return g1 = 0;
T_partials_return g2 = 0;
grad_reg_inc_beta(g1, g2, (T_partials_return)0.5,
0.5 * nu_dbl, r,
digammaHalf, digammaNu_vec[n],
digammaNuPlusHalf_vec[n],
betaNuHalf);
operands_and_partials.d_x2[n]
+= zJacobian * (- d_ibeta * (r / t) * (r / t) + 0.5 * g2) / Pn;
}
if (!is_constant_struct<T_loc>::value)
operands_and_partials.d_x3[n]
+= - zJacobian * d_ibeta * J * sigma_inv / Pn;
if (!is_constant_struct<T_scale>::value)
operands_and_partials.d_x4[n]
+= - zJacobian * d_ibeta * J * sigma_inv * t / Pn;
}
}
return operands_and_partials.value(P);
}
}
}
#endif
check_not_nan.hpp
stan::math::OperandsAndPartials::d_x2
VectorView< T_return_type, false, true > d_x2
Definition: OperandsAndPartials.hpp:39
lgamma.hpp
stan::math::check_finite
void check_finite(const char *function, const char *name, const T_y &y)
Check if y is finite.
Definition: check_finite.hpp:57
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::log
fvar< T > log(const fvar< T > &x)
Definition: log.hpp:14
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
square.hpp
stan::length
size_t length(const std::vector< T > &x)
Definition: length.hpp:10
is_constant_struct.hpp
stan::math::student_t_lcdf
return_type< T_y, T_dof, T_loc, T_scale >::type student_t_lcdf(const T_y &y, const T_dof &nu, const T_loc &mu, const T_scale &sigma)
Definition: student_t_lcdf.hpp:32
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
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::inc_beta
fvar< T > inc_beta(const fvar< T > &a, const fvar< T > &b, const fvar< T > &x)
Definition: inc_beta.hpp:19
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::math::grad_reg_inc_beta
void grad_reg_inc_beta(T &g1, T &g2, const T &a, const T &b, const T &z, const T &digammaA, const T &digammaB, const T &digammaSum, const T &betaAB)
Computes the gradients of the regularized incomplete beta function.
Definition: grad_reg_inc_beta.hpp:32
stan::math::exp
fvar< T > exp(const fvar< T > &x)
Definition: exp.hpp:10
stan::math::check_not_nan
void check_not_nan(const char *function, const char *name, const T_y &y)
Check if y is not NaN.
Definition: check_not_nan.hpp:57
stan::math::OperandsAndPartials
This class builds partial derivatives with respect to a set of operands.
Definition: OperandsAndPartials.hpp:37
stan::math::OperandsAndPartials::d_x3
VectorView< T_return_type, false, true > d_x3
Definition: OperandsAndPartials.hpp:40
stan::max_size
size_t max_size(const T1 &x1, const T2 &x2)
Definition: max_size.hpp:9
VectorBuilder.hpp
partials_return_type.hpp
OperandsAndPartials.hpp
length.hpp
grad_reg_inc_beta.hpp
stan::VectorBuilder
VectorBuilder allocates type T1 values to be used as intermediate values.
Definition: VectorBuilder.hpp:28
constants.hpp
check_finite.hpp
lbeta.hpp
inc_beta.hpp
stan::math::pow
fvar< T > pow(const fvar< T > &x1, const fvar< T > &x2)
Definition: pow.hpp:17
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::partials_return_type::type
boost::math::tools::promote_args< typename partials_type< typename scalar_type< T1 >::type >::type, typename partials_type< typename scalar_type< T2 >::type >::type, typename partials_type< typename scalar_type< T3 >::type >::type, typename partials_type< typename scalar_type< T4 >::type >::type, typename partials_type< typename scalar_type< T5 >::type >::type, typename partials_type< typename scalar_type< T6 >::type >::type >::type type
Definition: partials_return_type.hpp:26
check_consistent_sizes.hpp
stan::math::OperandsAndPartials::d_x1
VectorView< T_return_type, false, true > d_x1
Definition: OperandsAndPartials.hpp:38
stan::math::negative_infinity
double negative_infinity()
Return negative infinity.
Definition: constants.hpp:130
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
stan::math::OperandsAndPartials::d_x4
VectorView< T_return_type, false, true > d_x4
Definition: OperandsAndPartials.hpp:41

[ Stan Home Page ] © 2011–2016, Stan Development Team.