student_t_lpdf.hpp
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#ifndef STAN_MATH_PRIM_SCAL_PROB_STUDENT_T_LPDF_HPP
#define STAN_MATH_PRIM_SCAL_PROB_STUDENT_T_LPDF_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 <cmath>
namespace stan {
namespace math {
template <bool propto, 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_lpdf(const T_y& y, const T_dof& nu, const T_loc& mu,
const T_scale& sigma) {
static const char* function("student_t_lpdf");
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;
T_partials_return logp(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);
check_consistent_sizes(function,
"Random variable", y,
"Degrees of freedom parameter", nu,
"Location parameter", mu,
"Scale parameter", sigma);
if (!include_summand<propto, T_y, T_dof, T_loc, T_scale>::value)
return 0.0;
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);
using std::log;
using std::log;
VectorBuilder<include_summand<propto, T_y, T_dof, T_loc, T_scale>::value,
T_partials_return, T_dof> half_nu(length(nu));
for (size_t i = 0; i < length(nu); i++)
if (include_summand<propto, T_y, T_dof, T_loc, T_scale>::value)
half_nu[i] = 0.5 * value_of(nu_vec[i]);
VectorBuilder<include_summand<propto, T_dof>::value,
T_partials_return, T_dof> lgamma_half_nu(length(nu));
VectorBuilder<include_summand<propto, T_dof>::value,
T_partials_return, T_dof>
lgamma_half_nu_plus_half(length(nu));
if (include_summand<propto, T_dof>::value) {
for (size_t i = 0; i < length(nu); i++) {
lgamma_half_nu[i] = lgamma(half_nu[i]);
lgamma_half_nu_plus_half[i] = lgamma(half_nu[i] + 0.5);
}
}
VectorBuilder<!is_constant_struct<T_dof>::value,
T_partials_return, T_dof> digamma_half_nu(length(nu));
VectorBuilder<!is_constant_struct<T_dof>::value,
T_partials_return, T_dof>
digamma_half_nu_plus_half(length(nu));
if (!is_constant_struct<T_dof>::value) {
for (size_t i = 0; i < length(nu); i++) {
digamma_half_nu[i] = digamma(half_nu[i]);
digamma_half_nu_plus_half[i] = digamma(half_nu[i] + 0.5);
}
}
VectorBuilder<include_summand<propto, T_dof>::value,
T_partials_return, T_dof> log_nu(length(nu));
for (size_t i = 0; i < length(nu); i++)
if (include_summand<propto, T_dof>::value)
log_nu[i] = log(value_of(nu_vec[i]));
VectorBuilder<include_summand<propto, T_scale>::value,
T_partials_return, T_scale> log_sigma(length(sigma));
for (size_t i = 0; i < length(sigma); i++)
if (include_summand<propto, T_scale>::value)
log_sigma[i] = log(value_of(sigma_vec[i]));
VectorBuilder<include_summand<propto, T_y, T_dof, T_loc, T_scale>::value,
T_partials_return, T_y, T_dof, T_loc, T_scale>
square_y_minus_mu_over_sigma__over_nu(N);
VectorBuilder<include_summand<propto, T_y, T_dof, T_loc, T_scale>::value,
T_partials_return, T_y, T_dof, T_loc, T_scale>
log1p_exp(N);
for (size_t i = 0; i < N; i++)
if (include_summand<propto, T_y, T_dof, T_loc, T_scale>::value) {
const T_partials_return y_dbl = value_of(y_vec[i]);
const T_partials_return mu_dbl = value_of(mu_vec[i]);
const T_partials_return sigma_dbl = value_of(sigma_vec[i]);
const T_partials_return nu_dbl = value_of(nu_vec[i]);
square_y_minus_mu_over_sigma__over_nu[i]
= square((y_dbl - mu_dbl) / sigma_dbl) / nu_dbl;
log1p_exp[i] = log1p(square_y_minus_mu_over_sigma__over_nu[i]);
}
OperandsAndPartials<T_y, T_dof, T_loc, T_scale>
operands_and_partials(y, nu, mu, sigma);
for (size_t n = 0; n < N; n++) {
const T_partials_return y_dbl = value_of(y_vec[n]);
const T_partials_return mu_dbl = value_of(mu_vec[n]);
const T_partials_return sigma_dbl = value_of(sigma_vec[n]);
const T_partials_return nu_dbl = value_of(nu_vec[n]);
if (include_summand<propto>::value)
logp += NEG_LOG_SQRT_PI;
if (include_summand<propto, T_dof>::value)
logp += lgamma_half_nu_plus_half[n] - lgamma_half_nu[n]
- 0.5 * log_nu[n];
if (include_summand<propto, T_scale>::value)
logp -= log_sigma[n];
if (include_summand<propto, T_y, T_dof, T_loc, T_scale>::value)
logp -= (half_nu[n] + 0.5)
* log1p_exp[n];
if (!is_constant_struct<T_y>::value) {
operands_and_partials.d_x1[n]
+= -(half_nu[n]+0.5)
* 1.0 / (1.0 + square_y_minus_mu_over_sigma__over_nu[n])
* (2.0 * (y_dbl - mu_dbl) / square(sigma_dbl) / nu_dbl);
}
if (!is_constant_struct<T_dof>::value) {
const T_partials_return inv_nu = 1.0 / nu_dbl;
operands_and_partials.d_x2[n]
+= 0.5*digamma_half_nu_plus_half[n] - 0.5*digamma_half_nu[n]
- 0.5 * inv_nu
- 0.5*log1p_exp[n]
+ (half_nu[n] + 0.5)
* (1.0/(1.0 + square_y_minus_mu_over_sigma__over_nu[n])
* square_y_minus_mu_over_sigma__over_nu[n] * inv_nu);
}
if (!is_constant_struct<T_loc>::value) {
operands_and_partials.d_x3[n]
-= (half_nu[n] + 0.5)
/ (1.0 + square_y_minus_mu_over_sigma__over_nu[n])
* (2.0 * (mu_dbl - y_dbl) / (sigma_dbl*sigma_dbl*nu_dbl));
}
if (!is_constant_struct<T_scale>::value) {
const T_partials_return inv_sigma = 1.0 / sigma_dbl;
operands_and_partials.d_x4[n]
+= -inv_sigma
+ (nu_dbl + 1.0) / (1.0 + square_y_minus_mu_over_sigma__over_nu[n])
* (square_y_minus_mu_over_sigma__over_nu[n] * inv_sigma);
}
}
return operands_and_partials.value(logp);
}
template <typename T_y, typename T_dof, typename T_loc, typename T_scale>
inline
typename return_type<T_y, T_dof, T_loc, T_scale>::type
student_t_lpdf(const T_y& y, const T_dof& nu, const T_loc& mu,
const T_scale& sigma) {
return student_t_lpdf<false>(y, nu, mu, sigma);
}
}
}
#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
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
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
stan::math::NEG_LOG_SQRT_PI
const double NEG_LOG_SQRT_PI
Definition: constants.hpp:186
square.hpp
stan::length
size_t length(const std::vector< T > &x)
Definition: length.hpp:10
is_constant_struct.hpp
stan::math::include_summand
Template metaprogram to calculate whether a summand needs to be included in a proportional (log) prob...
Definition: include_summand.hpp:35
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
stan::math::square
fvar< T > square(const fvar< T > &x)
Definition: square.hpp:14
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::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::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
stan::math::log1p_exp
fvar< T > log1p_exp(const fvar< T > &x)
Definition: log1p_exp.hpp:13
stan::math::student_t_lpdf
return_type< T_y, T_dof, T_loc, T_scale >::type student_t_lpdf(const T_y &y, const T_dof &nu, const T_loc &mu, const T_scale &sigma)
The log of the Student-t density for the given y, nu, mean, and scale parameter.
Definition: student_t_lpdf.hpp:57
check_finite.hpp
lbeta.hpp
stan::math::log1p
fvar< T > log1p(const fvar< T > &x)
Definition: log1p.hpp:11
inc_beta.hpp
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
stan::math::OperandsAndPartials::d_x4
VectorView< T_return_type, false, true > d_x4
Definition: OperandsAndPartials.hpp:41

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