1 #ifndef STAN_MATH_PRIM_SCAL_PROB_STUDENT_T_LPDF_HPP 2 #define STAN_MATH_PRIM_SCAL_PROB_STUDENT_T_LPDF_HPP 23 #include <boost/random/student_t_distribution.hpp> 24 #include <boost/random/variate_generator.hpp> 55 template <
bool propto,
typename T_y,
typename T_dof,
56 typename T_loc,
typename T_scale>
59 const T_scale& sigma) {
60 static const char*
function(
"student_t_lpdf");
71 T_partials_return logp(0.0);
79 "Degrees of freedom parameter", nu,
80 "Location parameter", mu,
81 "Scale parameter", sigma);
90 size_t N =
max_size(y, nu, mu, sigma);
96 T_partials_return, T_dof> half_nu(
length(nu));
97 for (
size_t i = 0; i <
length(nu); i++)
99 half_nu[i] = 0.5 *
value_of(nu_vec[i]);
102 T_partials_return, T_dof> lgamma_half_nu(
length(nu));
104 T_partials_return, T_dof>
105 lgamma_half_nu_plus_half(
length(nu));
107 for (
size_t i = 0; i <
length(nu); i++) {
108 lgamma_half_nu[i] =
lgamma(half_nu[i]);
109 lgamma_half_nu_plus_half[i] =
lgamma(half_nu[i] + 0.5);
114 T_partials_return, T_dof> digamma_half_nu(
length(nu));
116 T_partials_return, T_dof>
117 digamma_half_nu_plus_half(
length(nu));
119 for (
size_t i = 0; i <
length(nu); i++) {
120 digamma_half_nu[i] =
digamma(half_nu[i]);
121 digamma_half_nu_plus_half[i] =
digamma(half_nu[i] + 0.5);
126 T_partials_return, T_dof> log_nu(
length(nu));
127 for (
size_t i = 0; i <
length(nu); i++)
132 T_partials_return, T_scale> log_sigma(
length(sigma));
133 for (
size_t i = 0; i <
length(sigma); i++)
138 T_partials_return, T_y, T_dof, T_loc, T_scale>
139 square_y_minus_mu_over_sigma__over_nu(N);
142 T_partials_return, T_y, T_dof, T_loc, T_scale>
145 for (
size_t i = 0; i < N; i++)
147 const T_partials_return y_dbl =
value_of(y_vec[i]);
148 const T_partials_return mu_dbl =
value_of(mu_vec[i]);
149 const T_partials_return sigma_dbl =
value_of(sigma_vec[i]);
150 const T_partials_return nu_dbl =
value_of(nu_vec[i]);
151 square_y_minus_mu_over_sigma__over_nu[i]
152 =
square((y_dbl - mu_dbl) / sigma_dbl) / nu_dbl;
153 log1p_exp[i] =
log1p(square_y_minus_mu_over_sigma__over_nu[i]);
157 operands_and_partials(y, nu, mu, sigma);
158 for (
size_t n = 0; n < N; n++) {
159 const T_partials_return y_dbl =
value_of(y_vec[n]);
160 const T_partials_return mu_dbl =
value_of(mu_vec[n]);
161 const T_partials_return sigma_dbl =
value_of(sigma_vec[n]);
162 const T_partials_return nu_dbl =
value_of(nu_vec[n]);
166 logp += lgamma_half_nu_plus_half[n] - lgamma_half_nu[n]
169 logp -= log_sigma[n];
171 logp -= (half_nu[n] + 0.5)
175 operands_and_partials.
d_x1[n]
177 * 1.0 / (1.0 + square_y_minus_mu_over_sigma__over_nu[n])
178 * (2.0 * (y_dbl - mu_dbl) /
square(sigma_dbl) / nu_dbl);
181 const T_partials_return inv_nu = 1.0 / nu_dbl;
182 operands_and_partials.
d_x2[n]
183 += 0.5*digamma_half_nu_plus_half[n] - 0.5*digamma_half_nu[n]
187 * (1.0/(1.0 + square_y_minus_mu_over_sigma__over_nu[n])
188 * square_y_minus_mu_over_sigma__over_nu[n] * inv_nu);
191 operands_and_partials.
d_x3[n]
192 -= (half_nu[n] + 0.5)
193 / (1.0 + square_y_minus_mu_over_sigma__over_nu[n])
194 * (2.0 * (mu_dbl - y_dbl) / (sigma_dbl*sigma_dbl*nu_dbl));
197 const T_partials_return inv_sigma = 1.0 / sigma_dbl;
198 operands_and_partials.
d_x4[n]
200 + (nu_dbl + 1.0) / (1.0 + square_y_minus_mu_over_sigma__over_nu[n])
201 * (square_y_minus_mu_over_sigma__over_nu[n] * inv_sigma);
204 return operands_and_partials.
value(logp);
207 template <
typename T_y,
typename T_dof,
typename T_loc,
typename T_scale>
211 const T_scale& sigma) {
212 return student_t_lpdf<false>(y, nu, mu, sigma);
VectorView< T_return_type, false, true > d_x2
void check_finite(const char *function, const char *name, const T_y &y)
Check if y is finite.
fvar< T > lgamma(const fvar< T > &x)
Return the natural logarithm of the gamma function applied to the specified argument.
T value_of(const fvar< T > &v)
Return the value of the specified variable.
fvar< T > log(const fvar< T > &x)
T_return_type value(double value)
Returns a T_return_type with the value specified with the partial derivatves.
const double NEG_LOG_SQRT_PI
scalar_seq_view provides a uniform sequence-like wrapper around either a scalar or a sequence of scal...
size_t length(const std::vector< T > &x)
Template metaprogram to calculate whether a summand needs to be included in a proportional (log) prob...
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
fvar< T > square(const fvar< T > &x)
Metaprogram to determine if a type has a base scalar type that can be assigned to type double...
void check_positive_finite(const char *function, const char *name, const T_y &y)
Check if y is positive and finite.
void check_not_nan(const char *function, const char *name, const T_y &y)
Check if y is not NaN.
This class builds partial derivatives with respect to a set of operands.
VectorView< T_return_type, false, true > d_x3
size_t max_size(const T1 &x1, const T2 &x2)
VectorBuilder allocates type T1 values to be used as intermediate values.
fvar< T > log1p_exp(const fvar< T > &x)
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.
fvar< T > log1p(const fvar< T > &x)
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.
VectorView< T_return_type, false, true > d_x1
fvar< T > digamma(const fvar< T > &x)
Return the derivative of the log gamma function at the specified argument.
VectorView< T_return_type, false, true > d_x4