1 #ifndef STAN_MATH_PRIM_SCAL_PROB_STUDENT_T_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_STUDENT_T_LOG_HPP
4 #include <boost/random/student_t_distribution.hpp>
5 #include <boost/random/variate_generator.hpp>
53 template <
bool propto,
typename T_y,
typename T_dof,
54 typename T_loc,
typename T_scale>
55 typename return_type<T_y, T_dof, T_loc, T_scale>::type
57 const T_scale& sigma) {
58 static const char*
function(
"stan::math::student_t_log");
75 T_partials_return logp(0.0);
84 "Degrees of freedom parameter", nu,
85 "Location parameter", mu,
86 "Scale parameter", sigma);
96 size_t N =
max_size(y, nu, mu, sigma);
106 T_partials_return, T_dof> half_nu(
length(nu));
107 for (
size_t i = 0; i <
length(nu); i++)
109 half_nu[i] = 0.5 *
value_of(nu_vec[i]);
112 T_partials_return, T_dof> lgamma_half_nu(
length(nu));
114 T_partials_return, T_dof>
115 lgamma_half_nu_plus_half(
length(nu));
117 for (
size_t i = 0; i <
length(nu); i++) {
118 lgamma_half_nu[i] =
lgamma(half_nu[i]);
119 lgamma_half_nu_plus_half[i] =
lgamma(half_nu[i] + 0.5);
124 T_partials_return, T_dof> digamma_half_nu(
length(nu));
126 T_partials_return, T_dof>
127 digamma_half_nu_plus_half(
length(nu));
129 for (
size_t i = 0; i <
length(nu); i++) {
130 digamma_half_nu[i] =
digamma(half_nu[i]);
131 digamma_half_nu_plus_half[i] =
digamma(half_nu[i] + 0.5);
136 T_partials_return, T_dof> log_nu(
length(nu));
137 for (
size_t i = 0; i <
length(nu); i++)
142 T_partials_return, T_scale> log_sigma(
length(sigma));
143 for (
size_t i = 0; i <
length(sigma); i++)
148 T_partials_return, T_y, T_dof, T_loc, T_scale>
149 square_y_minus_mu_over_sigma__over_nu(N);
152 T_partials_return, T_y, T_dof, T_loc, T_scale>
155 for (
size_t i = 0; i < N; i++)
157 const T_partials_return y_dbl =
value_of(y_vec[i]);
158 const T_partials_return mu_dbl =
value_of(mu_vec[i]);
159 const T_partials_return sigma_dbl =
value_of(sigma_vec[i]);
160 const T_partials_return nu_dbl =
value_of(nu_vec[i]);
161 square_y_minus_mu_over_sigma__over_nu[i]
162 =
square((y_dbl - mu_dbl) / sigma_dbl) / nu_dbl;
163 log1p_exp[i] =
log1p(square_y_minus_mu_over_sigma__over_nu[i]);
167 operands_and_partials(y, nu, mu, sigma);
168 for (
size_t n = 0; n < N; n++) {
169 const T_partials_return y_dbl =
value_of(y_vec[n]);
170 const T_partials_return mu_dbl =
value_of(mu_vec[n]);
171 const T_partials_return sigma_dbl =
value_of(sigma_vec[n]);
172 const T_partials_return nu_dbl =
value_of(nu_vec[n]);
176 logp += lgamma_half_nu_plus_half[n] - lgamma_half_nu[n]
179 logp -= log_sigma[n];
181 logp -= (half_nu[n] + 0.5)
185 operands_and_partials.
d_x1[n]
187 * 1.0 / (1.0 + square_y_minus_mu_over_sigma__over_nu[n])
188 * (2.0 * (y_dbl - mu_dbl) /
square(sigma_dbl) / nu_dbl);
191 const T_partials_return inv_nu = 1.0 / nu_dbl;
192 operands_and_partials.
d_x2[n]
193 += 0.5*digamma_half_nu_plus_half[n] - 0.5*digamma_half_nu[n]
197 * (1.0/(1.0 + square_y_minus_mu_over_sigma__over_nu[n])
198 * square_y_minus_mu_over_sigma__over_nu[n] * inv_nu);
201 operands_and_partials.
d_x3[n]
202 -= (half_nu[n] + 0.5)
203 / (1.0 + square_y_minus_mu_over_sigma__over_nu[n])
204 * (2.0 * (mu_dbl - y_dbl) / (sigma_dbl*sigma_dbl*nu_dbl));
207 const T_partials_return inv_sigma = 1.0 / sigma_dbl;
208 operands_and_partials.
d_x4[n]
210 + (nu_dbl + 1.0) / (1.0 + square_y_minus_mu_over_sigma__over_nu[n])
211 * (square_y_minus_mu_over_sigma__over_nu[n] * inv_sigma);
214 return operands_and_partials.
to_var(logp, y, nu, mu, sigma);
217 template <
typename T_y,
typename T_dof,
typename T_loc,
typename T_scale>
221 const T_scale& sigma) {
222 return student_t_log<false>(y, nu, mu, sigma);
fvar< T > lgamma(const fvar< T > &x)
bool check_not_nan(const char *function, const char *name, const T_y &y)
Return true if y is not NaN.
T value_of(const fvar< T > &v)
Return the value of the specified variable.
fvar< T > log(const fvar< T > &x)
const double NEG_LOG_SQRT_PI
size_t length(const std::vector< T > &x)
T_return_type to_var(T_partials_return logp, const T1 &x1=0, const T2 &x2=0, const T3 &x3=0, const T4 &x4=0, const T5 &x5=0, const T6 &x6=0)
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)
VectorView< T_partials_return, is_vector< T1 >::value, is_constant_struct< T1 >::value > d_x1
Metaprogram to determine if a type has a base scalar type that can be assigned to type double...
VectorView< T_partials_return, is_vector< T3 >::value, is_constant_struct< T3 >::value > d_x3
VectorView< T_partials_return, is_vector< T4 >::value, is_constant_struct< T4 >::value > d_x4
A variable implementation that stores operands and derivatives with respect to the variable...
size_t max_size(const T1 &x1, const T2 &x2)
bool check_finite(const char *function, const char *name, const T_y &y)
Return true if y is finite.
fvar< T > log1p_exp(const fvar< T > &x)
bool check_consistent_sizes(const char *function, const char *name1, const T1 &x1, const char *name2, const T2 &x2)
Return true if the dimension of x1 is consistent with x2.
VectorView< T_partials_return, is_vector< T2 >::value, is_constant_struct< T2 >::value > d_x2
fvar< T > log1p(const fvar< T > &x)
return_type< T_y, T_dof, T_loc, T_scale >::type student_t_log(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.
VectorView is a template metaprogram that takes its argument and allows it to be used like a vector...
bool check_positive_finite(const char *function, const char *name, const T_y &y)
Return true if y is positive and finite.
fvar< T > digamma(const fvar< T > &x)