1 #ifndef STAN_MATH_PRIM_SCAL_PROB_SCALED_INV_CHI_SQUARE_LPDF_HPP 2 #define STAN_MATH_PRIM_SCAL_PROB_SCALED_INV_CHI_SQUARE_LPDF_HPP 22 #include <boost/random/chi_squared_distribution.hpp> 23 #include <boost/random/variate_generator.hpp> 48 template <
bool propto,
49 typename T_y,
typename T_dof,
typename T_scale>
52 const T_dof& nu,
const T_scale& s) {
53 static const char*
function(
"scaled_inv_chi_square_lpdf");
62 T_partials_return logp(0.0);
68 "Degrees of freedom parameter", nu,
69 "Scale parameter", s);
79 for (
size_t n = 0; n < N; n++) {
87 T_partials_return, T_dof> half_nu(
length(nu));
88 for (
size_t i = 0; i <
length(nu); i++)
90 half_nu[i] = 0.5 *
value_of(nu_vec[i]);
93 T_partials_return, T_y> log_y(
length(y));
94 for (
size_t i = 0; i <
length(y); i++)
99 T_partials_return, T_y> inv_y(
length(y));
100 for (
size_t i = 0; i <
length(y); i++)
102 inv_y[i] = 1.0 /
value_of(y_vec[i]);
105 T_partials_return, T_scale> log_s(
length(s));
106 for (
size_t i = 0; i <
length(s); i++)
111 T_partials_return, T_dof> log_half_nu(
length(nu));
113 T_partials_return, T_dof> lgamma_half_nu(
length(nu));
115 T_partials_return, T_dof>
116 digamma_half_nu_over_two(
length(nu));
117 for (
size_t i = 0; i <
length(nu); i++) {
119 lgamma_half_nu[i] =
lgamma(half_nu[i]);
121 log_half_nu[i] =
log(half_nu[i]);
123 digamma_half_nu_over_two[i] =
digamma(half_nu[i]) * 0.5;
127 operands_and_partials(y, nu, s);
128 for (
size_t n = 0; n < N; n++) {
129 const T_partials_return s_dbl =
value_of(s_vec[n]);
130 const T_partials_return nu_dbl =
value_of(nu_vec[n]);
132 logp += half_nu[n] * log_half_nu[n] - lgamma_half_nu[n];
134 logp += nu_dbl * log_s[n];
136 logp -= (half_nu[n]+1.0) * log_y[n];
138 logp -= half_nu[n] * s_dbl*s_dbl * inv_y[n];
141 operands_and_partials.
d_x1[n]
142 += -(half_nu[n] + 1.0) * inv_y[n]
143 + half_nu[n] * s_dbl*s_dbl * inv_y[n]*inv_y[n];
146 operands_and_partials.
d_x2[n]
147 += 0.5 * log_half_nu[n] + 0.5
148 - digamma_half_nu_over_two[n]
151 - 0.5* s_dbl*s_dbl * inv_y[n];
154 operands_and_partials.
d_x3[n]
155 += nu_dbl / s_dbl - nu_dbl * inv_y[n] * s_dbl;
158 return operands_and_partials.
value(logp);
161 template <
typename T_y,
typename T_dof,
typename T_scale>
166 return scaled_inv_chi_square_lpdf<false>(y, nu, s);
VectorView< T_return_type, false, true > d_x2
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.
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
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
return_type< T_y, T_dof, T_scale >::type scaled_inv_chi_square_lpdf(const T_y &y, const T_dof &nu, const T_scale &s)
The log of a scaled inverse chi-squared density for y with the specified degrees of freedom parameter...
size_t max_size(const T1 &x1, const T2 &x2)
VectorBuilder allocates type T1 values to be used as intermediate values.
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[].
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.
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
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.