Stan Math Library  2.15.0
reverse mode automatic differentiation
student_t_lpdf.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_STUDENT_T_LPDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_STUDENT_T_LPDF_HPP
3 
23 #include <boost/random/student_t_distribution.hpp>
24 #include <boost/random/variate_generator.hpp>
25 #include <cmath>
26 
27 namespace stan {
28  namespace math {
29 
55  template <bool propto, typename T_y, typename T_dof,
56  typename T_loc, typename T_scale>
58  student_t_lpdf(const T_y& y, const T_dof& nu, const T_loc& mu,
59  const T_scale& sigma) {
60  static const char* function("student_t_lpdf");
61  typedef typename stan::partials_return_type<T_y, T_dof, T_loc,
62  T_scale>::type
63  T_partials_return;
64 
65  if (!(stan::length(y)
66  && stan::length(nu)
67  && stan::length(mu)
68  && stan::length(sigma)))
69  return 0.0;
70 
71  T_partials_return logp(0.0);
72 
73  check_not_nan(function, "Random variable", y);
74  check_positive_finite(function, "Degrees of freedom parameter", nu);
75  check_finite(function, "Location parameter", mu);
76  check_positive_finite(function, "Scale parameter", sigma);
77  check_consistent_sizes(function,
78  "Random variable", y,
79  "Degrees of freedom parameter", nu,
80  "Location parameter", mu,
81  "Scale parameter", sigma);
82 
84  return 0.0;
85 
89  scalar_seq_view<const T_scale> sigma_vec(sigma);
90  size_t N = max_size(y, nu, mu, sigma);
91 
92  using std::log;
93  using std::log;
94 
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]);
100 
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);
110  }
111  }
112 
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);
122  }
123  }
124 
126  T_partials_return, T_dof> log_nu(length(nu));
127  for (size_t i = 0; i < length(nu); i++)
129  log_nu[i] = log(value_of(nu_vec[i]));
130 
132  T_partials_return, T_scale> log_sigma(length(sigma));
133  for (size_t i = 0; i < length(sigma); i++)
135  log_sigma[i] = log(value_of(sigma_vec[i]));
136 
138  T_partials_return, T_y, T_dof, T_loc, T_scale>
139  square_y_minus_mu_over_sigma__over_nu(N);
140 
142  T_partials_return, T_y, T_dof, T_loc, T_scale>
143  log1p_exp(N);
144 
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]);
154  }
155 
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]);
164  logp += NEG_LOG_SQRT_PI;
166  logp += lgamma_half_nu_plus_half[n] - lgamma_half_nu[n]
167  - 0.5 * log_nu[n];
169  logp -= log_sigma[n];
171  logp -= (half_nu[n] + 0.5)
172  * log1p_exp[n];
173 
175  operands_and_partials.d_x1[n]
176  += -(half_nu[n]+0.5)
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);
179  }
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]
184  - 0.5 * inv_nu
185  - 0.5*log1p_exp[n]
186  + (half_nu[n] + 0.5)
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);
189  }
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));
195  }
197  const T_partials_return inv_sigma = 1.0 / sigma_dbl;
198  operands_and_partials.d_x4[n]
199  += -inv_sigma
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);
202  }
203  }
204  return operands_and_partials.value(logp);
205  }
206 
207  template <typename T_y, typename T_dof, typename T_loc, typename T_scale>
208  inline
210  student_t_lpdf(const T_y& y, const T_dof& nu, const T_loc& mu,
211  const T_scale& sigma) {
212  return student_t_lpdf<false>(y, nu, mu, sigma);
213  }
214 
215  }
216 }
217 #endif
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.
Definition: lgamma.hpp:20
T value_of(const fvar< T > &v)
Return the value of the specified variable.
Definition: value_of.hpp:16
fvar< T > log(const fvar< T > &x)
Definition: log.hpp:14
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
Definition: constants.hpp:186
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)
Definition: length.hpp:10
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
Definition: return_type.hpp:27
fvar< T > square(const fvar< T > &x)
Definition: square.hpp:14
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)
Definition: max_size.hpp:9
VectorBuilder allocates type T1 values to be used as intermediate values.
fvar< T > log1p_exp(const fvar< T > &x)
Definition: log1p_exp.hpp:13
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)
Definition: log1p.hpp:11
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.
Definition: digamma.hpp:22
VectorView< T_return_type, false, true > d_x4

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