Stan Math Library  2.15.0
reverse mode automatic differentiation
normal_sufficient_lpdf.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_NORMAL_SUFFICIENT_LPDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_NORMAL_SUFFICIENT_LPDF_HPP
3 
6 
18 
19 namespace stan {
20 
21  namespace math {
22 
50  template <bool propto,
51  typename T_y, typename T_s, typename T_n, typename T_loc,
52  typename T_scale>
54  normal_sufficient_lpdf(const T_y& y_bar, const T_s& s_squared,
55  const T_n& n_obs, const T_loc& mu,
56  const T_scale& sigma) {
57  static const char*
58  function = "stan::math::normal_sufficient_lpdf(%1%)";
59  typedef typename
61  T_partials_return;
62 
63  using std::log;
71 
72  // check if any vectors are zero length
73  if (!(stan::length(y_bar)
74  && stan::length(s_squared)
75  && stan::length(n_obs)
76  && stan::length(mu)
77  && stan::length(sigma)))
78  return 0.0;
79 
80  // set up return value accumulator
81  T_partials_return logp(0.0);
82 
83  // validate args (here done over var, which should be OK)
84  check_finite(function,
85  "Location parameter sufficient statistic", y_bar);
86  check_finite(function,
87  "Scale parameter sufficient statistic", s_squared);
88  check_nonnegative(function,
89  "Scale parameter sufficient statistic", s_squared);
90  check_finite(function,
91  "Number of observations", n_obs);
92  check_positive(function,
93  "Number of observations", n_obs);
94  check_finite(function,
95  "Location parameter", mu);
96  check_finite(function, "Scale parameter", sigma);
97  check_positive(function, "Scale parameter", sigma);
98  check_consistent_sizes(function,
99  "Location parameter sufficient statistic",
100  y_bar,
101  "Scale parameter sufficient statistic",
102  s_squared,
103  "Number of observations", n_obs,
104  "Location parameter", mu,
105  "Scale parameter", sigma);
106  // check if no variables are involved and prop-to
108  return 0.0;
109 
110  // set up template expressions wrapping scalars into vector views
112  operands_and_partials(y_bar, s_squared, mu, sigma);
113 
114  scalar_seq_view<const T_y> y_bar_vec(y_bar);
115  scalar_seq_view<const T_s> s_squared_vec(s_squared);
116  scalar_seq_view<const T_n> n_obs_vec(n_obs);
117  scalar_seq_view<const T_loc> mu_vec(mu);
118  scalar_seq_view<const T_scale> sigma_vec(sigma);
119  size_t N = max_size(y_bar, s_squared, n_obs, mu, sigma);
120 
121  for (size_t i = 0; i < N; i++) {
122  const T_partials_return y_bar_dbl = value_of(y_bar_vec[i]);
123  const T_partials_return s_squared_dbl =
124  value_of(s_squared_vec[i]);
125  const T_partials_return n_obs_dbl = n_obs_vec[i];
126  const T_partials_return mu_dbl = value_of(mu_vec[i]);
127  const T_partials_return sigma_dbl = value_of(sigma_vec[i]);
128  const T_partials_return sigma_squared = pow(sigma_dbl, 2);
129 
131  logp += NEG_LOG_SQRT_TWO_PI * n_obs_dbl;
132 
134  logp -= n_obs_dbl * log(sigma_dbl);
135 
136  const T_partials_return cons_expr =
137  (s_squared_dbl
138  + n_obs_dbl * pow(y_bar_dbl - mu_dbl, 2));
139 
140  logp -= cons_expr / (2 * sigma_squared);
141 
142  // gradients
145  const T_partials_return common_derivative =
146  n_obs_dbl * (mu_dbl - y_bar_dbl) / sigma_squared;
148  operands_and_partials.d_x1[i] += common_derivative;
150  operands_and_partials.d_x3[i] -= common_derivative;
151  }
153  operands_and_partials.d_x2[i] -=
154  0.5 / sigma_squared;
156  operands_and_partials.d_x4[i]
157  += cons_expr / pow(sigma_dbl, 3) - n_obs_dbl / sigma_dbl;
158  }
159  return operands_and_partials.value(logp);
160  }
161 
162  template <typename T_y, typename T_s, typename T_n,
163  typename T_loc, typename T_scale>
164  inline
166  normal_sufficient_lpdf(const T_y& y_bar, const T_s& s_squared,
167  const T_n& n_obs, const T_loc& mu,
168  const T_scale& sigma) {
169  return
170  normal_sufficient_lpdf<false>(y_bar, s_squared,
171  n_obs, mu, sigma);
172  }
173 
174  }
175 }
176 #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.
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.
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...
void check_nonnegative(const char *function, const char *name, const T_y &y)
Check if y is non-negative.
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
Metaprogram to determine if a type has a base scalar type that can be assigned to type double...
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_s, T_loc, T_scale >::type normal_sufficient_lpdf(const T_y &y_bar, const T_s &s_squared, const T_n &n_obs, const T_loc &mu, const T_scale &sigma)
The log of the normal density for the specified scalar(s) given the specified mean(s) and deviation(s...
size_t max_size(const T1 &x1, const T2 &x2)
Definition: max_size.hpp:9
const double NEG_LOG_SQRT_TWO_PI
Definition: constants.hpp:181
void check_positive(const char *function, const char *name, const T_y &y)
Check if y is positive.
fvar< T > pow(const fvar< T > &x1, const fvar< T > &x2)
Definition: pow.hpp:17
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
VectorView< T_return_type, false, true > d_x4

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