Stan Math Library  2.15.0
reverse mode automatic differentiation
beta_lpdf.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_BETA_LPDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_BETA_LPDF_HPP
3 
25 #include <boost/math/special_functions/gamma.hpp>
26 #include <boost/random/gamma_distribution.hpp>
27 #include <boost/random/variate_generator.hpp>
28 #include <cmath>
29 
30 namespace stan {
31  namespace math {
32 
51  template <bool propto,
52  typename T_y, typename T_scale_succ, typename T_scale_fail>
54  beta_lpdf(const T_y& y,
55  const T_scale_succ& alpha, const T_scale_fail& beta) {
56  static const char* function("beta_lpdf");
57 
58  typedef typename stan::partials_return_type<T_y,
59  T_scale_succ,
60  T_scale_fail>::type
61  T_partials_return;
62 
64  using stan::is_vector;
65  using std::log;
66 
67  if (!(stan::length(y)
68  && stan::length(alpha)
69  && stan::length(beta)))
70  return 0.0;
71 
72  T_partials_return logp(0.0);
73 
74  check_positive_finite(function, "First shape parameter", alpha);
75  check_positive_finite(function, "Second shape parameter", beta);
76  check_not_nan(function, "Random variable", y);
77  check_consistent_sizes(function,
78  "Random variable", y,
79  "First shape parameter", alpha,
80  "Second shape parameter", beta);
81  check_nonnegative(function, "Random variable", y);
82  check_less_or_equal(function, "Random variable", y, 1);
83 
85  return 0.0;
86 
88  scalar_seq_view<const T_scale_succ> alpha_vec(alpha);
90  size_t N = max_size(y, alpha, beta);
91 
92  for (size_t n = 0; n < N; n++) {
93  const T_partials_return y_dbl = value_of(y_vec[n]);
94  if (y_dbl < 0 || y_dbl > 1)
95  return LOG_ZERO;
96  }
97 
99  operands_and_partials(y, alpha, beta);
100 
102  T_partials_return, T_y>
103  log_y(length(y));
105  T_partials_return, T_y>
106  log1m_y(length(y));
107 
108  for (size_t n = 0; n < length(y); n++) {
110  log_y[n] = log(value_of(y_vec[n]));
112  log1m_y[n] = log1m(value_of(y_vec[n]));
113  }
114 
116  T_partials_return, T_scale_succ>
117  lgamma_alpha(length(alpha));
119  T_partials_return, T_scale_succ>
120  digamma_alpha(length(alpha));
121  for (size_t n = 0; n < length(alpha); n++) {
123  lgamma_alpha[n] = lgamma(value_of(alpha_vec[n]));
125  digamma_alpha[n] = digamma(value_of(alpha_vec[n]));
126  }
127 
129  T_partials_return, T_scale_fail>
130  lgamma_beta(length(beta));
132  T_partials_return, T_scale_fail>
133  digamma_beta(length(beta));
134 
135  for (size_t n = 0; n < length(beta); n++) {
137  lgamma_beta[n] = lgamma(value_of(beta_vec[n]));
139  digamma_beta[n] = digamma(value_of(beta_vec[n]));
140  }
141 
143  T_partials_return, T_scale_succ, T_scale_fail>
144  lgamma_alpha_beta(max_size(alpha, beta));
145 
147  T_scale_fail>::value,
148  T_partials_return, T_scale_succ, T_scale_fail>
149  digamma_alpha_beta(max_size(alpha, beta));
150 
151  for (size_t n = 0; n < max_size(alpha, beta); n++) {
152  const T_partials_return alpha_beta = value_of(alpha_vec[n])
153  + value_of(beta_vec[n]);
155  lgamma_alpha_beta[n] = lgamma(alpha_beta);
157  digamma_alpha_beta[n] = digamma(alpha_beta);
158  }
159 
160  for (size_t n = 0; n < N; n++) {
161  const T_partials_return y_dbl = value_of(y_vec[n]);
162  const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
163  const T_partials_return beta_dbl = value_of(beta_vec[n]);
164 
166  logp += lgamma_alpha_beta[n];
168  logp -= lgamma_alpha[n];
170  logp -= lgamma_beta[n];
172  logp += (alpha_dbl-1.0) * log_y[n];
174  logp += (beta_dbl-1.0) * log1m_y[n];
175 
177  operands_and_partials.d_x1[n] += (alpha_dbl-1)/y_dbl
178  + (beta_dbl-1)/(y_dbl-1);
180  operands_and_partials.d_x2[n]
181  += log_y[n] + digamma_alpha_beta[n] - digamma_alpha[n];
183  operands_and_partials.d_x3[n]
184  += log1m_y[n] + digamma_alpha_beta[n] - digamma_beta[n];
185  }
186  return operands_and_partials.value(logp);
187  }
188 
189  template <typename T_y, typename T_scale_succ, typename T_scale_fail>
191  beta_lpdf(const T_y& y, const T_scale_succ& alpha,
192  const T_scale_fail& beta) {
193  return beta_lpdf<false>(y, alpha, beta);
194  }
195 
196  }
197 }
198 #endif
VectorView< T_return_type, false, true > d_x2
void check_less_or_equal(const char *function, const char *name, const T_y &y, const T_high &high)
Check if y is less or equal to high.
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.
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
const double LOG_ZERO
Definition: constants.hpp:172
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_positive_finite(const char *function, const char *name, const T_y &y)
Check if y is positive and finite.
return_type< T_y, T_scale_succ, T_scale_fail >::type beta_lpdf(const T_y &y, const T_scale_succ &alpha, const T_scale_fail &beta)
The log of the beta density for the specified scalar(s) given the specified sample size(s)...
Definition: beta_lpdf.hpp:54
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.
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.
fvar< T > log1m(const fvar< T > &x)
Definition: log1m.hpp:13
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

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