Stan Math Library  2.14.0
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 
24 #include <boost/math/special_functions/gamma.hpp>
25 #include <boost/random/gamma_distribution.hpp>
26 #include <boost/random/variate_generator.hpp>
27 #include <cmath>
28 
29 namespace stan {
30  namespace math {
31 
50  template <bool propto,
51  typename T_y, typename T_scale_succ, typename T_scale_fail>
53  beta_lpdf(const T_y& y,
54  const T_scale_succ& alpha, const T_scale_fail& beta) {
55  static const char* function("beta_lpdf");
56 
57  typedef typename stan::partials_return_type<T_y,
58  T_scale_succ,
59  T_scale_fail>::type
60  T_partials_return;
61 
63  using stan::is_vector;
64  using std::log;
65 
66  if (!(stan::length(y)
67  && stan::length(alpha)
68  && stan::length(beta)))
69  return 0.0;
70 
71  T_partials_return logp(0.0);
72 
73  check_positive_finite(function, "First shape parameter", alpha);
74  check_positive_finite(function, "Second shape parameter", beta);
75  check_not_nan(function, "Random variable", y);
76  check_consistent_sizes(function,
77  "Random variable", y,
78  "First shape parameter", alpha,
79  "Second shape parameter", beta);
80  check_nonnegative(function, "Random variable", y);
81  check_less_or_equal(function, "Random variable", y, 1);
82 
84  return 0.0;
85 
86  VectorView<const T_y> y_vec(y);
87  VectorView<const T_scale_succ> alpha_vec(alpha);
88  VectorView<const T_scale_fail> beta_vec(beta);
89  size_t N = max_size(y, alpha, beta);
90 
91  for (size_t n = 0; n < N; n++) {
92  const T_partials_return y_dbl = value_of(y_vec[n]);
93  if (y_dbl < 0 || y_dbl > 1)
94  return LOG_ZERO;
95  }
96 
98  operands_and_partials(y, alpha, beta);
99 
101  T_partials_return, T_y>
102  log_y(length(y));
104  T_partials_return, T_y>
105  log1m_y(length(y));
106 
107  for (size_t n = 0; n < length(y); n++) {
109  log_y[n] = log(value_of(y_vec[n]));
111  log1m_y[n] = log1m(value_of(y_vec[n]));
112  }
113 
115  T_partials_return, T_scale_succ>
116  lgamma_alpha(length(alpha));
118  T_partials_return, T_scale_succ>
119  digamma_alpha(length(alpha));
120  for (size_t n = 0; n < length(alpha); n++) {
122  lgamma_alpha[n] = lgamma(value_of(alpha_vec[n]));
124  digamma_alpha[n] = digamma(value_of(alpha_vec[n]));
125  }
126 
128  T_partials_return, T_scale_fail>
129  lgamma_beta(length(beta));
131  T_partials_return, T_scale_fail>
132  digamma_beta(length(beta));
133 
134  for (size_t n = 0; n < length(beta); n++) {
136  lgamma_beta[n] = lgamma(value_of(beta_vec[n]));
138  digamma_beta[n] = digamma(value_of(beta_vec[n]));
139  }
140 
142  T_partials_return, T_scale_succ, T_scale_fail>
143  lgamma_alpha_beta(max_size(alpha, beta));
144 
146  T_scale_fail>::value,
147  T_partials_return, T_scale_succ, T_scale_fail>
148  digamma_alpha_beta(max_size(alpha, beta));
149 
150  for (size_t n = 0; n < max_size(alpha, beta); n++) {
151  const T_partials_return alpha_beta = value_of(alpha_vec[n])
152  + value_of(beta_vec[n]);
154  lgamma_alpha_beta[n] = lgamma(alpha_beta);
156  digamma_alpha_beta[n] = digamma(alpha_beta);
157  }
158 
159  for (size_t n = 0; n < N; n++) {
160  const T_partials_return y_dbl = value_of(y_vec[n]);
161  const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
162  const T_partials_return beta_dbl = value_of(beta_vec[n]);
163 
165  logp += lgamma_alpha_beta[n];
167  logp -= lgamma_alpha[n];
169  logp -= lgamma_beta[n];
171  logp += (alpha_dbl-1.0) * log_y[n];
173  logp += (beta_dbl-1.0) * log1m_y[n];
174 
176  operands_and_partials.d_x1[n] += (alpha_dbl-1)/y_dbl
177  + (beta_dbl-1)/(y_dbl-1);
179  operands_and_partials.d_x2[n]
180  += log_y[n] + digamma_alpha_beta[n] - digamma_alpha[n];
182  operands_and_partials.d_x3[n]
183  += log1m_y[n] + digamma_alpha_beta[n] - digamma_beta[n];
184  }
185  return operands_and_partials.value(logp);
186  }
187 
188  template <typename T_y, typename T_scale_succ, typename T_scale_fail>
190  beta_lpdf(const T_y& y, const T_scale_succ& alpha,
191  const T_scale_fail& beta) {
192  return beta_lpdf<false>(y, alpha, beta);
193  }
194 
195  }
196 }
197 #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.
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:53
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.
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[].
Definition: VectorView.hpp:48
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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