Stan Math Library  2.14.0
reverse mode automatic differentiation
beta_binomial_log.hpp
Go to the documentation of this file.
1 #ifndef STAN_MATH_PRIM_SCAL_PROB_BETA_BINOMIAL_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_BETA_BINOMIAL_LOG_HPP
3 
22 
23 namespace stan {
24  namespace math {
25 
26  // BetaBinomial(n|alpha, beta) [alpha > 0; beta > 0; n >= 0]
27  template <bool propto,
28  typename T_n, typename T_N,
29  typename T_size1, typename T_size2>
31  beta_binomial_log(const T_n& n,
32  const T_N& N,
33  const T_size1& alpha,
34  const T_size2& beta) {
35  static const char* function("beta_binomial_log");
37  T_partials_return;
38 
39  if (!(stan::length(n)
40  && stan::length(N)
41  && stan::length(alpha)
42  && stan::length(beta)))
43  return 0.0;
44 
45  T_partials_return logp(0.0);
46  check_nonnegative(function, "Population size parameter", N);
47  check_positive_finite(function,
48  "First prior sample size parameter", alpha);
49  check_positive_finite(function,
50  "Second prior sample size parameter", beta);
51  check_consistent_sizes(function,
52  "Successes variable", n,
53  "Population size parameter", N,
54  "First prior sample size parameter", alpha,
55  "Second prior sample size parameter", beta);
56 
58  return 0.0;
59 
61  operands_and_partials(alpha, beta);
62 
63  VectorView<const T_n> n_vec(n);
64  VectorView<const T_N> N_vec(N);
65  VectorView<const T_size1> alpha_vec(alpha);
66  VectorView<const T_size2> beta_vec(beta);
67  size_t size = max_size(n, N, alpha, beta);
68 
69  for (size_t i = 0; i < size; i++) {
70  if (n_vec[i] < 0 || n_vec[i] > N_vec[i])
71  return operands_and_partials.value(LOG_ZERO);
72  }
73 
75  T_partials_return, T_n, T_N>
76  normalizing_constant(max_size(N, n));
77  for (size_t i = 0; i < max_size(N, n); i++)
79  normalizing_constant[i]
80  = binomial_coefficient_log(N_vec[i], n_vec[i]);
81 
83  T_partials_return, T_n, T_N, T_size1, T_size2>
84  lbeta_numerator(size);
85  for (size_t i = 0; i < size; i++)
87  lbeta_numerator[i] = lbeta(n_vec[i] + value_of(alpha_vec[i]),
88  N_vec[i] - n_vec[i]
89  + value_of(beta_vec[i]));
90 
92  T_partials_return, T_size1, T_size2>
93  lbeta_denominator(max_size(alpha, beta));
94  for (size_t i = 0; i < max_size(alpha, beta); i++)
96  lbeta_denominator[i] = lbeta(value_of(alpha_vec[i]),
97  value_of(beta_vec[i]));
98 
100  T_partials_return, T_n, T_size1>
101  digamma_n_plus_alpha(max_size(n, alpha));
102  for (size_t i = 0; i < max_size(n, alpha); i++)
104  digamma_n_plus_alpha[i]
105  = digamma(n_vec[i] + value_of(alpha_vec[i]));
106 
108  T_partials_return, T_N, T_size1, T_size2>
109  digamma_N_plus_alpha_plus_beta(max_size(N, alpha, beta));
110  for (size_t i = 0; i < max_size(N, alpha, beta); i++)
112  digamma_N_plus_alpha_plus_beta[i]
113  = digamma(N_vec[i] + value_of(alpha_vec[i])
114  + value_of(beta_vec[i]));
115 
117  T_partials_return, T_size1, T_size2>
118  digamma_alpha_plus_beta(max_size(alpha, beta));
119  for (size_t i = 0; i < max_size(alpha, beta); i++)
121  digamma_alpha_plus_beta[i]
122  = digamma(value_of(alpha_vec[i]) + value_of(beta_vec[i]));
123 
125  T_partials_return, T_size1> digamma_alpha(length(alpha));
126  for (size_t i = 0; i < length(alpha); i++)
128  digamma_alpha[i] = digamma(value_of(alpha_vec[i]));
129 
131  T_partials_return, T_size2>
132  digamma_beta(length(beta));
133  for (size_t i = 0; i < length(beta); i++)
135  digamma_beta[i] = digamma(value_of(beta_vec[i]));
136 
137  for (size_t i = 0; i < size; i++) {
139  logp += normalizing_constant[i];
141  logp += lbeta_numerator[i] - lbeta_denominator[i];
142 
144  operands_and_partials.d_x1[i]
145  += digamma_n_plus_alpha[i]
146  - digamma_N_plus_alpha_plus_beta[i]
147  + digamma_alpha_plus_beta[i]
148  - digamma_alpha[i];
150  operands_and_partials.d_x2[i]
151  += digamma(value_of(N_vec[i]-n_vec[i]+beta_vec[i]))
152  - digamma_N_plus_alpha_plus_beta[i]
153  + digamma_alpha_plus_beta[i]
154  - digamma_beta[i];
155  }
156  return operands_and_partials.value(logp);
157  }
158 
159  template <typename T_n,
160  typename T_N,
161  typename T_size1,
162  typename T_size2>
164  beta_binomial_log(const T_n& n, const T_N& N,
165  const T_size1& alpha, const T_size2& beta) {
166  return beta_binomial_log<false>(n, N, alpha, beta);
167  }
168 
169  }
170 }
171 #endif
VectorView< T_return_type, false, true > d_x2
fvar< T > binomial_coefficient_log(const fvar< T > &x1, const fvar< T > &x2)
T value_of(const fvar< T > &v)
Return the value of the specified variable.
Definition: value_of.hpp:16
fvar< T > lbeta(const fvar< T > &x1, const fvar< T > &x2)
Definition: lbeta.hpp:15
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.
This class builds partial derivatives with respect to a set of operands.
return_type< T_size1, T_size2 >::type beta_binomial_log(const T_n &n, const T_N &N, const T_size1 &alpha, const T_size2 &beta)
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.
int size(const std::vector< T > &x)
Return the size of the specified standard vector.
Definition: size.hpp:17
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.
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.
Definition: digamma.hpp:22

     [ Stan Home Page ] © 2011–2016, Stan Development Team.