Stan Math Library  2.12.0
reverse mode automatic differentiation
beta_binomial_cdf.hpp
Go to the documentation of this file.
1 #ifndef STAN_MATH_PRIM_SCAL_PROB_BETA_BINOMIAL_CDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_BETA_BINOMIAL_CDF_HPP
3 
21 #include <cmath>
22 
23 namespace stan {
24  namespace math {
25 
26  // Beta-Binomial CDF
27  template <typename T_n, typename T_N,
28  typename T_size1, typename T_size2>
29  typename return_type<T_size1, T_size2>::type
30  beta_binomial_cdf(const T_n& n, const T_N& N, const T_size1& alpha,
31  const T_size2& beta) {
32  static const char* function("beta_binomial_cdf");
33  typedef typename stan::partials_return_type<T_n, T_N, T_size1,
34  T_size2>::type
35  T_partials_return;
36 
37  if (!(stan::length(n) && stan::length(N) && stan::length(alpha)
38  && stan::length(beta)))
39  return 1.0;
40 
41  T_partials_return P(1.0);
42 
43  check_nonnegative(function, "Population size parameter", N);
44  check_positive_finite(function,
45  "First prior sample size parameter", alpha);
46  check_positive_finite(function,
47  "Second prior sample size parameter", beta);
48  check_consistent_sizes(function,
49  "Successes variable", n,
50  "Population size parameter", N,
51  "First prior sample size parameter", alpha,
52  "Second prior sample size parameter", beta);
53 
54  VectorView<const T_n> n_vec(n);
55  VectorView<const T_N> N_vec(N);
56  VectorView<const T_size1> alpha_vec(alpha);
57  VectorView<const T_size2> beta_vec(beta);
58  size_t size = max_size(n, N, alpha, beta);
59 
60  using std::exp;
61  using std::exp;
62 
64  operands_and_partials(alpha, beta);
65 
66  // Explicit return for extreme values
67  // The gradients are technically ill-defined, but treated as zero
68  for (size_t i = 0; i < stan::length(n); i++) {
69  if (value_of(n_vec[i]) <= 0)
70  return operands_and_partials.value(0.0);
71  }
72 
73  for (size_t i = 0; i < size; i++) {
74  // Explicit results for extreme values
75  // The gradients are technically ill-defined, but treated as zero
76  if (value_of(n_vec[i]) >= value_of(N_vec[i])) {
77  continue;
78  }
79 
80  const T_partials_return n_dbl = value_of(n_vec[i]);
81  const T_partials_return N_dbl = value_of(N_vec[i]);
82  const T_partials_return alpha_dbl = value_of(alpha_vec[i]);
83  const T_partials_return beta_dbl = value_of(beta_vec[i]);
84 
85  const T_partials_return mu = alpha_dbl + n_dbl + 1;
86  const T_partials_return nu = beta_dbl + N_dbl - n_dbl - 1;
87 
88  const T_partials_return F = F32((T_partials_return)1, mu,
89  -N_dbl + n_dbl + 1,
90  n_dbl + 2, 1 - nu,
91  (T_partials_return)1);
92 
93  T_partials_return C = lgamma(nu) - lgamma(N_dbl - n_dbl);
94  C += lgamma(mu) - lgamma(n_dbl + 2);
95  C += lgamma(N_dbl + 2) - lgamma(N_dbl + alpha_dbl + beta_dbl);
96  C = exp(C);
97 
98  C *= F / exp(lbeta(alpha_dbl, beta_dbl));
99  C /= N_dbl + 1;
100 
101  const T_partials_return Pi = 1 - C;
102 
103  P *= Pi;
104 
105  T_partials_return dF[6];
106  T_partials_return digammaOne = 0;
107  T_partials_return digammaTwo = 0;
108 
110  digammaOne = digamma(mu + nu);
111  digammaTwo = digamma(alpha_dbl + beta_dbl);
112  grad_F32(dF, (T_partials_return)1, mu, -N_dbl + n_dbl + 1,
113  n_dbl + 2,
114  1 - nu, (T_partials_return)1);
115  }
117  const T_partials_return g
118  = - C * (digamma(mu) - digammaOne + dF[1] / F
119  - digamma(alpha_dbl) + digammaTwo);
120  operands_and_partials.d_x1[i]
121  += g / Pi;
122  }
124  const T_partials_return g
125  = - C * (digamma(nu) - digammaOne - dF[4] / F - digamma(beta_dbl)
126  + digammaTwo);
127  operands_and_partials.d_x2[i]
128  += g / Pi;
129  }
130  }
131 
133  for (size_t i = 0; i < stan::length(alpha); ++i)
134  operands_and_partials.d_x1[i] *= P;
135  }
137  for (size_t i = 0; i < stan::length(beta); ++i)
138  operands_and_partials.d_x2[i] *= P;
139  }
140 
141  return operands_and_partials.value(P);
142  }
143 
144  }
145 }
146 #endif
VectorView< T_return_type, false, true > d_x2
fvar< T > lgamma(const fvar< T > &x)
Definition: lgamma.hpp:14
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
Metaprogram to determine if a type has a base scalar type that can be assigned to type double...
return_type< T_size1, T_size2 >::type beta_binomial_cdf(const T_n &n, const T_N &N, const T_size1 &alpha, const T_size2 &beta)
fvar< T > exp(const fvar< T > &x)
Definition: exp.hpp:10
This class builds partial derivatives with respect to a set of operands.
size_t max_size(const T1 &x1, const T2 &x2)
Definition: max_size.hpp:9
void grad_F32(T *g, T a, T b, T c, T d, T e, T z, T precision=1e-6)
Definition: grad_F32.hpp:10
int size(const std::vector< T > &x)
Return the size of the specified standard vector.
Definition: size.hpp:17
bool check_consistent_sizes(const char *function, const char *name1, const T1 &x1, const char *name2, const T2 &x2)
Return true if the dimension of x1 is consistent with x2.
bool check_nonnegative(const char *function, const char *name, const T_y &y)
Return true if y is non-negative.
T F32(T a, T b, T c, T d, T e, T z, T precision=1e-6)
Definition: F32.hpp:10
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
bool check_positive_finite(const char *function, const char *name, const T_y &y)
Return true if y is positive and finite.
VectorView< T_return_type, false, true > d_x1
fvar< T > digamma(const fvar< T > &x)
Definition: digamma.hpp:15

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