Stan Math Library  2.20.0
reverse mode automatic differentiation
beta_binomial_cdf.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_BETA_BINOMIAL_CDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_BETA_BINOMIAL_CDF_HPP
3 
16 #include <cmath>
17 
18 namespace stan {
19 namespace math {
20 
38 template <typename T_n, typename T_N, typename T_size1, typename T_size2>
40  const T_n& n, const T_N& N, const T_size1& alpha, const T_size2& beta) {
41  static const char* function = "beta_binomial_cdf";
43  T_partials_return;
44 
45  if (size_zero(n, N, alpha, beta))
46  return 1.0;
47 
48  T_partials_return P(1.0);
49 
50  check_nonnegative(function, "Population size parameter", N);
51  check_positive_finite(function, "First prior sample size parameter", alpha);
52  check_positive_finite(function, "Second prior sample size parameter", beta);
53  check_consistent_sizes(function, "Successes variable", n,
54  "Population size parameter", N,
55  "First prior sample size parameter", alpha,
56  "Second prior sample size parameter", beta);
57 
58  scalar_seq_view<T_n> n_vec(n);
59  scalar_seq_view<T_N> N_vec(N);
60  scalar_seq_view<T_size1> alpha_vec(alpha);
61  scalar_seq_view<T_size2> beta_vec(beta);
62  size_t size = max_size(n, N, alpha, beta);
63 
64  using std::exp;
65  using std::exp;
66 
67  operands_and_partials<T_size1, T_size2> ops_partials(alpha, beta);
68 
69  // Explicit return for extreme values
70  // The gradients are technically ill-defined, but treated as zero
71  for (size_t i = 0; i < stan::length(n); i++) {
72  if (value_of(n_vec[i]) <= 0)
73  return ops_partials.build(0.0);
74  }
75 
76  for (size_t i = 0; i < size; i++) {
77  // Explicit results for extreme values
78  // The gradients are technically ill-defined, but treated as zero
79  if (value_of(n_vec[i]) >= value_of(N_vec[i])) {
80  continue;
81  }
82 
83  const T_partials_return n_dbl = value_of(n_vec[i]);
84  const T_partials_return N_dbl = value_of(N_vec[i]);
85  const T_partials_return alpha_dbl = value_of(alpha_vec[i]);
86  const T_partials_return beta_dbl = value_of(beta_vec[i]);
87 
88  const T_partials_return mu = alpha_dbl + n_dbl + 1;
89  const T_partials_return nu = beta_dbl + N_dbl - n_dbl - 1;
90 
91  const T_partials_return F
92  = F32((T_partials_return)1, mu, -N_dbl + n_dbl + 1, n_dbl + 2, 1 - nu,
93  (T_partials_return)1);
94 
95  T_partials_return C = lgamma(nu) - lgamma(N_dbl - n_dbl);
96  C += lgamma(mu) - lgamma(n_dbl + 2);
97  C += lgamma(N_dbl + 2) - lgamma(N_dbl + alpha_dbl + beta_dbl);
98  C = exp(C);
99 
100  C *= F / stan::math::beta(alpha_dbl, beta_dbl);
101  C /= N_dbl + 1;
102 
103  const T_partials_return Pi = 1 - C;
104 
105  P *= Pi;
106 
107  T_partials_return dF[6];
108  T_partials_return digammaOne = 0;
109  T_partials_return digammaTwo = 0;
110 
112  digammaOne = digamma(mu + nu);
113  digammaTwo = digamma(alpha_dbl + beta_dbl);
114  grad_F32(dF, (T_partials_return)1, mu, -N_dbl + n_dbl + 1, n_dbl + 2,
115  1 - nu, (T_partials_return)1);
116  }
118  const T_partials_return g = -C
119  * (digamma(mu) - digammaOne + dF[1] / F
120  - digamma(alpha_dbl) + digammaTwo);
121  ops_partials.edge1_.partials_[i] += g / Pi;
122  }
124  const T_partials_return g = -C
125  * (digamma(nu) - digammaOne - dF[4] / F
126  - digamma(beta_dbl) + digammaTwo);
127  ops_partials.edge2_.partials_[i] += g / Pi;
128  }
129  }
130 
132  for (size_t i = 0; i < stan::length(alpha); ++i)
133  ops_partials.edge1_.partials_[i] *= P;
134  }
136  for (size_t i = 0; i < stan::length(beta); ++i)
137  ops_partials.edge2_.partials_[i] *= P;
138  }
139 
140  return ops_partials.build(P);
141 }
142 
143 } // namespace math
144 } // namespace stan
145 #endif
boost::math::tools::promote_args< double, typename partials_type< typename scalar_type< T >::type >::type, typename partials_return_type< T_pack... >::type >::type type
fvar< T > lgamma(const fvar< T > &x)
Return the natural logarithm of the gamma function applied to the specified argument.
Definition: lgamma.hpp:21
T F32(const T &a1, const T &a2, const T &a3, const T &b1, const T &b2, const T &z, double precision=1e-6, int max_steps=1e5)
Hypergeometric function (3F2).
Definition: F32.hpp:51
T value_of(const fvar< T > &v)
Return the value of the specified variable.
Definition: value_of.hpp:17
Extends std::true_type when instantiated with zero or more template parameters, all of which extend t...
Definition: conjunction.hpp:14
scalar_seq_view provides a uniform sequence-like wrapper around either a scalar or a sequence of scal...
This template builds partial derivatives with respect to a set of operands.
size_t length(const std::vector< T > &x)
Returns the length of the provided std::vector.
Definition: length.hpp:16
bool size_zero(T &x)
Returns 1 if input is of length 0, returns 0 otherwise.
Definition: size_zero.hpp:18
void check_nonnegative(const char *function, const char *name, const T_y &y)
Check if y is non-negative.
fvar< T > beta(const fvar< T > &x1, const fvar< T > &x2)
Return fvar with the beta function applied to the specified arguments and its gradient.
Definition: beta.hpp:51
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)
Returns the CDF of the Beta-Binomial distribution with given population size, prior success...
void check_positive_finite(const char *function, const char *name, const T_y &y)
Check if y is positive and finite.
boost::math::tools::promote_args< double, typename scalar_type< T >::type, typename return_type< Types_pack... >::type >::type type
Definition: return_type.hpp:36
fvar< T > exp(const fvar< T > &x)
Definition: exp.hpp:11
size_t max_size(const T1 &x1, const T2 &x2)
Definition: max_size.hpp:9
T_return_type build(double value)
Build the node to be stored on the autodiff graph.
internal::ops_partials_edge< double, Op2 > edge2_
int size(const std::vector< T > &x)
Return the size of the specified standard vector.
Definition: size.hpp:17
void grad_F32(T *g, const T &a1, const T &a2, const T &a3, const T &b1, const T &b2, const T &z, const T &precision=1e-6, int max_steps=1e5)
Gradients of the hypergeometric function, 3F2.
Definition: grad_F32.hpp:38
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.
internal::ops_partials_edge< double, Op1 > edge1_
fvar< T > digamma(const fvar< T > &x)
Return the derivative of the log gamma function at the specified argument.
Definition: digamma.hpp:23

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