Stan Math Library  2.15.0
reverse mode automatic differentiation
beta_binomial_lccdf.hpp
Go to the documentation of this file.
1 #ifndef STAN_MATH_PRIM_SCAL_PROB_BETA_BINOMIAL_LCCDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_BETA_BINOMIAL_LCCDF_HPP
3 
22 #include <cmath>
23 
24 namespace stan {
25  namespace math {
26 
44  template <typename T_n, typename T_N,
45  typename T_size1, typename T_size2>
47  beta_binomial_lccdf(const T_n& n, const T_N& N, const T_size1& alpha,
48  const T_size2& beta) {
49  static const char* function("beta_binomial_lccdf");
50  typedef typename stan::partials_return_type<T_n, T_N, T_size1,
51  T_size2>::type
52  T_partials_return;
53 
54  if (!(stan::length(n) && stan::length(N) && stan::length(alpha)
55  && stan::length(beta)))
56  return 0.0;
57 
58  T_partials_return P(0.0);
59 
60  check_nonnegative(function, "Population size parameter", N);
61  check_positive_finite(function,
62  "First prior sample size parameter", alpha);
63  check_positive_finite(function,
64  "Second prior sample size parameter", beta);
65  check_consistent_sizes(function,
66  "Successes variable", n,
67  "Population size parameter", N,
68  "First prior sample size parameter", alpha,
69  "Second prior sample size parameter", beta);
70 
73  scalar_seq_view<const T_size1> alpha_vec(alpha);
74  scalar_seq_view<const T_size2> beta_vec(beta);
75  size_t size = max_size(n, N, alpha, beta);
76 
77  using std::exp;
78  using std::log;
79  using std::exp;
80 
82  operands_and_partials(alpha, beta);
83 
84  // Explicit return for extreme values
85  // The gradients are technically ill-defined, but treated as neg infinity
86  for (size_t i = 0; i < stan::length(n); i++) {
87  if (value_of(n_vec[i]) <= 0)
88  return operands_and_partials.value(0.0);
89  }
90 
91  for (size_t i = 0; i < size; i++) {
92  // Explicit results for extreme values
93  // The gradients are technically ill-defined, but treated as zero
94  if (value_of(n_vec[i]) >= value_of(N_vec[i])) {
95  return operands_and_partials.value(negative_infinity());
96  }
97 
98  const T_partials_return n_dbl = value_of(n_vec[i]);
99  const T_partials_return N_dbl = value_of(N_vec[i]);
100  const T_partials_return alpha_dbl = value_of(alpha_vec[i]);
101  const T_partials_return beta_dbl = value_of(beta_vec[i]);
102 
103  const T_partials_return mu = alpha_dbl + n_dbl + 1;
104  const T_partials_return nu = beta_dbl + N_dbl - n_dbl - 1;
105 
106  const T_partials_return F = F32((T_partials_return)1, mu,
107  -N_dbl + n_dbl + 1,
108  n_dbl + 2, 1 - nu,
109  (T_partials_return)1);
110 
111  T_partials_return C = lgamma(nu) - lgamma(N_dbl - n_dbl);
112  C += lgamma(mu) - lgamma(n_dbl + 2);
113  C += lgamma(N_dbl + 2) - lgamma(N_dbl + alpha_dbl + beta_dbl);
114  C = exp(C);
115 
116  C *= F / exp(lbeta(alpha_dbl, beta_dbl));
117  C /= N_dbl + 1;
118 
119  const T_partials_return Pi = C;
120 
121  P += log(Pi);
122 
123  T_partials_return dF[6];
124  T_partials_return digammaOne = 0;
125  T_partials_return digammaTwo = 0;
126 
128  digammaOne = digamma(mu + nu);
129  digammaTwo = digamma(alpha_dbl + beta_dbl);
130  grad_F32(dF, (T_partials_return)1, mu, -N_dbl + n_dbl + 1,
131  n_dbl + 2, 1 - nu, (T_partials_return)1);
132  }
134  const T_partials_return g
135  = - C * (digamma(mu) - digammaOne + dF[1] / F
136  - digamma(alpha_dbl) + digammaTwo);
137  operands_and_partials.d_x1[i] -= g / Pi;
138  }
140  const T_partials_return g
141  = - C * (digamma(nu) - digammaOne - dF[4] / F - digamma(beta_dbl)
142  + digammaTwo);
143  operands_and_partials.d_x2[i] -= g / Pi;
144  }
145  }
146 
147  return operands_and_partials.value(P);
148  }
149 
150  }
151 }
152 #endif
VectorView< T_return_type, false, true > d_x2
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 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:16
fvar< T > lbeta(const fvar< T > &x1, const fvar< T > &x2)
Definition: lbeta.hpp:15
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
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.
fvar< T > exp(const fvar< T > &x)
Definition: exp.hpp:10
return_type< T_size1, T_size2 >::type beta_binomial_lccdf(const T_n &n, const T_N &N, const T_size1 &alpha, const T_size2 &beta)
Returns the log CCDF of the Beta-Binomial distribution with given population size, prior success, and prior failure parameters.
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
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:36
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.
VectorView< T_return_type, false, true > d_x1
double negative_infinity()
Return negative infinity.
Definition: constants.hpp:130
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.