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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 
19 #include <cmath>
20 
21 namespace stan {
22 
23  namespace math {
24 
25  // Beta-Binomial CDF
26  template <typename T_n, typename T_N,
27  typename T_size1, typename T_size2>
28  typename return_type<T_size1, T_size2>::type
29  beta_binomial_cdf(const T_n& n, const T_N& N, const T_size1& alpha,
30  const T_size2& beta) {
31  static const char* function("stan::math::beta_binomial_cdf");
32  typedef typename stan::partials_return_type<T_n, T_N, T_size1,
33  T_size2>::type
34  T_partials_return;
35 
41 
42  // Ensure non-zero argument lengths
43  if (!(stan::length(n) && stan::length(N) && stan::length(alpha)
44  && stan::length(beta)))
45  return 1.0;
46 
47  T_partials_return P(1.0);
48 
49  // Validate arguments
50  check_nonnegative(function, "Population size parameter", N);
51  check_positive_finite(function,
52  "First prior sample size parameter", alpha);
53  check_positive_finite(function,
54  "Second prior sample size parameter", beta);
55  check_consistent_sizes(function,
56  "Successes variable", n,
57  "Population size parameter", N,
58  "First prior sample size parameter", alpha,
59  "Second prior sample size parameter", beta);
60 
61  // Wrap arguments in vector views
62  VectorView<const T_n> n_vec(n);
63  VectorView<const T_N> N_vec(N);
64  VectorView<const T_size1> alpha_vec(alpha);
65  VectorView<const T_size2> beta_vec(beta);
66  size_t size = max_size(n, N, alpha, beta);
67 
68  // Compute vectorized CDF and gradient
69  using stan::math::lgamma;
70  using stan::math::lbeta;
71  using stan::math::digamma;
72  using std::exp;
73  using std::exp;
74 
76  operands_and_partials(alpha, beta);
77 
78  // Explicit return for extreme values
79  // The gradients are technically ill-defined, but treated as zero
80  for (size_t i = 0; i < stan::length(n); i++) {
81  if (value_of(n_vec[i]) <= 0)
82  return operands_and_partials.to_var(0.0, alpha, beta);
83  }
84 
85  for (size_t i = 0; i < size; i++) {
86  // Explicit results for extreme values
87  // The gradients are technically ill-defined, but treated as zero
88  if (value_of(n_vec[i]) >= value_of(N_vec[i])) {
89  continue;
90  }
91 
92  const T_partials_return n_dbl = value_of(n_vec[i]);
93  const T_partials_return N_dbl = value_of(N_vec[i]);
94  const T_partials_return alpha_dbl = value_of(alpha_vec[i]);
95  const T_partials_return beta_dbl = value_of(beta_vec[i]);
96 
97  const T_partials_return mu = alpha_dbl + n_dbl + 1;
98  const T_partials_return nu = beta_dbl + N_dbl - n_dbl - 1;
99 
100  const T_partials_return F = stan::math::F32((T_partials_return)1, mu,
101  -N_dbl + n_dbl + 1,
102  n_dbl + 2, 1 - nu,
103  (T_partials_return)1);
104 
105  T_partials_return C = lgamma(nu) - lgamma(N_dbl - n_dbl);
106  C += lgamma(mu) - lgamma(n_dbl + 2);
107  C += lgamma(N_dbl + 2) - lgamma(N_dbl + alpha_dbl + beta_dbl);
108  C = exp(C);
109 
110  C *= F / exp(lbeta(alpha_dbl, beta_dbl));
111  C /= N_dbl + 1;
112 
113  const T_partials_return Pi = 1 - C;
114 
115  P *= Pi;
116 
117  T_partials_return dF[6];
118  T_partials_return digammaOne = 0;
119  T_partials_return digammaTwo = 0;
120 
122  digammaOne = digamma(mu + nu);
123  digammaTwo = digamma(alpha_dbl + beta_dbl);
124  stan::math::grad_F32(dF, (T_partials_return)1, mu, -N_dbl + n_dbl + 1,
125  n_dbl + 2,
126  1 - nu, (T_partials_return)1);
127  }
129  const T_partials_return g
130  = - C * (digamma(mu) - digammaOne + dF[1] / F
131  - digamma(alpha_dbl) + digammaTwo);
132  operands_and_partials.d_x1[i]
133  += g / Pi;
134  }
136  const T_partials_return g
137  = - C * (digamma(nu) - digammaOne - dF[4] / F - digamma(beta_dbl)
138  + digammaTwo);
139  operands_and_partials.d_x2[i]
140  += g / Pi;
141  }
142  }
143 
145  for (size_t i = 0; i < stan::length(alpha); ++i)
146  operands_and_partials.d_x1[i] *= P;
147  }
149  for (size_t i = 0; i < stan::length(beta); ++i)
150  operands_and_partials.d_x2[i] *= P;
151  }
152 
153  return operands_and_partials.to_var(P, alpha, beta);
154  }
155 
156  }
157 }
158 #endif
fvar< T > lgamma(const fvar< T > &x)
Definition: lgamma.hpp:15
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:16
size_t length(const std::vector< T > &x)
Definition: length.hpp:10
T_return_type to_var(T_partials_return logp, const T1 &x1=0, const T2 &x2=0, const T3 &x3=0, const T4 &x4=0, const T5 &x5=0, const T6 &x6=0)
Template metaprogram to calculate whether a summand needs to be included in a proportional (log) prob...
VectorView< T_partials_return, is_vector< T1 >::value, is_constant_struct< T1 >::value > d_x1
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
A variable implementation that stores operands and derivatives with respect to the variable...
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:11
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.
VectorView< T_partials_return, is_vector< T2 >::value, is_constant_struct< T2 >::value > d_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:11
VectorView is a template metaprogram that takes its argument and allows it to be used like a vector...
Definition: VectorView.hpp:41
bool check_positive_finite(const char *function, const char *name, const T_y &y)
Return true if y is positive and finite.
fvar< T > digamma(const fvar< T > &x)
Definition: digamma.hpp:16

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