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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
4 #include <stan/math/prim/scal/meta/OperandsAndPartials.hpp>
5 #include <stan/math/prim/scal/err/check_consistent_sizes.hpp>
6 #include <stan/math/prim/scal/err/check_nonnegative.hpp>
7 #include <stan/math/prim/scal/err/check_positive_finite.hpp>
8 #include <stan/math/prim/scal/fun/constants.hpp>
9 #include <stan/math/prim/scal/fun/lbeta.hpp>
10 #include <stan/math/prim/scal/fun/digamma.hpp>
11 #include <stan/math/prim/scal/fun/lgamma.hpp>
12 #include <stan/math/prim/scal/fun/binomial_coefficient_log.hpp>
13 #include <stan/math/prim/scal/fun/value_of.hpp>
14 #include <stan/math/prim/scal/meta/contains_nonconstant_struct.hpp>
15 #include <stan/math/prim/scal/meta/include_summand.hpp>
16 #include <stan/math/prim/scal/prob/beta_rng.hpp>
17 #include <stan/math/prim/scal/fun/F32.hpp>
18 #include <stan/math/prim/scal/fun/grad_F32.hpp>
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
36 using stan::math::check_positive_finite;
37 using stan::math::check_nonnegative;
38 using stan::math::value_of;
39 using stan::math::check_consistent_sizes;
40 using stan::math::include_summand;
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
75 OperandsAndPartials<T_size1, T_size2>
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
121 if (contains_nonconstant_struct<T_size1, T_size2>::value) {
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 }
128 if (!is_constant_struct<T_size1>::value) {
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 }
135 if (!is_constant_struct<T_size2>::value) {
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
144 if (!is_constant_struct<T_size1>::value) {
145 for (size_t i = 0; i < stan::length(alpha); ++i)
146 operands_and_partials.d_x1[i] *= P;
147 }
148 if (!is_constant_struct<T_size2>::value) {
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
lgamma.hpp
stan::math::lgamma
fvar< T > lgamma(const fvar< T > &x)
Definition: lgamma.hpp:15
check_positive_finite.hpp
stan::math::value_of
T value_of(const fvar< T > &v)
Return the value of the specified variable.
Definition: value_of.hpp:16
stan::math::lbeta
fvar< T > lbeta(const fvar< T > &x1, const fvar< T > &x2)
Definition: lbeta.hpp:16
digamma.hpp
contains_nonconstant_struct.hpp
stan::length
size_t length(const std::vector< T > &x)
Definition: length.hpp:10
binomial_coefficient_log.hpp
stan::math::OperandsAndPartials::to_var
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)
Definition: OperandsAndPartials.hpp:322
stan::math::include_summand
Template metaprogram to calculate whether a summand needs to be included in a proportional (log) prob...
Definition: include_summand.hpp:36
F32.hpp
include_summand.hpp
stan::math::OperandsAndPartials::d_x1
VectorView< T_partials_return, is_vector< T1 >::value, is_constant_struct< T1 >::value > d_x1
Definition: OperandsAndPartials.hpp:253
check_nonnegative.hpp
stan::is_constant_struct
Metaprogram to determine if a type has a base scalar type that can be assigned to type double...
Definition: is_constant_struct.hpp:16
stan::math::beta_binomial_cdf
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)
Definition: beta_binomial_cdf.hpp:29
stan::partials_return_type
Definition: partials_return_type.hpp:16
stan::math::exp
fvar< T > exp(const fvar< T > &x)
Definition: exp.hpp:10
beta_rng.hpp
stan::math::OperandsAndPartials
A variable implementation that stores operands and derivatives with respect to the variable...
Definition: OperandsAndPartials.hpp:238
OperandsAndPartials.hpp
stan::max_size
size_t max_size(const T1 &x1, const T2 &x2)
Definition: max_size.hpp:9
stan::contains_nonconstant_struct
Definition: contains_nonconstant_struct.hpp:14
grad_F32.hpp
stan::math::grad_F32
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
constants.hpp
stan::math::size
int size(const std::vector< T > &x)
Definition: size.hpp:11
stan::math::check_consistent_sizes
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.
Definition: check_consistent_sizes.hpp:31
lbeta.hpp
stan::math::OperandsAndPartials::d_x2
VectorView< T_partials_return, is_vector< T2 >::value, is_constant_struct< T2 >::value > d_x2
Definition: OperandsAndPartials.hpp:256
stan::math::check_nonnegative
bool check_nonnegative(const char *function, const char *name, const T_y &y)
Return true if y is non-negative.
Definition: check_nonnegative.hpp:66
stan::math::F32
T F32(T a, T b, T c, T d, T e, T z, T precision=1e-6)
Definition: F32.hpp:11
value_of.hpp
stan::VectorView
VectorView is a template metaprogram that takes its argument and allows it to be used like a vector...
Definition: VectorView.hpp:41
check_consistent_sizes.hpp
stan::math::check_positive_finite
bool check_positive_finite(const char *function, const char *name, const T_y &y)
Return true if y is positive and finite.
Definition: check_positive_finite.hpp:28
stan::math::digamma
fvar< T > digamma(const fvar< T > &x)
Definition: digamma.hpp:16

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