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beta_binomial_cdf_log.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_BETA_BINOMIAL_CDF_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_BETA_BINOMIAL_CDF_LOG_HPP
3
4 #include <stan/math/prim/scal/meta/is_constant_struct.hpp>
5 #include <stan/math/prim/scal/meta/partials_return_type.hpp>
6 #include <stan/math/prim/scal/meta/OperandsAndPartials.hpp>
7 #include <stan/math/prim/scal/err/check_consistent_sizes.hpp>
8 #include <stan/math/prim/scal/err/check_nonnegative.hpp>
9 #include <stan/math/prim/scal/err/check_positive_finite.hpp>
10 #include <stan/math/prim/scal/fun/constants.hpp>
11 #include <stan/math/prim/scal/fun/binomial_coefficient_log.hpp>
12 #include <stan/math/prim/scal/fun/lbeta.hpp>
13 #include <stan/math/prim/scal/fun/digamma.hpp>
14 #include <stan/math/prim/scal/fun/lgamma.hpp>
15 #include <stan/math/prim/scal/fun/value_of.hpp>
16 #include <stan/math/prim/scal/meta/contains_nonconstant_struct.hpp>
17 #include <stan/math/prim/scal/meta/include_summand.hpp>
18 #include <stan/math/prim/scal/prob/beta_rng.hpp>
19 #include <stan/math/prim/scal/fun/F32.hpp>
20 #include <stan/math/prim/scal/fun/grad_F32.hpp>
21 #include <cmath>
22
23 namespace stan {
24 namespace math {
25
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_log(const T_n& n, const T_N& N, const T_size1& alpha,
30 const T_size2& beta) {
31 static const char* function("beta_binomial_cdf_log");
32 typedef typename stan::partials_return_type<T_n, T_N, T_size1,
33 T_size2>::type
34 T_partials_return;
35
36 if (!(stan::length(n) && stan::length(N) && stan::length(alpha)
37 && stan::length(beta)))
38 return 0.0;
39
40 T_partials_return P(0.0);
41
42 check_nonnegative(function, "Population size parameter", N);
43 check_positive_finite(function,
44 "First prior sample size parameter", alpha);
45 check_positive_finite(function,
46 "Second prior sample size parameter", beta);
47 check_consistent_sizes(function,
48 "Successes variable", n,
49 "Population size parameter", N,
50 "First prior sample size parameter", alpha,
51 "Second prior sample size parameter", beta);
52
53 VectorView<const T_n> n_vec(n);
54 VectorView<const T_N> N_vec(N);
55 VectorView<const T_size1> alpha_vec(alpha);
56 VectorView<const T_size2> beta_vec(beta);
57 size_t size = max_size(n, N, alpha, beta);
58
59 using std::exp;
60 using std::log;
61 using std::exp;
62
63 OperandsAndPartials<T_size1, T_size2>
64 operands_and_partials(alpha, beta);
65
66 // Explicit return for extreme values
67 // The gradients are technically ill-defined, but treated as neg infinity
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(negative_infinity());
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 += log(Pi);
104
105 T_partials_return dF[6];
106 T_partials_return digammaOne = 0;
107 T_partials_return digammaTwo = 0;
108
109 if (contains_nonconstant_struct<T_size1, T_size2>::value) {
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, 1 - nu, (T_partials_return)1);
114 }
115 if (!is_constant_struct<T_size1>::value) {
116 const T_partials_return g
117 = - C * (digamma(mu) - digammaOne + dF[1] / F
118 - digamma(alpha_dbl) + digammaTwo);
119 operands_and_partials.d_x1[i] += g / Pi;
120 }
121 if (!is_constant_struct<T_size2>::value) {
122 const T_partials_return g
123 = - C * (digamma(nu) - digammaOne - dF[4] / F - digamma(beta_dbl)
124 + digammaTwo);
125 operands_and_partials.d_x2[i] += g / Pi;
126 }
127 }
128
129 return operands_and_partials.value(P);
130 }
131
132 }
133 }
134 #endif
stan::math::OperandsAndPartials::d_x2
VectorView< T_return_type, false, true > d_x2
Definition: OperandsAndPartials.hpp:39
lgamma.hpp
stan::math::lgamma
fvar< T > lgamma(const fvar< T > &x)
Definition: lgamma.hpp:14
check_positive_finite.hpp
stan
Definition: log_sum_exp.hpp:8
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:15
digamma.hpp
stan::math::log
fvar< T > log(const fvar< T > &x)
Definition: log.hpp:14
stan::math::OperandsAndPartials::value
T_return_type value(double value)
Returns a T_return_type with the value specified with the partial derivatves.
Definition: OperandsAndPartials.hpp:67
contains_nonconstant_struct.hpp
stan::length
size_t length(const std::vector< T > &x)
Definition: length.hpp:10
stan::math::beta_binomial_cdf_log
return_type< T_size1, T_size2 >::type beta_binomial_cdf_log(const T_n &n, const T_N &N, const T_size1 &alpha, const T_size2 &beta)
Definition: beta_binomial_cdf_log.hpp:29
binomial_coefficient_log.hpp
is_constant_struct.hpp
F32.hpp
include_summand.hpp
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:13
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
This class builds partial derivatives with respect to a set of operands.
Definition: OperandsAndPartials.hpp:37
stan::max_size
size_t max_size(const T1 &x1, const T2 &x2)
Definition: max_size.hpp:9
partials_return_type.hpp
OperandsAndPartials.hpp
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:10
constants.hpp
stan::math::size
int size(const std::vector< T > &x)
Return the size of the specified standard vector.
Definition: size.hpp:17
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::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:64
stan::math::F32
T F32(T a, T b, T c, T d, T e, T z, T precision=1e-6)
Definition: F32.hpp:10
value_of.hpp
stan::VectorView
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
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::OperandsAndPartials::d_x1
VectorView< T_return_type, false, true > d_x1
Definition: OperandsAndPartials.hpp:38
stan::math::negative_infinity
double negative_infinity()
Return negative infinity.
Definition: constants.hpp:130
stan::math::digamma
fvar< T > digamma(const fvar< T > &x)
Definition: digamma.hpp:15

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