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beta_binomial_ccdf_log.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_BETA_BINOMIAL_CCDF_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_BETA_BINOMIAL_CCDF_LOG_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/binomial_coefficient_log.hpp>
10 #include <stan/math/prim/scal/fun/lbeta.hpp>
11 #include <stan/math/prim/scal/fun/digamma.hpp>
12 #include <stan/math/prim/scal/fun/lgamma.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 template <typename T_n, typename T_N,
26 typename T_size1, typename T_size2>
27 typename return_type<T_size1, T_size2>::type
28 beta_binomial_ccdf_log(const T_n& n, const T_N& N, const T_size1& alpha,
29 const T_size2& beta) {
30 static const char* function("stan::math::beta_binomial_ccdf_log");
31 typedef typename stan::partials_return_type<T_n, T_N, T_size1,
32 T_size2>::type
33 T_partials_return;
34
35 using stan::math::check_positive_finite;
36 using stan::math::check_nonnegative;
37 using stan::math::value_of;
38 using stan::math::check_consistent_sizes;
39 using stan::math::include_summand;
40
41 // Ensure non-zero argument lengths
42 if (!(stan::length(n) && stan::length(N) && stan::length(alpha)
43 && stan::length(beta)))
44 return 0.0;
45
46 T_partials_return P(0.0);
47
48 // Validate arguments
49 check_nonnegative(function, "Population size parameter", N);
50 check_positive_finite(function,
51 "First prior sample size parameter", alpha);
52 check_positive_finite(function,
53 "Second prior sample size parameter", beta);
54 check_consistent_sizes(function,
55 "Successes variable", n,
56 "Population size parameter", N,
57 "First prior sample size parameter", alpha,
58 "Second prior sample size parameter", beta);
59
60 // Wrap arguments in vector views
61 VectorView<const T_n> n_vec(n);
62 VectorView<const T_N> N_vec(N);
63 VectorView<const T_size1> alpha_vec(alpha);
64 VectorView<const T_size2> beta_vec(beta);
65 size_t size = max_size(n, N, alpha, beta);
66
67 // Compute vectorized cdf_log and gradient
68 using stan::math::lgamma;
69 using stan::math::lbeta;
70 using stan::math::digamma;
71 using std::exp;
72 using std::log;
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 neg infinity
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 return operands_and_partials.to_var(stan::math::negative_infinity(),
90 alpha, beta);
91 }
92
93 const T_partials_return n_dbl = value_of(n_vec[i]);
94 const T_partials_return N_dbl = value_of(N_vec[i]);
95 const T_partials_return alpha_dbl = value_of(alpha_vec[i]);
96 const T_partials_return beta_dbl = value_of(beta_vec[i]);
97
98 const T_partials_return mu = alpha_dbl + n_dbl + 1;
99 const T_partials_return nu = beta_dbl + N_dbl - n_dbl - 1;
100
101 const T_partials_return F = stan::math::F32((T_partials_return)1, mu,
102 -N_dbl + n_dbl + 1,
103 n_dbl + 2, 1 - nu,
104 (T_partials_return)1);
105
106 T_partials_return C = lgamma(nu) - lgamma(N_dbl - n_dbl);
107 C += lgamma(mu) - lgamma(n_dbl + 2);
108 C += lgamma(N_dbl + 2) - lgamma(N_dbl + alpha_dbl + beta_dbl);
109 C = exp(C);
110
111 C *= F / exp(lbeta(alpha_dbl, beta_dbl));
112 C /= N_dbl + 1;
113
114 const T_partials_return Pi = C;
115
116 P += log(Pi);
117
118 T_partials_return dF[6];
119 T_partials_return digammaOne = 0;
120 T_partials_return digammaTwo = 0;
121
122 if (contains_nonconstant_struct<T_size1, T_size2>::value) {
123 digammaOne = digamma(mu + nu);
124 digammaTwo = digamma(alpha_dbl + beta_dbl);
125 stan::math::grad_F32(dF, (T_partials_return)1, mu, -N_dbl + n_dbl + 1,
126 n_dbl + 2, 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] -= g / Pi;
133 }
134 if (!is_constant_struct<T_size2>::value) {
135 const T_partials_return g
136 = - C * (digamma(nu) - digammaOne - dF[4] / F - digamma(beta_dbl)
137 + digammaTwo);
138 operands_and_partials.d_x2[i] -= g / Pi;
139 }
140 }
141
142 return operands_and_partials.to_var(P, alpha, beta);
143 }
144
145 }
146 }
147 #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
stan::math::log
fvar< T > log(const fvar< T > &x)
Definition: log.hpp:15
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::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::beta_binomial_ccdf_log
return_type< T_size1, T_size2 >::type beta_binomial_ccdf_log(const T_n &n, const T_N &N, const T_size1 &alpha, const T_size2 &beta)
Definition: beta_binomial_ccdf_log.hpp:28
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::negative_infinity
double negative_infinity()
Return negative infinity.
Definition: constants.hpp:132
stan::math::digamma
fvar< T > digamma(const fvar< T > &x)
Definition: digamma.hpp:16

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