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beta_binomial_log.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_BETA_BINOMIAL_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_BETA_BINOMIAL_LOG_HPP
3 
20 
21 namespace stan {
22 
23  namespace math {
24 
25  // BetaBinomial(n|alpha, beta) [alpha > 0; beta > 0; n >= 0]
26  template <bool propto,
27  typename T_n, typename T_N,
28  typename T_size1, typename T_size2>
29  typename return_type<T_size1, T_size2>::type
30  beta_binomial_log(const T_n& n,
31  const T_N& N,
32  const T_size1& alpha,
33  const T_size2& beta) {
34  static const char* function("stan::math::beta_binomial_log");
36  T_partials_return;
37 
43 
44  // check if any vectors are zero length
45  if (!(stan::length(n)
46  && stan::length(N)
47  && stan::length(alpha)
48  && stan::length(beta)))
49  return 0.0;
50 
51  T_partials_return logp(0.0);
52  check_nonnegative(function, "Population size parameter", N);
53  check_positive_finite(function,
54  "First prior sample size parameter", alpha);
55  check_positive_finite(function,
56  "Second prior sample size parameter", beta);
57  check_consistent_sizes(function,
58  "Successes variable", n,
59  "Population size parameter", N,
60  "First prior sample size parameter", alpha,
61  "Second prior sample size parameter", beta);
62 
63  // check if no variables are involved and prop-to
65  return 0.0;
66 
68  operands_and_partials(alpha, beta);
69 
70  VectorView<const T_n> n_vec(n);
71  VectorView<const T_N> N_vec(N);
72  VectorView<const T_size1> alpha_vec(alpha);
73  VectorView<const T_size2> beta_vec(beta);
74  size_t size = max_size(n, N, alpha, beta);
75 
76  for (size_t i = 0; i < size; i++) {
77  if (n_vec[i] < 0 || n_vec[i] > N_vec[i])
78  return operands_and_partials.to_var(LOG_ZERO, alpha, beta);
79  }
80 
81  using stan::math::lbeta;
83  using stan::math::digamma;
84 
86  T_partials_return, T_n, T_N>
87  normalizing_constant(max_size(N, n));
88  for (size_t i = 0; i < max_size(N, n); i++)
90  normalizing_constant[i]
91  = binomial_coefficient_log(N_vec[i], n_vec[i]);
92 
94  T_partials_return, T_n, T_N, T_size1, T_size2>
95  lbeta_numerator(size);
96  for (size_t i = 0; i < size; i++)
98  lbeta_numerator[i] = lbeta(n_vec[i] + value_of(alpha_vec[i]),
99  N_vec[i] - n_vec[i]
100  + value_of(beta_vec[i]));
101 
103  T_partials_return, T_size1, T_size2>
104  lbeta_denominator(max_size(alpha, beta));
105  for (size_t i = 0; i < max_size(alpha, beta); i++)
107  lbeta_denominator[i] = lbeta(value_of(alpha_vec[i]),
108  value_of(beta_vec[i]));
109 
111  T_partials_return, T_n, T_size1>
112  digamma_n_plus_alpha(max_size(n, alpha));
113  for (size_t i = 0; i < max_size(n, alpha); i++)
115  digamma_n_plus_alpha[i]
116  = digamma(n_vec[i] + value_of(alpha_vec[i]));
117 
119  T_partials_return, T_N, T_size1, T_size2>
120  digamma_N_plus_alpha_plus_beta(max_size(N, alpha, beta));
121  for (size_t i = 0; i < max_size(N, alpha, beta); i++)
123  digamma_N_plus_alpha_plus_beta[i]
124  = digamma(N_vec[i] + value_of(alpha_vec[i])
125  + value_of(beta_vec[i]));
126 
128  T_partials_return, T_size1, T_size2>
129  digamma_alpha_plus_beta(max_size(alpha, beta));
130  for (size_t i = 0; i < max_size(alpha, beta); i++)
132  digamma_alpha_plus_beta[i]
133  = digamma(value_of(alpha_vec[i]) + value_of(beta_vec[i]));
134 
136  T_partials_return, T_size1> digamma_alpha(length(alpha));
137  for (size_t i = 0; i < length(alpha); i++)
139  digamma_alpha[i] = digamma(value_of(alpha_vec[i]));
140 
142  T_partials_return, T_size2>
143  digamma_beta(length(beta));
144  for (size_t i = 0; i < length(beta); i++)
146  digamma_beta[i] = digamma(value_of(beta_vec[i]));
147 
148  for (size_t i = 0; i < size; i++) {
150  logp += normalizing_constant[i];
152  logp += lbeta_numerator[i] - lbeta_denominator[i];
153 
155  operands_and_partials.d_x1[i]
156  += digamma_n_plus_alpha[i]
157  - digamma_N_plus_alpha_plus_beta[i]
158  + digamma_alpha_plus_beta[i]
159  - digamma_alpha[i];
161  operands_and_partials.d_x2[i]
162  += digamma(value_of(N_vec[i]-n_vec[i]+beta_vec[i]))
163  - digamma_N_plus_alpha_plus_beta[i]
164  + digamma_alpha_plus_beta[i]
165  - digamma_beta[i];
166  }
167  return operands_and_partials.to_var(logp, alpha, beta);
168  }
169 
170  template <typename T_n,
171  typename T_N,
172  typename T_size1,
173  typename T_size2>
175  beta_binomial_log(const T_n& n, const T_N& N,
176  const T_size1& alpha, const T_size2& beta) {
177  return beta_binomial_log<false>(n, N, alpha, beta);
178  }
179 
180  }
181 }
182 #endif
fvar< T > binomial_coefficient_log(const fvar< T > &x1, const fvar< T > &x2)
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)
const double LOG_ZERO
Definition: constants.hpp:175
Template metaprogram to calculate whether a summand needs to be included in a proportional (log) prob...
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
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...
A variable implementation that stores operands and derivatives with respect to the variable...
return_type< T_size1, T_size2 >::type beta_binomial_log(const T_n &n, const T_N &N, const T_size1 &alpha, const T_size2 &beta)
size_t max_size(const T1 &x1, const T2 &x2)
Definition: max_size.hpp:9
int size(const std::vector< T > &x)
Definition: size.hpp:11
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.
VectorView is a template metaprogram that takes its argument and allows it to be used like a vector...
Definition: VectorView.hpp:41
boost::math::tools::promote_args< typename partials_type< typename scalar_type< T1 >::type >::type, typename partials_type< typename scalar_type< T2 >::type >::type, typename partials_type< typename scalar_type< T3 >::type >::type, typename partials_type< typename scalar_type< T4 >::type >::type, typename partials_type< typename scalar_type< T5 >::type >::type, typename partials_type< typename scalar_type< T6 >::type >::type >::type type
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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