Stan Math Library  2.20.0
reverse mode automatic differentiation
beta_binomial_lpmf.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_BETA_BINOMIAL_LPMF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_BETA_BINOMIAL_LPMF_HPP
3 
17 
18 namespace stan {
19 namespace math {
20 
38 template <bool propto, typename T_n, typename T_N, typename T_size1,
39  typename T_size2>
41  const T_n& n, const T_N& N, const T_size1& alpha, const T_size2& beta) {
42  static const char* function = "beta_binomial_lpmf";
44  T_partials_return;
45 
46  if (size_zero(n, N, alpha, beta))
47  return 0.0;
48 
49  T_partials_return logp(0.0);
50  check_nonnegative(function, "Population size parameter", N);
51  check_positive_finite(function, "First prior sample size parameter", alpha);
52  check_positive_finite(function, "Second prior sample size parameter", beta);
53  check_consistent_sizes(function, "Successes variable", n,
54  "Population size parameter", N,
55  "First prior sample size parameter", alpha,
56  "Second prior sample size parameter", beta);
57 
59  return 0.0;
60 
61  operands_and_partials<T_size1, T_size2> ops_partials(alpha, beta);
62 
63  scalar_seq_view<T_n> n_vec(n);
64  scalar_seq_view<T_N> N_vec(N);
65  scalar_seq_view<T_size1> alpha_vec(alpha);
66  scalar_seq_view<T_size2> beta_vec(beta);
67  size_t size = max_size(n, N, alpha, beta);
68 
69  for (size_t i = 0; i < size; i++) {
70  if (n_vec[i] < 0 || n_vec[i] > N_vec[i])
71  return ops_partials.build(LOG_ZERO);
72  }
73 
74  VectorBuilder<include_summand<propto>::value, T_partials_return, T_n, T_N>
75  normalizing_constant(max_size(N, n));
76  for (size_t i = 0; i < max_size(N, n); i++)
78  normalizing_constant[i] = binomial_coefficient_log(N_vec[i], n_vec[i]);
79 
81  T_partials_return, T_n, T_N, T_size1, T_size2>
82  lbeta_numerator(size);
83  for (size_t i = 0; i < size; i++)
85  lbeta_numerator[i] = lbeta(n_vec[i] + value_of(alpha_vec[i]),
86  N_vec[i] - n_vec[i] + value_of(beta_vec[i]));
87 
89  T_partials_return, T_size1, T_size2>
90  lbeta_denominator(max_size(alpha, beta));
91  for (size_t i = 0; i < max_size(alpha, beta); i++)
93  lbeta_denominator[i]
94  = lbeta(value_of(alpha_vec[i]), value_of(beta_vec[i]));
95 
96  VectorBuilder<!is_constant_all<T_size1>::value, T_partials_return, T_n,
97  T_size1>
98  digamma_n_plus_alpha(max_size(n, alpha));
99  for (size_t i = 0; i < max_size(n, alpha); i++)
101  digamma_n_plus_alpha[i] = digamma(n_vec[i] + value_of(alpha_vec[i]));
102 
104  T_N, T_size1, T_size2>
105  digamma_N_plus_alpha_plus_beta(max_size(N, alpha, beta));
106  for (size_t i = 0; i < max_size(N, alpha, beta); i++)
108  digamma_N_plus_alpha_plus_beta[i]
109  = digamma(N_vec[i] + value_of(alpha_vec[i]) + value_of(beta_vec[i]));
110 
112  T_size1, T_size2>
113  digamma_alpha_plus_beta(max_size(alpha, beta));
114  for (size_t i = 0; i < max_size(alpha, beta); i++)
116  digamma_alpha_plus_beta[i]
117  = digamma(value_of(alpha_vec[i]) + value_of(beta_vec[i]));
118 
119  VectorBuilder<!is_constant_all<T_size1>::value, T_partials_return, T_size1>
120  digamma_alpha(length(alpha));
121  for (size_t i = 0; i < length(alpha); i++)
123  digamma_alpha[i] = digamma(value_of(alpha_vec[i]));
124 
125  VectorBuilder<!is_constant_all<T_size2>::value, T_partials_return, T_size2>
126  digamma_beta(length(beta));
127  for (size_t i = 0; i < length(beta); i++)
129  digamma_beta[i] = digamma(value_of(beta_vec[i]));
130 
131  for (size_t i = 0; i < size; i++) {
133  logp += normalizing_constant[i];
135  logp += lbeta_numerator[i] - lbeta_denominator[i];
136 
138  ops_partials.edge1_.partials_[i]
139  += digamma_n_plus_alpha[i] - digamma_N_plus_alpha_plus_beta[i]
140  + digamma_alpha_plus_beta[i] - digamma_alpha[i];
142  ops_partials.edge2_.partials_[i]
143  += digamma(value_of(N_vec[i] - n_vec[i] + beta_vec[i]))
144  - digamma_N_plus_alpha_plus_beta[i] + digamma_alpha_plus_beta[i]
145  - digamma_beta[i];
146  }
147  return ops_partials.build(logp);
148 }
149 
150 template <typename T_n, typename T_N, typename T_size1, typename T_size2>
152  const T_n& n, const T_N& N, const T_size1& alpha, const T_size2& beta) {
153  return beta_binomial_lpmf<false>(n, N, alpha, beta);
154 }
155 
156 } // namespace math
157 } // namespace stan
158 #endif
boost::math::tools::promote_args< double, typename partials_type< typename scalar_type< T >::type >::type, typename partials_return_type< T_pack... >::type >::type type
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:17
fvar< T > lbeta(const fvar< T > &x1, const fvar< T > &x2)
Definition: lbeta.hpp:14
Extends std::true_type when instantiated with zero or more template parameters, all of which extend t...
Definition: conjunction.hpp:14
scalar_seq_view provides a uniform sequence-like wrapper around either a scalar or a sequence of scal...
This template builds partial derivatives with respect to a set of operands.
size_t length(const std::vector< T > &x)
Returns the length of the provided std::vector.
Definition: length.hpp:16
bool size_zero(T &x)
Returns 1 if input is of length 0, returns 0 otherwise.
Definition: size_zero.hpp:18
const double LOG_ZERO
Definition: constants.hpp:150
Template metaprogram to calculate whether a summand needs to be included in a proportional (log) prob...
void check_nonnegative(const char *function, const char *name, const T_y &y)
Check if y is non-negative.
return_type< T_size1, T_size2 >::type beta_binomial_lpmf(const T_n &n, const T_N &N, const T_size1 &alpha, const T_size2 &beta)
Returns the log PMF of the Beta-Binomial distribution with given population size, prior success...
fvar< T > beta(const fvar< T > &x1, const fvar< T > &x2)
Return fvar with the beta function applied to the specified arguments and its gradient.
Definition: beta.hpp:51
void check_positive_finite(const char *function, const char *name, const T_y &y)
Check if y is positive and finite.
boost::math::tools::promote_args< double, typename scalar_type< T >::type, typename return_type< Types_pack... >::type >::type type
Definition: return_type.hpp:36
size_t max_size(const T1 &x1, const T2 &x2)
Definition: max_size.hpp:9
T_return_type build(double value)
Build the node to be stored on the autodiff graph.
VectorBuilder allocates type T1 values to be used as intermediate values.
internal::ops_partials_edge< double, Op2 > edge2_
int size(const std::vector< T > &x)
Return the size of the specified standard vector.
Definition: size.hpp:17
void check_consistent_sizes(const char *function, const char *name1, const T1 &x1, const char *name2, const T2 &x2)
Check if the dimension of x1 is consistent with x2.
internal::ops_partials_edge< double, Op1 > edge1_
fvar< T > digamma(const fvar< T > &x)
Return the derivative of the log gamma function at the specified argument.
Definition: digamma.hpp:23

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