Stan Math Library  2.10.0
reverse mode automatic differentiation
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 
22 
23 namespace stan {
24 
25  namespace math {
26 
27  // BetaBinomial(n|alpha, beta) [alpha > 0; beta > 0; n >= 0]
28  template <bool propto,
29  typename T_n, typename T_N,
30  typename T_size1, typename T_size2>
31  typename return_type<T_size1, T_size2>::type
32  beta_binomial_log(const T_n& n,
33  const T_N& N,
34  const T_size1& alpha,
35  const T_size2& beta) {
36  static const char* function("stan::math::beta_binomial_log");
38  T_partials_return;
39 
45 
46  // check if any vectors are zero length
47  if (!(stan::length(n)
48  && stan::length(N)
49  && stan::length(alpha)
50  && stan::length(beta)))
51  return 0.0;
52 
53  T_partials_return logp(0.0);
54  check_nonnegative(function, "Population size parameter", N);
55  check_positive_finite(function,
56  "First prior sample size parameter", alpha);
57  check_positive_finite(function,
58  "Second prior sample size parameter", beta);
59  check_consistent_sizes(function,
60  "Successes variable", n,
61  "Population size parameter", N,
62  "First prior sample size parameter", alpha,
63  "Second prior sample size parameter", beta);
64 
65  // check if no variables are involved and prop-to
67  return 0.0;
68 
70  operands_and_partials(alpha, beta);
71 
72  VectorView<const T_n> n_vec(n);
73  VectorView<const T_N> N_vec(N);
74  VectorView<const T_size1> alpha_vec(alpha);
75  VectorView<const T_size2> beta_vec(beta);
76  size_t size = max_size(n, N, alpha, beta);
77 
78  for (size_t i = 0; i < size; i++) {
79  if (n_vec[i] < 0 || n_vec[i] > N_vec[i])
80  return operands_and_partials.value(LOG_ZERO);
81  }
82 
83  using stan::math::lbeta;
85  using stan::math::digamma;
86 
88  T_partials_return, T_n, T_N>
89  normalizing_constant(max_size(N, n));
90  for (size_t i = 0; i < max_size(N, n); i++)
92  normalizing_constant[i]
93  = binomial_coefficient_log(N_vec[i], n_vec[i]);
94 
96  T_partials_return, T_n, T_N, T_size1, T_size2>
97  lbeta_numerator(size);
98  for (size_t i = 0; i < size; i++)
100  lbeta_numerator[i] = lbeta(n_vec[i] + value_of(alpha_vec[i]),
101  N_vec[i] - n_vec[i]
102  + value_of(beta_vec[i]));
103 
105  T_partials_return, T_size1, T_size2>
106  lbeta_denominator(max_size(alpha, beta));
107  for (size_t i = 0; i < max_size(alpha, beta); i++)
109  lbeta_denominator[i] = lbeta(value_of(alpha_vec[i]),
110  value_of(beta_vec[i]));
111 
113  T_partials_return, T_n, T_size1>
114  digamma_n_plus_alpha(max_size(n, alpha));
115  for (size_t i = 0; i < max_size(n, alpha); i++)
117  digamma_n_plus_alpha[i]
118  = digamma(n_vec[i] + value_of(alpha_vec[i]));
119 
121  T_partials_return, T_N, T_size1, T_size2>
122  digamma_N_plus_alpha_plus_beta(max_size(N, alpha, beta));
123  for (size_t i = 0; i < max_size(N, alpha, beta); i++)
125  digamma_N_plus_alpha_plus_beta[i]
126  = digamma(N_vec[i] + value_of(alpha_vec[i])
127  + value_of(beta_vec[i]));
128 
130  T_partials_return, T_size1, T_size2>
131  digamma_alpha_plus_beta(max_size(alpha, beta));
132  for (size_t i = 0; i < max_size(alpha, beta); i++)
134  digamma_alpha_plus_beta[i]
135  = digamma(value_of(alpha_vec[i]) + value_of(beta_vec[i]));
136 
138  T_partials_return, T_size1> digamma_alpha(length(alpha));
139  for (size_t i = 0; i < length(alpha); i++)
141  digamma_alpha[i] = digamma(value_of(alpha_vec[i]));
142 
144  T_partials_return, T_size2>
145  digamma_beta(length(beta));
146  for (size_t i = 0; i < length(beta); i++)
148  digamma_beta[i] = digamma(value_of(beta_vec[i]));
149 
150  for (size_t i = 0; i < size; i++) {
152  logp += normalizing_constant[i];
154  logp += lbeta_numerator[i] - lbeta_denominator[i];
155 
157  operands_and_partials.d_x1[i]
158  += digamma_n_plus_alpha[i]
159  - digamma_N_plus_alpha_plus_beta[i]
160  + digamma_alpha_plus_beta[i]
161  - digamma_alpha[i];
163  operands_and_partials.d_x2[i]
164  += digamma(value_of(N_vec[i]-n_vec[i]+beta_vec[i]))
165  - digamma_N_plus_alpha_plus_beta[i]
166  + digamma_alpha_plus_beta[i]
167  - digamma_beta[i];
168  }
169  return operands_and_partials.value(logp);
170  }
171 
172  template <typename T_n,
173  typename T_N,
174  typename T_size1,
175  typename T_size2>
177  beta_binomial_log(const T_n& n, const T_N& N,
178  const T_size1& alpha, const T_size2& beta) {
179  return beta_binomial_log<false>(n, N, alpha, beta);
180  }
181 
182  }
183 }
184 #endif
VectorView< T_return_type, false, true > d_x2
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
T_return_type value(double value)
Returns a T_return_type with the value specified with the partial derivatves.
size_t length(const std::vector< T > &x)
Definition: length.hpp:10
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
Metaprogram to determine if a type has a base scalar type that can be assigned to type double...
This class builds partial derivatives with respect to a set of operands.
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
VectorBuilder allocates type T1 values to be used as intermediate values.
int size(const std::vector< T > &x)
Return the size of the specified standard vector.
Definition: size.hpp:17
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.
bool check_nonnegative(const char *function, const char *name, const T_y &y)
Return true if y is non-negative.
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
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.
VectorView< T_return_type, false, true > d_x1
fvar< T > digamma(const fvar< T > &x)
Definition: digamma.hpp:16

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