Stan Math Library  2.15.0
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 
23 
24 namespace stan {
25  namespace math {
26 
44  template <bool propto,
45  typename T_n, typename T_N,
46  typename T_size1, typename T_size2>
48  beta_binomial_lpmf(const T_n& n,
49  const T_N& N,
50  const T_size1& alpha,
51  const T_size2& beta) {
52  static const char* function("beta_binomial_lpmf");
54  T_partials_return;
55 
56  if (!(stan::length(n)
57  && stan::length(N)
58  && stan::length(alpha)
59  && stan::length(beta)))
60  return 0.0;
61 
62  T_partials_return logp(0.0);
63  check_nonnegative(function, "Population size parameter", N);
64  check_positive_finite(function,
65  "First prior sample size parameter", alpha);
66  check_positive_finite(function,
67  "Second prior sample size parameter", beta);
68  check_consistent_sizes(function,
69  "Successes variable", n,
70  "Population size parameter", N,
71  "First prior sample size parameter", alpha,
72  "Second prior sample size parameter", beta);
73 
75  return 0.0;
76 
78  operands_and_partials(alpha, beta);
79 
82  scalar_seq_view<const T_size1> alpha_vec(alpha);
83  scalar_seq_view<const T_size2> beta_vec(beta);
84  size_t size = max_size(n, N, alpha, beta);
85 
86  for (size_t i = 0; i < size; i++) {
87  if (n_vec[i] < 0 || n_vec[i] > N_vec[i])
88  return operands_and_partials.value(LOG_ZERO);
89  }
90 
92  T_partials_return, T_n, T_N>
93  normalizing_constant(max_size(N, n));
94  for (size_t i = 0; i < max_size(N, n); i++)
96  normalizing_constant[i]
97  = binomial_coefficient_log(N_vec[i], n_vec[i]);
98 
100  T_partials_return, T_n, T_N, T_size1, T_size2>
101  lbeta_numerator(size);
102  for (size_t i = 0; i < size; i++)
104  lbeta_numerator[i] = lbeta(n_vec[i] + value_of(alpha_vec[i]),
105  N_vec[i] - n_vec[i]
106  + value_of(beta_vec[i]));
107 
109  T_partials_return, T_size1, T_size2>
110  lbeta_denominator(max_size(alpha, beta));
111  for (size_t i = 0; i < max_size(alpha, beta); i++)
113  lbeta_denominator[i] = lbeta(value_of(alpha_vec[i]),
114  value_of(beta_vec[i]));
115 
117  T_partials_return, T_n, T_size1>
118  digamma_n_plus_alpha(max_size(n, alpha));
119  for (size_t i = 0; i < max_size(n, alpha); i++)
121  digamma_n_plus_alpha[i]
122  = digamma(n_vec[i] + value_of(alpha_vec[i]));
123 
125  T_partials_return, T_N, T_size1, T_size2>
126  digamma_N_plus_alpha_plus_beta(max_size(N, alpha, beta));
127  for (size_t i = 0; i < max_size(N, alpha, beta); i++)
129  digamma_N_plus_alpha_plus_beta[i]
130  = digamma(N_vec[i] + value_of(alpha_vec[i])
131  + value_of(beta_vec[i]));
132 
134  T_partials_return, T_size1, T_size2>
135  digamma_alpha_plus_beta(max_size(alpha, beta));
136  for (size_t i = 0; i < max_size(alpha, beta); i++)
138  digamma_alpha_plus_beta[i]
139  = digamma(value_of(alpha_vec[i]) + value_of(beta_vec[i]));
140 
142  T_partials_return, T_size1> digamma_alpha(length(alpha));
143  for (size_t i = 0; i < length(alpha); i++)
145  digamma_alpha[i] = digamma(value_of(alpha_vec[i]));
146 
148  T_partials_return, T_size2>
149  digamma_beta(length(beta));
150  for (size_t i = 0; i < length(beta); i++)
152  digamma_beta[i] = digamma(value_of(beta_vec[i]));
153 
154  for (size_t i = 0; i < size; i++) {
156  logp += normalizing_constant[i];
158  logp += lbeta_numerator[i] - lbeta_denominator[i];
159 
161  operands_and_partials.d_x1[i]
162  += digamma_n_plus_alpha[i]
163  - digamma_N_plus_alpha_plus_beta[i]
164  + digamma_alpha_plus_beta[i]
165  - digamma_alpha[i];
167  operands_and_partials.d_x2[i]
168  += digamma(value_of(N_vec[i]-n_vec[i]+beta_vec[i]))
169  - digamma_N_plus_alpha_plus_beta[i]
170  + digamma_alpha_plus_beta[i]
171  - digamma_beta[i];
172  }
173  return operands_and_partials.value(logp);
174  }
175 
176  template <typename T_n,
177  typename T_N,
178  typename T_size1,
179  typename T_size2>
181  beta_binomial_lpmf(const T_n& n, const T_N& N,
182  const T_size1& alpha, const T_size2& beta) {
183  return beta_binomial_lpmf<false>(n, N, alpha, beta);
184  }
185 
186  }
187 }
188 #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:15
T_return_type value(double value)
Returns a T_return_type with the value specified with the partial derivatves.
scalar_seq_view provides a uniform sequence-like wrapper around either a scalar or a sequence of scal...
size_t length(const std::vector< T > &x)
Definition: length.hpp:10
const double LOG_ZERO
Definition: constants.hpp:172
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.
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
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...
Metaprogram to determine if a type has a base scalar type that can be assigned to type double...
void check_positive_finite(const char *function, const char *name, const T_y &y)
Check if y is positive and finite.
This class builds partial derivatives with respect to a set of operands.
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
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.
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
VectorView< T_return_type, false, true > d_x1
fvar< T > digamma(const fvar< T > &x)
Return the derivative of the log gamma function at the specified argument.
Definition: digamma.hpp:22

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