Stan Math Library  2.15.0
reverse mode automatic differentiation
neg_binomial_2_lpmf.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_NEG_BINOMIAL_2_LPMF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_NEG_BINOMIAL_2_LPMF_HPP
3 
24 #include <boost/math/special_functions/digamma.hpp>
25 #include <boost/random/negative_binomial_distribution.hpp>
26 #include <boost/random/variate_generator.hpp>
27 #include <cmath>
28 
29 namespace stan {
30  namespace math {
31 
32  // NegBinomial(n|mu, phi) [mu >= 0; phi > 0; n >= 0]
33  template <bool propto,
34  typename T_n,
35  typename T_location, typename T_precision>
37  neg_binomial_2_lpmf(const T_n& n,
38  const T_location& mu,
39  const T_precision& phi) {
40  typedef typename stan::partials_return_type<T_n, T_location,
41  T_precision>::type
42  T_partials_return;
43 
44  static const char* function("neg_binomial_2_lpmf");
45 
46  if (!(stan::length(n)
47  && stan::length(mu)
48  && stan::length(phi)))
49  return 0.0;
50 
51  T_partials_return logp(0.0);
52  check_nonnegative(function, "Failures variable", n);
53  check_positive_finite(function, "Location parameter", mu);
54  check_positive_finite(function, "Precision parameter", phi);
55  check_consistent_sizes(function,
56  "Failures variable", n,
57  "Location parameter", mu,
58  "Precision parameter", phi);
59 
61  return 0.0;
62 
63  using std::log;
64  using std::log;
65 
69  size_t size = max_size(n, mu, phi);
70 
72  operands_and_partials(mu, phi);
73 
74  size_t len_ep = max_size(mu, phi);
75  size_t len_np = max_size(n, phi);
76 
78  for (size_t i = 0, size = length(mu); i < size; ++i)
79  mu__[i] = value_of(mu_vec[i]);
80 
82  for (size_t i = 0, size = length(phi); i < size; ++i)
83  phi__[i] = value_of(phi_vec[i]);
84 
86  for (size_t i = 0, size = length(phi); i < size; ++i)
87  log_phi[i] = log(phi__[i]);
88 
90  log_mu_plus_phi(len_ep);
91  for (size_t i = 0; i < len_ep; ++i)
92  log_mu_plus_phi[i] = log(mu__[i] + phi__[i]);
93 
95  n_plus_phi(len_np);
96  for (size_t i = 0; i < len_np; ++i)
97  n_plus_phi[i] = n_vec[i] + phi__[i];
98 
99  for (size_t i = 0; i < size; i++) {
101  logp -= lgamma(n_vec[i] + 1.0);
103  logp += multiply_log(phi__[i], phi__[i]) - lgamma(phi__[i]);
105  logp -= (n_plus_phi[i])*log_mu_plus_phi[i];
107  logp += multiply_log(n_vec[i], mu__[i]);
109  logp += lgamma(n_plus_phi[i]);
110 
111  // if phi is large we probably overflow, defer to Poisson:
112  if (phi__[i] > 1e5) {
113  logp = poisson_lpmf(n_vec[i], mu__[i]);
114  }
115 
117  operands_and_partials.d_x1[i]
118  += n_vec[i]/mu__[i]
119  - (n_vec[i] + phi__[i])
120  / (mu__[i] + phi__[i]);
122  operands_and_partials.d_x2[i]
123  += 1.0 - n_plus_phi[i]/(mu__[i] + phi__[i])
124  + log_phi[i] - log_mu_plus_phi[i] - digamma(phi__[i])
125  + digamma(n_plus_phi[i]);
126  }
127  return operands_and_partials.value(logp);
128  }
129 
130  template <typename T_n,
131  typename T_location, typename T_precision>
132  inline
134  neg_binomial_2_lpmf(const T_n& n,
135  const T_location& mu,
136  const T_precision& phi) {
137  return neg_binomial_2_lpmf<false>(n, mu, phi);
138  }
139 
140  }
141 }
142 #endif
VectorView< T_return_type, false, true > d_x2
fvar< T > lgamma(const fvar< T > &x)
Return the natural logarithm of the gamma function applied to the specified argument.
Definition: lgamma.hpp:20
T value_of(const fvar< T > &v)
Return the value of the specified variable.
Definition: value_of.hpp:16
fvar< T > log(const fvar< T > &x)
Definition: log.hpp:14
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
Template metaprogram to calculate whether a summand needs to be included in a proportional (log) prob...
return_type< T_location, T_precision >::type neg_binomial_2_lpmf(const T_n &n, const T_location &mu, const T_precision &phi)
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
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
fvar< T > multiply_log(const fvar< T > &x1, const fvar< T > &x2)
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.
return_type< T_rate >::type poisson_lpmf(const T_n &n, const T_rate &lambda)
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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