Stan Math Library  2.20.0
reverse mode automatic differentiation
beta_proportion_lpdf.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_BETA_PROPORTION_LPDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_BETA_PROPORTION_LPDF_HPP
3 
16 #include <cmath>
17 
18 namespace stan {
19 namespace math {
20 
42 template <bool propto, typename T_y, typename T_loc, typename T_prec>
44  const T_y& y, const T_loc& mu, const T_prec& kappa) {
45  static const char* function = "beta_proportion_lpdf";
46 
48  T_partials_return;
49  using std::log;
50  check_positive(function, "Location parameter", mu);
51  check_less_or_equal(function, "Location parameter", mu, 1.0);
52  check_positive_finite(function, "Precision parameter", kappa);
53  check_not_nan(function, "Random variable", y);
54  check_nonnegative(function, "Random variable", y);
55  check_less_or_equal(function, "Random variable", y, 1.0);
56  check_consistent_sizes(function, "Random variable", y, "Location parameter",
57  mu, "Precision parameter", kappa);
58  if (size_zero(y, mu, kappa))
59  return 0;
61  return 0;
62  T_partials_return logp(0);
63 
64  scalar_seq_view<T_y> y_vec(y);
65  scalar_seq_view<T_loc> mu_vec(mu);
66  scalar_seq_view<T_prec> kappa_vec(kappa);
67  size_t N = max_size(y, mu, kappa);
68  size_t N_mukappa = max_size(mu, kappa);
69 
70  for (size_t n = 0; n < N; n++) {
71  const T_partials_return y_dbl = value_of(y_vec[n]);
72  if (y_dbl < 0 || y_dbl > 1)
73  return LOG_ZERO;
74  }
75 
76  operands_and_partials<T_y, T_loc, T_prec> ops_partials(y, mu, kappa);
77 
79  T_partials_return, T_y>
80  log_y(length(y));
82  T_partials_return, T_y>
83  log1m_y(length(y));
84 
85  for (size_t n = 0; n < length(y); n++) {
87  log_y[n] = log(value_of(y_vec[n]));
88  log1m_y[n] = log1m(value_of(y_vec[n]));
89  }
90  }
91 
93  T_partials_return, T_loc, T_prec>
94  lgamma_mukappa(N_mukappa);
96  T_partials_return, T_loc, T_prec>
97  lgamma_kappa_mukappa(N_mukappa);
99  T_loc, T_prec>
100  digamma_mukappa(N_mukappa);
102  T_loc, T_prec>
103  digamma_kappa_mukappa(N_mukappa);
104 
105  for (size_t n = 0; n < N_mukappa; n++) {
106  const T_partials_return mukappa_dbl
107  = value_of(mu_vec[n]) * value_of(kappa_vec[n]);
108  const T_partials_return kappa_mukappa_dbl
109  = value_of(kappa_vec[n]) - mukappa_dbl;
110 
112  lgamma_mukappa[n] = lgamma(mukappa_dbl);
113  lgamma_kappa_mukappa[n] = lgamma(kappa_mukappa_dbl);
114  }
115 
117  digamma_mukappa[n] = digamma(mukappa_dbl);
118  digamma_kappa_mukappa[n] = digamma(kappa_mukappa_dbl);
119  }
120  }
121 
123  T_prec>
124  lgamma_kappa(length(kappa));
125  VectorBuilder<!is_constant_all<T_prec>::value, T_partials_return, T_prec>
126  digamma_kappa(length(kappa));
127 
128  for (size_t n = 0; n < length(kappa); n++) {
130  lgamma_kappa[n] = lgamma(value_of(kappa_vec[n]));
131 
133  digamma_kappa[n] = digamma(value_of(kappa_vec[n]));
134  }
135 
136  for (size_t n = 0; n < N; n++) {
137  const T_partials_return y_dbl = value_of(y_vec[n]);
138  const T_partials_return mu_dbl = value_of(mu_vec[n]);
139  const T_partials_return kappa_dbl = value_of(kappa_vec[n]);
140 
142  logp += lgamma_kappa[n];
144  logp -= lgamma_mukappa[n] + lgamma_kappa_mukappa[n];
146  const T_partials_return mukappa_dbl = mu_dbl * kappa_dbl;
147  logp += (mukappa_dbl - 1) * log_y[n]
148  + (kappa_dbl - mukappa_dbl - 1) * log1m_y[n];
149  }
150 
152  const T_partials_return mukappa_dbl = mu_dbl * kappa_dbl;
153  ops_partials.edge1_.partials_[n]
154  += (mukappa_dbl - 1) / y_dbl
155  + (kappa_dbl - mukappa_dbl - 1) / (y_dbl - 1);
156  }
158  ops_partials.edge2_.partials_[n]
159  += kappa_dbl
160  * (digamma_kappa_mukappa[n] - digamma_mukappa[n] + log_y[n]
161  - log1m_y[n]);
163  ops_partials.edge3_.partials_[n]
164  += digamma_kappa[n] + mu_dbl * (log_y[n] - digamma_mukappa[n])
165  + (1 - mu_dbl) * (log1m_y[n] - digamma_kappa_mukappa[n]);
166  }
167  return ops_partials.build(logp);
168 }
169 
170 template <typename T_y, typename T_loc, typename T_prec>
172  const T_y& y, const T_loc& mu, const T_prec& kappa) {
173  return beta_proportion_lpdf<false>(y, mu, kappa);
174 }
175 
176 } // namespace math
177 } // namespace stan
178 #endif
void check_less_or_equal(const char *function, const char *name, const T_y &y, const T_high &high)
Check if y is less or equal to high.
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 > lgamma(const fvar< T > &x)
Return the natural logarithm of the gamma function applied to the specified argument.
Definition: lgamma.hpp:21
T value_of(const fvar< T > &v)
Return the value of the specified variable.
Definition: value_of.hpp:17
Extends std::true_type when instantiated with zero or more template parameters, all of which extend t...
Definition: conjunction.hpp:14
fvar< T > log(const fvar< T > &x)
Definition: log.hpp:12
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.
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
void check_not_nan(const char *function, const char *name, const T_y &y)
Check if y is not NaN.
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_
void check_positive(const char *function, const char *name, const T_y &y)
Check if y is positive.
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.
fvar< T > log1m(const fvar< T > &x)
Definition: log1m.hpp:12
internal::ops_partials_edge< double, Op3 > edge3_
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
return_type< T_y, T_loc, T_prec >::type beta_proportion_lpdf(const T_y &y, const T_loc &mu, const T_prec &kappa)
The log of the beta density for specified y, location, and precision: beta_proportion_lpdf(y | mu...

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