Stan Math Library  2.15.0
reverse mode automatic differentiation
wiener_lpdf.hpp
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29 
30 #ifndef STAN_MATH_PRIM_MAT_PROB_WIENER_LPDF_HPP
31 #define STAN_MATH_PRIM_MAT_PROB_WIENER_LPDF_HPP
32 
44 #include <boost/math/distributions.hpp>
45 #include <algorithm>
46 #include <cmath>
47 #include <string>
48 
49 namespace stan {
50  namespace math {
51 
70  template <bool propto,
71  typename T_y, typename T_alpha, typename T_tau,
72  typename T_beta, typename T_delta>
74  wiener_lpdf(const T_y& y, const T_alpha& alpha, const T_tau& tau,
75  const T_beta& beta, const T_delta& delta) {
76  static const char* function("wiener_lpdf(%1%)");
77 
78  using std::log;
79  using std::exp;
80  using std::pow;
81 
82  static const double WIENER_ERR = 0.000001;
83  static const double PI_TIMES_WIENER_ERR = pi() * WIENER_ERR;
84  static const double LOG_PI_LOG_WIENER_ERR =
85  LOG_PI + log(WIENER_ERR);
86  static const double
87  TWO_TIMES_SQRT_2_TIMES_SQRT_PI_TIMES_WIENER_ERR =
88  2.0 * SQRT_2_TIMES_SQRT_PI * WIENER_ERR;
89  static const double LOG_TWO_OVER_TWO_PLUS_LOG_SQRT_PI =
90  LOG_TWO / 2 + LOG_SQRT_PI;
91  static const double SQUARE_PI_OVER_TWO = square(pi()) * 0.5;
92  static const double TWO_TIMES_LOG_SQRT_PI = 2.0 * LOG_SQRT_PI;
93 
94  if (!(stan::length(y)
95  && stan::length(alpha)
96  && stan::length(beta)
97  && stan::length(tau)
98  && stan::length(delta)))
99  return 0.0;
100 
101  typedef typename return_type<T_y, T_alpha, T_tau,
102  T_beta, T_delta>::type T_return_type;
103  T_return_type lp(0.0);
104 
105  check_not_nan(function, "Random variable", y);
106  check_not_nan(function, "Boundary separation", alpha);
107  check_not_nan(function, "A-priori bias", beta);
108  check_not_nan(function, "Nondecision time", tau);
109  check_not_nan(function, "Drift rate", delta);
110  check_finite(function, "Boundary separation", alpha);
111  check_finite(function, "A-priori bias", beta);
112  check_finite(function, "Nondecision time", tau);
113  check_finite(function, "Drift rate", delta);
114  check_positive(function, "Random variable", y);
115  check_positive(function, "Boundary separation", alpha);
116  check_positive(function, "Nondecision time", tau);
117  check_bounded(function, "A-priori bias", beta , 0, 1);
118  check_consistent_sizes(function, "Random variable", y,
119  "Boundary separation", alpha,
120  "A-priori bias", beta,
121  "Nondecision time", tau, "Drift rate", delta);
122 
123  size_t N = std::max(max_size(y, alpha, beta), max_size(tau, delta));
124  if (!N) return 0.0;
125 
127  scalar_seq_view<const T_alpha> alpha_vec(alpha);
128  scalar_seq_view<const T_beta> beta_vec(beta);
129  scalar_seq_view<const T_tau> tau_vec(tau);
130  scalar_seq_view<const T_delta> delta_vec(delta);
131 
132  size_t N_y_tau = max_size(y, tau);
133  for (size_t i = 0; i < N_y_tau; ++i) {
134  if (y_vec[i] <= tau_vec[i]) {
135  std::stringstream msg;
136  msg << ", but must be greater than nondecision time = " << tau_vec[i];
137  std::string msg_str(msg.str());
138  domain_error(function, "Random variable", y_vec[i], " = ",
139  msg_str.c_str());
140  }
141  }
142 
144  return 0;
145 
146  for (size_t i = 0; i < N; i++) {
147  typename scalar_type<T_beta>::type one_minus_beta = 1.0 - beta_vec[i];
148  typename scalar_type<T_alpha>::type alpha2 = square(alpha_vec[i]);
149  T_return_type x = (y_vec[i] - tau_vec[i]) / alpha2;
150  T_return_type kl, ks, tmp = 0;
151  T_return_type k, K;
152  T_return_type sqrt_x = sqrt(x);
153  T_return_type log_x = log(x);
154  T_return_type one_over_pi_times_sqrt_x = 1.0 / pi() * sqrt_x;
155 
156  // calculate number of terms needed for large t:
157  // if error threshold is set low enough
158  if (PI_TIMES_WIENER_ERR * x < 1) {
159  // compute bound
160  kl = sqrt(-2.0 * SQRT_PI * (LOG_PI_LOG_WIENER_ERR + log_x)) / sqrt_x;
161  // ensure boundary conditions met
162  kl = (kl > one_over_pi_times_sqrt_x) ? kl : one_over_pi_times_sqrt_x;
163  } else {
164  kl = one_over_pi_times_sqrt_x; // set to boundary condition
165  }
166  // calculate number of terms needed for small t:
167  // if error threshold is set low enough
168  T_return_type tmp_expr0
169  = TWO_TIMES_SQRT_2_TIMES_SQRT_PI_TIMES_WIENER_ERR * sqrt_x;
170  if (tmp_expr0 < 1) {
171  // compute bound
172  ks = 2.0 + sqrt_x * sqrt(-2 * log(tmp_expr0));
173  // ensure boundary conditions are met
174  T_return_type sqrt_x_plus_one = sqrt_x + 1.0;
175  ks = (ks > sqrt_x_plus_one) ? ks : sqrt_x_plus_one;
176  } else { // if error threshold was set too high
177  ks = 2.0; // minimal kappa for that case
178  }
179  if (ks < kl) { // small t
180  K = ceil(ks); // round to smallest integer meeting error
181  T_return_type tmp_expr1 = (K - 1.0) / 2.0;
182  T_return_type tmp_expr2 = ceil(tmp_expr1);
183  for (k = -floor(tmp_expr1); k <= tmp_expr2; k++)
184  tmp += (one_minus_beta + 2.0 * k) *
185  exp(-(square(one_minus_beta + 2.0 * k)) * 0.5 / x);
186  tmp = log(tmp) - LOG_TWO_OVER_TWO_PLUS_LOG_SQRT_PI - 1.5 * log_x;
187  } else { // if large t is better...
188  K = ceil(kl); // round to smallest integer meeting error
189  for (k = 1; k <= K; ++k)
190  tmp += k * exp(-(square(k)) * (SQUARE_PI_OVER_TWO * x))
191  * sin(k * pi() * one_minus_beta);
192  tmp = log(tmp) + TWO_TIMES_LOG_SQRT_PI;
193  }
194 
195  // convert to f(t|v,a,w) and return result
196  lp += delta_vec[i] * alpha_vec[i] * one_minus_beta
197  - square(delta_vec[i]) * x * alpha2 / 2.0
198  - log(alpha2) + tmp;
199  }
200  return lp;
201  }
202 
203  template <typename T_y, typename T_alpha, typename T_tau,
204  typename T_beta, typename T_delta>
205  inline
207  wiener_lpdf(const T_y& y, const T_alpha& alpha, const T_tau& tau,
208  const T_beta& beta, const T_delta& delta) {
209  return wiener_lpdf<false>(y, alpha, tau, beta, delta);
210  }
211 
212  }
213 }
214 #endif
void check_finite(const char *function, const char *name, const T_y &y)
Check if y is finite.
fvar< T > sqrt(const fvar< T > &x)
Definition: sqrt.hpp:14
void check_bounded(const char *function, const char *name, const T_y &y, const T_low &low, const T_high &high)
Check if the value is between the low and high values, inclusively.
const double LOG_PI
Definition: constants.hpp:167
fvar< T > log(const fvar< T > &x)
Definition: log.hpp:14
scalar_seq_view provides a uniform sequence-like wrapper around either a scalar or a sequence of scal...
const double LOG_SQRT_PI
Definition: constants.hpp:170
size_t length(const std::vector< T > &x)
Definition: length.hpp:10
Metaprogram to calculate the base scalar return type resulting from promoting all the scalar types of...
Definition: return_type.hpp:19
scalar_type_helper< is_vector< T >::value, T >::type type
Definition: scalar_type.hpp:34
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
fvar< T > square(const fvar< T > &x)
Definition: square.hpp:14
const double LOG_TWO
Definition: constants.hpp:174
const double SQRT_2_TIMES_SQRT_PI
Definition: constants.hpp:156
fvar< T > sin(const fvar< T > &x)
Definition: sin.hpp:12
fvar< T > exp(const fvar< T > &x)
Definition: exp.hpp:10
void check_not_nan(const char *function, const char *name, const T_y &y)
Check if y is not NaN.
return_type< T_y, T_alpha, T_tau, T_beta, T_delta >::type wiener_lpdf(const T_y &y, const T_alpha &alpha, const T_tau &tau, const T_beta &beta, const T_delta &delta)
The log of the first passage time density function for a (Wiener) drift diffusion model for the given...
Definition: wiener_lpdf.hpp:74
size_t max_size(const T1 &x1, const T2 &x2)
Definition: max_size.hpp:9
void domain_error(const char *function, const char *name, const T &y, const char *msg1, const char *msg2)
Throw a domain error with a consistently formatted message.
int max(const std::vector< int > &x)
Returns the maximum coefficient in the specified column vector.
Definition: max.hpp:22
fvar< T > floor(const fvar< T > &x)
Definition: floor.hpp:11
void check_positive(const char *function, const char *name, const T_y &y)
Check if y is positive.
double pi()
Return the value of pi.
Definition: constants.hpp:85
fvar< T > pow(const fvar< T > &x1, const fvar< T > &x2)
Definition: pow.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.
const double SQRT_PI
Definition: constants.hpp:154
fvar< T > ceil(const fvar< T > &x)
Definition: ceil.hpp:11

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