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beta_binomial.hpp
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1 #ifndef STAN__PROB__DISTRIBUTIONS__UNIVARIATE__DISCRETE__BETA_BINOMIAL_HPP
2 #define STAN__PROB__DISTRIBUTIONS__UNIVARIATE__DISCRETE__BETA_BINOMIAL_HPP
3 
4 #include <stan/prob/distributions/univariate/discrete/binomial.hpp>
5 #include <stan/prob/distributions/univariate/continuous/beta.hpp>
6 
7 #include <stan/agrad/partials_vari.hpp>
8 #include <stan/math/error_handling.hpp>
9 #include <stan/math/constants.hpp>
10 #include <stan/math/functions/lbeta.hpp>
11 #include <stan/math/functions/value_of.hpp>
12 #include <stan/meta/traits.hpp>
13 #include <stan/prob/traits.hpp>
14 #include <stan/prob/constants.hpp>
15 #include <stan/prob/internal_math.hpp>
16 
17 #include <stan/math/functions/binomial_coefficient_log.hpp>
18 
19 namespace stan {
20 
21  namespace prob {
22 
23  // BetaBinomial(n|alpha,beta) [alpha > 0; beta > 0; n >= 0]
24  template <bool propto,
25  typename T_n, typename T_N,
26  typename T_size1, typename T_size2>
27  typename return_type<T_size1,T_size2>::type
28  beta_binomial_log(const T_n& n,
29  const T_N& N,
30  const T_size1& alpha,
31  const T_size2& beta) {
32  static const char* function = "stan::prob::beta_binomial_log(%1%)";
33 
34  using stan::math::check_positive_finite;
35  using stan::math::check_nonnegative;
36  using stan::math::value_of;
37  using stan::math::check_consistent_sizes;
38  using stan::prob::include_summand;
39 
40  // check if any vectors are zero length
41  if (!(stan::length(n)
42  && stan::length(N)
43  && stan::length(alpha)
44  && stan::length(beta)))
45  return 0.0;
46 
47  double logp(0.0);
48  check_nonnegative(function, N, "Population size parameter", &logp);
49  check_positive_finite(function, alpha,
50  "First prior sample size parameter",
51  &logp);
52  check_positive_finite(function, beta,
53  "Second prior sample size parameter",
54  &logp);
55  check_consistent_sizes(function,
56  n,N,alpha,beta,
57  "Successes variable",
58  "Population size parameter",
59  "First prior sample size parameter",
60  "Second prior sample size parameter",
61  &logp);
62 
63  // check if no variables are involved and prop-to
64  if (!include_summand<propto,T_size1,T_size2>::value)
65  return 0.0;
66 
67  VectorView<const T_n> n_vec(n);
68  VectorView<const T_N> N_vec(N);
69  VectorView<const T_size1> alpha_vec(alpha);
70  VectorView<const T_size2> beta_vec(beta);
71  size_t size = max_size(n, N, alpha, beta);
72 
73  for (size_t i = 0; i < size; i++) {
74  if (n_vec[i] < 0 || n_vec[i] > N_vec[i])
75  return LOG_ZERO;
76  }
77 
78  using stan::math::lbeta;
79  using stan::math::binomial_coefficient_log;
80  using boost::math::digamma;
81 
82  DoubleVectorView<include_summand<propto>::value,
83  is_vector<T_n>::value || is_vector<T_N>::value>
84  normalizing_constant(max_size(N,n));
85  for (size_t i = 0; i < max_size(N,n); i++)
86  if (include_summand<propto>::value)
87  normalizing_constant[i]
88  = binomial_coefficient_log(N_vec[i],n_vec[i]);
89 
90  DoubleVectorView<include_summand<propto,T_size1,T_size2>::value,
91  is_vector<T_n>::value || is_vector<T_N>::value
92  || is_vector<T_size1>::value || is_vector<T_size2>::value>
93  lbeta_numerator(size);
94  for (size_t i = 0; i < size; i++)
95  if (include_summand<propto,T_size1,T_size2>::value)
96  lbeta_numerator[i] = lbeta(n_vec[i] + value_of(alpha_vec[i]),
97  N_vec[i] - n_vec[i]
98  + value_of(beta_vec[i]));
99  DoubleVectorView<include_summand<propto,T_size1,T_size2>::value,
100  is_vector<T_size1>::value || is_vector<T_size2>::value>
101  lbeta_denominator(max_size(alpha,beta));
102 for (size_t i = 0; i < max_size(alpha,beta); i++)
103  if (include_summand<propto,T_size1,T_size2>::value)
104  lbeta_denominator[i] = lbeta(value_of(alpha_vec[i]),
105  value_of(beta_vec[i]));
106 
107 DoubleVectorView<!is_constant_struct<T_size1>::value,
108  is_vector<T_n>::value || is_vector<T_size1>::value>
109  digamma_n_plus_alpha(max_size(n,alpha));
110  for (size_t i = 0; i < max_size(n,alpha); i++)
111  if (!is_constant_struct<T_size1>::value)
112  digamma_n_plus_alpha[i]
113  = digamma(n_vec[i] + value_of(alpha_vec[i]));
114 
115  DoubleVectorView<!is_constant_struct<T_size1>::value
116  || !is_constant_struct<T_size2>::value,
117  is_vector<T_N>::value
118  || is_vector<T_size1>::value
119  || is_vector<T_size1>::value>
120  digamma_N_plus_alpha_plus_beta(max_size(N,alpha,beta));
121  for (size_t i = 0; i < max_size(N,alpha,beta); i++)
122  if (!is_constant_struct<T_size1>::value
123  || !is_constant_struct<T_size2>::value)
124  digamma_N_plus_alpha_plus_beta[i]
125  = digamma(N_vec[i] + value_of(alpha_vec[i]) + value_of(beta_vec[i]));
126 
127  DoubleVectorView<!is_constant_struct<T_size1>::value
128  || !is_constant_struct<T_size2>::value,
129  is_vector<T_size1>::value
130  || is_vector<T_size1>::value>
131  digamma_alpha_plus_beta(max_size(alpha,beta));
132  for (size_t i = 0; i < max_size(alpha,beta); i++)
133  if (!is_constant_struct<T_size1>::value
134  || !is_constant_struct<T_size2>::value)
135  digamma_alpha_plus_beta[i]
136  = digamma(value_of(alpha_vec[i]) + value_of(beta_vec[i]));
137 
138  DoubleVectorView<!is_constant_struct<T_size1>::value,
139  is_vector<T_size1>::value>
140  digamma_alpha(length(alpha));
141  for (size_t i = 0; i < length(alpha); i++)
142  if (!is_constant_struct<T_size1>::value)
143  digamma_alpha[i] = digamma(value_of(alpha_vec[i]));
144 
145  DoubleVectorView<!is_constant_struct<T_size2>::value,
146  is_vector<T_size2>::value>
147  digamma_beta(length(beta));
148  for (size_t i = 0; i < length(beta); i++)
149  if (!is_constant_struct<T_size2>::value)
150  digamma_beta[i] = digamma(value_of(beta_vec[i]));
151 
152  agrad::OperandsAndPartials<T_n,T_N,T_size1,T_size2>
153  operands_and_partials(n,N,alpha,beta);
154  for (size_t i = 0; i < size; i++) {
155  if (include_summand<propto>::value)
156  logp += normalizing_constant[i];
157  if (include_summand<propto,T_size1,T_size2>::value)
158  logp += lbeta_numerator[i]
159  - lbeta_denominator[i];
160 
161  if (!is_constant_struct<T_size1>::value)
162  operands_and_partials.d_x3[i]
163  += digamma_n_plus_alpha[i]
164  - digamma_N_plus_alpha_plus_beta[i]
165  + digamma_alpha_plus_beta[i]
166  - digamma_alpha[i];
167  if (!is_constant_struct<T_size2>::value)
168  operands_and_partials.d_x4[i]
169  += digamma(value_of(N_vec[i]-n_vec[i]+beta_vec[i]))
170  - digamma_N_plus_alpha_plus_beta[i]
171  + digamma_alpha_plus_beta[i]
172  - digamma_beta[i];
173  }
174  return operands_and_partials.to_var(logp);
175  }
176 
177  template <typename T_n,
178  typename T_N,
179  typename T_size1,
180  typename T_size2>
181  typename return_type<T_size1,T_size2>::type
182  beta_binomial_log(const T_n& n, const T_N& N,
183  const T_size1& alpha, const T_size2& beta) {
184  return beta_binomial_log<false>(n,N,alpha,beta);
185  }
186 
187  // Beta-Binomial CDF
188  template <typename T_n, typename T_N,
189  typename T_size1, typename T_size2>
190  typename return_type<T_size1,T_size2>::type
191  beta_binomial_cdf(const T_n& n, const T_N& N, const T_size1& alpha,
192  const T_size2& beta) {
193 
194  static const char* function = "stan::prob::beta_binomial_cdf(%1%)";
195 
196  using stan::math::check_positive_finite;
197  using stan::math::check_nonnegative;
198  using stan::math::value_of;
199  using stan::math::check_consistent_sizes;
200  using stan::prob::include_summand;
201 
202  // Ensure non-zero argument lengths
203  if (!(stan::length(n) && stan::length(N) && stan::length(alpha)
204  && stan::length(beta)))
205  return 1.0;
206 
207  double P(1.0);
208 
209  // Validate arguments
210  check_nonnegative(function, N, "Population size parameter", &P);
211  check_positive_finite(function, alpha, "First prior sample size parameter",
212  &P);
213  check_positive_finite(function, beta, "Second prior sample size parameter",
214  &P);
215  check_consistent_sizes(function,
216  n, N, alpha, beta,
217  "Successes variable",
218  "Population size parameter",
219  "First prior sample size parameter",
220  "Second prior sample size parameter",
221  &P);
222 
223  // Wrap arguments in vector views
224  VectorView<const T_n> n_vec(n);
225  VectorView<const T_N> N_vec(N);
226  VectorView<const T_size1> alpha_vec(alpha);
227  VectorView<const T_size2> beta_vec(beta);
228  size_t size = max_size(n, N, alpha, beta);
229 
230  // Compute vectorized CDF and gradient
231  using boost::math::lgamma;
232  using boost::math::digamma;
233 
234  agrad::OperandsAndPartials<T_size1, T_size2>
235  operands_and_partials(alpha, beta);
236 
237  // Explicit return for extreme values
238  // The gradients are technically ill-defined, but treated as zero
239  for (size_t i = 0; i < stan::length(n); i++) {
240  if (value_of(n_vec[i]) <= 0)
241  return operands_and_partials.to_var(0.0);
242  }
243 
244  for (size_t i = 0; i < size; i++) {
245  // Explicit results for extreme values
246  // The gradients are technically ill-defined, but treated as zero
247  if (value_of(n_vec[i]) >= value_of(N_vec[i])) {
248  continue;
249  }
250 
251  const double n_dbl = value_of(n_vec[i]);
252  const double N_dbl = value_of(N_vec[i]);
253  const double alpha_dbl = value_of(alpha_vec[i]);
254  const double beta_dbl = value_of(beta_vec[i]);
255 
256  const double mu = alpha_dbl + n_dbl + 1;
257  const double nu = beta_dbl + N_dbl - n_dbl - 1;
258 
259  const double F = stan::math::F32(1, mu, -N_dbl + n_dbl + 1, n_dbl + 2,
260  1 - nu, 1);
261 
262  double C = lgamma(nu) - lgamma(N_dbl - n_dbl);
263  C += lgamma(mu) - lgamma(n_dbl + 2);
264  C += lgamma(N_dbl + 2) - lgamma(N_dbl + alpha_dbl + beta_dbl);
265  C = std::exp(C);
266 
267  C *= F / boost::math::beta(alpha_dbl, beta_dbl);
268  C /= N_dbl + 1;
269 
270  const double Pi = 1 - C;
271 
272  P *= Pi;
273 
274  double dF[6];
275  double digammaOne = 0;
276  double digammaTwo = 0;
277 
278  if ( (!is_constant_struct<T_size1>::value)
279  || (!is_constant_struct<T_size2>::value) ) {
280  digammaOne = digamma(mu + nu);
281  digammaTwo = digamma(alpha_dbl + beta_dbl);
282  stan::math::gradF32(dF, 1, mu, -N_dbl + n_dbl + 1, n_dbl + 2,
283  1 - nu, 1);
284  }
285  if (!is_constant_struct<T_size1>::value) {
286  const double g
287  = - C * (digamma(mu) - digammaOne + dF[1] / F
288  - digamma(alpha_dbl) + digammaTwo);
289  operands_and_partials.d_x1[i]
290  += g / Pi;
291  }
292  if (!is_constant_struct<T_size2>::value) {
293  const double g
294  = - C * (digamma(nu) - digammaOne - dF[4] / F - digamma(beta_dbl)
295  + digammaTwo);
296  operands_and_partials.d_x2[i]
297  += g / Pi;
298  }
299  }
300 
301  if (!is_constant_struct<T_size1>::value)
302  for(size_t i = 0; i < stan::length(alpha); ++i)
303  operands_and_partials.d_x1[i] *= P;
304  if (!is_constant_struct<T_size2>::value)
305  for(size_t i = 0; i < stan::length(beta); ++i)
306  operands_and_partials.d_x2[i] *= P;
307 
308  return operands_and_partials.to_var(P);
309  }
310 
311  template <typename T_n, typename T_N,
312  typename T_size1, typename T_size2>
313  typename return_type<T_size1,T_size2>::type
314  beta_binomial_cdf_log(const T_n& n, const T_N& N, const T_size1& alpha,
315  const T_size2& beta) {
316 
317  static const char* function = "stan::prob::beta_binomial_cdf_log(%1%)";
318 
319  using stan::math::check_positive_finite;
320  using stan::math::check_nonnegative;
321  using stan::math::value_of;
322  using stan::math::check_consistent_sizes;
323  using stan::prob::include_summand;
324 
325  // Ensure non-zero argument lengths
326  if (!(stan::length(n) && stan::length(N) && stan::length(alpha)
327  && stan::length(beta)))
328  return 0.0;
329 
330  double P(0.0);
331 
332  // Validate arguments
333  check_nonnegative(function, N, "Population size parameter", &P);
334  check_positive_finite(function, alpha, "First prior sample size parameter",
335  &P);
336  check_positive_finite(function, beta, "Second prior sample size parameter",
337  &P);
338  check_consistent_sizes(function,
339  n, N, alpha, beta,
340  "Successes variable",
341  "Population size parameter",
342  "First prior sample size parameter",
343  "Second prior sample size parameter",
344  &P);
345 
346  // Wrap arguments in vector views
347  VectorView<const T_n> n_vec(n);
348  VectorView<const T_N> N_vec(N);
349  VectorView<const T_size1> alpha_vec(alpha);
350  VectorView<const T_size2> beta_vec(beta);
351  size_t size = max_size(n, N, alpha, beta);
352 
353  // Compute vectorized cdf_log and gradient
354  using boost::math::lgamma;
355  using boost::math::digamma;
356 
357  agrad::OperandsAndPartials<T_size1, T_size2>
358  operands_and_partials(alpha, beta);
359 
360  // Explicit return for extreme values
361  // The gradients are technically ill-defined, but treated as neg infinity
362  for (size_t i = 0; i < stan::length(n); i++) {
363  if (value_of(n_vec[i]) <= 0)
364  return operands_and_partials.to_var(stan::math::negative_infinity());
365  }
366 
367  for (size_t i = 0; i < size; i++) {
368  // Explicit results for extreme values
369  // The gradients are technically ill-defined, but treated as zero
370  if (value_of(n_vec[i]) >= value_of(N_vec[i])) {
371  continue;
372  }
373 
374  const double n_dbl = value_of(n_vec[i]);
375  const double N_dbl = value_of(N_vec[i]);
376  const double alpha_dbl = value_of(alpha_vec[i]);
377  const double beta_dbl = value_of(beta_vec[i]);
378 
379  const double mu = alpha_dbl + n_dbl + 1;
380  const double nu = beta_dbl + N_dbl - n_dbl - 1;
381 
382  const double F = stan::math::F32(1, mu, -N_dbl + n_dbl + 1, n_dbl + 2,
383  1 - nu, 1);
384 
385  double C = lgamma(nu) - lgamma(N_dbl - n_dbl);
386  C += lgamma(mu) - lgamma(n_dbl + 2);
387  C += lgamma(N_dbl + 2) - lgamma(N_dbl + alpha_dbl + beta_dbl);
388  C = std::exp(C);
389 
390  C *= F / boost::math::beta(alpha_dbl, beta_dbl);
391  C /= N_dbl + 1;
392 
393  const double Pi = 1 - C;
394 
395  P += log(Pi);
396 
397  double dF[6];
398  double digammaOne = 0;
399  double digammaTwo = 0;
400 
401  if ( (!is_constant_struct<T_size1>::value)
402  || (!is_constant_struct<T_size2>::value) ) {
403  digammaOne = digamma(mu + nu);
404  digammaTwo = digamma(alpha_dbl + beta_dbl);
405  stan::math::gradF32(dF, 1, mu, -N_dbl + n_dbl + 1, n_dbl + 2,
406  1 - nu, 1);
407  }
408  if (!is_constant_struct<T_size1>::value) {
409  const double g
410  = - C * (digamma(mu) - digammaOne + dF[1] / F
411  - digamma(alpha_dbl) + digammaTwo);
412  operands_and_partials.d_x1[i] += g / Pi;
413  }
414  if (!is_constant_struct<T_size2>::value) {
415  const double g
416  = - C * (digamma(nu) - digammaOne - dF[4] / F - digamma(beta_dbl)
417  + digammaTwo);
418  operands_and_partials.d_x2[i] += g / Pi;
419  }
420  }
421 
422  return operands_and_partials.to_var(P);
423  }
424 
425  template <typename T_n, typename T_N,
426  typename T_size1, typename T_size2>
427  typename return_type<T_size1,T_size2>::type
428  beta_binomial_ccdf_log(const T_n& n, const T_N& N, const T_size1& alpha,
429  const T_size2& beta) {
430 
431  static const char* function = "stan::prob::beta_binomial_ccdf_log(%1%)";
432 
433  using stan::math::check_positive_finite;
434  using stan::math::check_nonnegative;
435  using stan::math::value_of;
436  using stan::math::check_consistent_sizes;
437  using stan::prob::include_summand;
438 
439  // Ensure non-zero argument lengths
440  if (!(stan::length(n) && stan::length(N) && stan::length(alpha)
441  && stan::length(beta)))
442  return 0.0;
443 
444  double P(0.0);
445 
446  // Validate arguments
447  check_nonnegative(function, N, "Population size parameter", &P);
448  check_positive_finite(function, alpha, "First prior sample size parameter",
449  &P);
450  check_positive_finite(function, beta, "Second prior sample size parameter",
451  &P);
452  check_consistent_sizes(function,
453  n, N, alpha, beta,
454  "Successes variable",
455  "Population size parameter",
456  "First prior sample size parameter",
457  "Second prior sample size parameter",
458  &P);
459 
460  // Wrap arguments in vector views
461  VectorView<const T_n> n_vec(n);
462  VectorView<const T_N> N_vec(N);
463  VectorView<const T_size1> alpha_vec(alpha);
464  VectorView<const T_size2> beta_vec(beta);
465  size_t size = max_size(n, N, alpha, beta);
466 
467  // Compute vectorized cdf_log and gradient
468  using boost::math::lgamma;
469  using boost::math::digamma;
470 
471  agrad::OperandsAndPartials<T_size1, T_size2>
472  operands_and_partials(alpha, beta);
473 
474  // Explicit return for extreme values
475  // The gradients are technically ill-defined, but treated as neg infinity
476  for (size_t i = 0; i < stan::length(n); i++) {
477  if (value_of(n_vec[i]) <= 0)
478  return operands_and_partials.to_var(0.0);
479  }
480 
481  for (size_t i = 0; i < size; i++) {
482  // Explicit results for extreme values
483  // The gradients are technically ill-defined, but treated as zero
484  if (value_of(n_vec[i]) >= value_of(N_vec[i])) {
485  return operands_and_partials.to_var(stan::math::negative_infinity());
486  }
487 
488  const double n_dbl = value_of(n_vec[i]);
489  const double N_dbl = value_of(N_vec[i]);
490  const double alpha_dbl = value_of(alpha_vec[i]);
491  const double beta_dbl = value_of(beta_vec[i]);
492 
493  const double mu = alpha_dbl + n_dbl + 1;
494  const double nu = beta_dbl + N_dbl - n_dbl - 1;
495 
496  const double F = stan::math::F32(1, mu, -N_dbl + n_dbl + 1, n_dbl + 2,
497  1 - nu, 1);
498 
499  double C = lgamma(nu) - lgamma(N_dbl - n_dbl);
500  C += lgamma(mu) - lgamma(n_dbl + 2);
501  C += lgamma(N_dbl + 2) - lgamma(N_dbl + alpha_dbl + beta_dbl);
502  C = std::exp(C);
503 
504  C *= F / boost::math::beta(alpha_dbl, beta_dbl);
505  C /= N_dbl + 1;
506 
507  const double Pi = C;
508 
509  P += log(Pi);
510 
511  double dF[6];
512  double digammaOne = 0;
513  double digammaTwo = 0;
514 
515  if ( (!is_constant_struct<T_size1>::value)
516  || (!is_constant_struct<T_size2>::value) ) {
517  digammaOne = digamma(mu + nu);
518  digammaTwo = digamma(alpha_dbl + beta_dbl);
519  stan::math::gradF32(dF, 1, mu, -N_dbl + n_dbl + 1, n_dbl + 2,
520  1 - nu, 1);
521  }
522  if (!is_constant_struct<T_size1>::value) {
523  const double g
524  = - C * (digamma(mu) - digammaOne + dF[1] / F
525  - digamma(alpha_dbl) + digammaTwo);
526  operands_and_partials.d_x1[i] -= g / Pi;
527  }
528  if (!is_constant_struct<T_size2>::value) {
529  const double g
530  = - C * (digamma(nu) - digammaOne - dF[4] / F - digamma(beta_dbl)
531  + digammaTwo);
532  operands_and_partials.d_x2[i] -= g / Pi;
533  }
534  }
535 
536  return operands_and_partials.to_var(P);
537  }
538 
539  template <class RNG>
540  inline int
541  beta_binomial_rng(const int N,
542  const double alpha,
543  const double beta,
544  RNG& rng) {
545 
546  static const char* function = "stan::prob::beta_binomial_rng(%1%)";
547 
548  using stan::math::check_positive_finite;
549  using stan::math::check_nonnegative;
550 
551  check_nonnegative(function, N, "Population size parameter", (double*)0);
552  check_positive_finite(function, alpha,
553  "First prior sample size parameter",
554  (double*)0);
555  check_positive_finite(function, beta,
556  "Second prior sample size parameter",
557  (double*)0);
558 
559  double a = stan::prob::beta_rng(alpha, beta, rng);
560  while(a > 1 || a < 0)
561  a = stan::prob::beta_rng(alpha, beta, rng);
562  return stan::prob::binomial_rng(N, a, rng);
563  }
564 }
565  }
566 #endif
stan::agrad::lbeta
fvar< T > lbeta(const fvar< T > &x1, const fvar< T > &x2)
Definition: lbeta.hpp:16
stan::agrad::OperandsAndPartials::to_var
T_return_type to_var(double logp)
Definition: partials_vari.hpp:138
stan::math::check_positive_finite
bool check_positive_finite(const char *function, const T_y &y, const char *name, T_result *result)
Definition: check_positive_finite.hpp:12
error_handling.hpp
stan::length
size_t length(const T &)
Definition: traits.hpp:159
stan::math::binomial_coefficient_log
boost::math::tools::promote_args< T_N, T_n >::type binomial_coefficient_log(const T_N N, const T_n n)
Return the log of the binomial coefficient for the specified arguments.
Definition: binomial_coefficient_log.hpp:63
stan::DoubleVectorView
DoubleVectorView allocates double values to be used as intermediate values.
Definition: traits.hpp:358
stan::prob::beta_binomial_ccdf_log
return_type< T_size1, T_size2 >::type beta_binomial_ccdf_log(const T_n &n, const T_N &N, const T_size1 &alpha, const T_size2 &beta)
Definition: beta_binomial.hpp:428
partials_vari.hpp
stan::agrad::value_of
T value_of(const fvar< T > &v)
Return the value of the specified variable.
Definition: value_of.hpp:16
stan::is_vector
Definition: traits.hpp:83
stan::agrad::lgamma
fvar< T > lgamma(const fvar< T > &x)
Definition: lgamma.hpp:15
stan::prob::binomial_rng
int binomial_rng(const int N, const double theta, RNG &rng)
Definition: binomial.hpp:470
stan::agrad::OperandsAndPartials
A variable implementation that stores operands and derivatives with respect to the variable...
Definition: partials_vari.hpp:76
stan::prob::beta_binomial_rng
int beta_binomial_rng(const int N, const double alpha, const double beta, RNG &rng)
Definition: beta_binomial.hpp:541
stan::return_type::type
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: traits.hpp:406
stan::is_constant_struct
Metaprogram to determine if a type has a base scalar type that can be assigned to type double...
Definition: traits.hpp:57
stan::math::value_of
double value_of(const T x)
Return the value of the specified scalar argument converted to a double value.
Definition: value_of.hpp:24
stan::prob::include_summand
Template metaprogram to calculate whether a summand needs to be included in a proportional (log) prob...
Definition: traits.hpp:35
stan::math::lbeta
boost::math::tools::promote_args< T1, T2 >::type lbeta(const T1 a, const T2 b)
Return the log of the beta function applied to the specified arguments.
Definition: lbeta.hpp:59
stan::agrad::OperandsAndPartials::d_x2
VectorView< double *, is_vector< T2 >::value, is_constant_struct< T2 >::value > d_x2
Definition: partials_vari.hpp:83
stan::math::gradF32
void gradF32(double *g, double a, double b, double c, double d, double e, double z, double precision=1e-6)
Definition: internal_math.hpp:50
stan::math::check_nonnegative
bool check_nonnegative(const char *function, const T_y &y, const char *name, T_result *result)
Definition: check_nonnegative.hpp:52
stan::prob::beta_binomial_cdf
return_type< T_size1, T_size2 >::type beta_binomial_cdf(const T_n &n, const T_N &N, const T_size1 &alpha, const T_size2 &beta)
Definition: beta_binomial.hpp:191
stan::math::F32
double F32(double a, double b, double c, double d, double e, double z, double precision=1e-6)
Definition: internal_math.hpp:14
stan::math::check_consistent_sizes
bool check_consistent_sizes(const char *function, const T1 &x1, const T2 &x2, const char *name1, const char *name2, T_result *result)
Definition: check_consistent_sizes.hpp:13
stan::max_size
size_t max_size(const T1 &x1, const T2 &x2)
Definition: traits.hpp:191
stan::prob::beta_rng
double beta_rng(const double alpha, const double beta, RNG &rng)
Definition: beta.hpp:593
internal_math.hpp
stan::prob::beta_binomial_cdf_log
return_type< T_size1, T_size2 >::type beta_binomial_cdf_log(const T_n &n, const T_N &N, const T_size1 &alpha, const T_size2 &beta)
Definition: beta_binomial.hpp:314
stan::prob::beta_binomial_log
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)
Definition: beta_binomial.hpp:28
stan::agrad::OperandsAndPartials::d_x4
VectorView< double *, is_vector< T4 >::value, is_constant_struct< T4 >::value > d_x4
Definition: partials_vari.hpp:85
stan::math::size
int size(const std::vector< T > &x)
Definition: size.hpp:11
stan::agrad::binomial_coefficient_log
fvar< T > binomial_coefficient_log(const fvar< T > &x1, const fvar< T > &x2)
Definition: binomial_coefficient_log.hpp:16
stan::agrad::digamma
fvar< T > digamma(const fvar< T > &x)
Definition: digamma.hpp:16
value_of.hpp
stan::agrad::OperandsAndPartials::d_x1
VectorView< double *, is_vector< T1 >::value, is_constant_struct< T1 >::value > d_x1
Definition: partials_vari.hpp:82
stan::agrad::OperandsAndPartials::d_x3
VectorView< double *, is_vector< T3 >::value, is_constant_struct< T3 >::value > d_x3
Definition: partials_vari.hpp:84
binomial_coefficient_log.hpp
stan::agrad::log
fvar< T > log(const fvar< T > &x)
Definition: log.hpp:15
stan::VectorView
VectorView is a template metaprogram that takes its argument and allows it to be used like a vector...
Definition: traits.hpp:275
stan::agrad::exp
fvar< T > exp(const fvar< T > &x)
Definition: exp.hpp:16
stan::math::negative_infinity
double negative_infinity()
Return negative infinity.
Definition: constants.hpp:123
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