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neg_binomial_2_log_log.hpp
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#ifndef STAN_MATH_PRIM_SCAL_PROB_NEG_BINOMIAL_2_LOG_LOG_HPP
#define STAN_MATH_PRIM_SCAL_PROB_NEG_BINOMIAL_2_LOG_LOG_HPP
#include <boost/math/special_functions/digamma.hpp>
#include <boost/random/negative_binomial_distribution.hpp>
#include <boost/random/variate_generator.hpp>
#include <stan/math/prim/scal/meta/OperandsAndPartials.hpp>
#include <stan/math/prim/scal/err/check_consistent_sizes.hpp>
#include <stan/math/prim/scal/err/check_positive_finite.hpp>
#include <stan/math/prim/scal/err/check_nonnegative.hpp>
#include <stan/math/prim/scal/err/check_less.hpp>
#include <stan/math/prim/scal/fun/constants.hpp>
#include <stan/math/prim/scal/fun/binomial_coefficient_log.hpp>
#include <stan/math/prim/scal/fun/multiply_log.hpp>
#include <stan/math/prim/scal/fun/digamma.hpp>
#include <stan/math/prim/scal/fun/lgamma.hpp>
#include <stan/math/prim/scal/fun/log_sum_exp.hpp>
#include <stan/math/prim/scal/fun/value_of.hpp>
#include <stan/math/prim/scal/meta/include_summand.hpp>
#include <stan/math/prim/scal/fun/grad_reg_inc_beta.hpp>
#include <stan/math/prim/scal/meta/VectorBuilder.hpp>
#include <cmath>
namespace stan {
namespace math {
// NegBinomial(n|eta, phi) [phi > 0; n >= 0]
template <bool propto,
typename T_n,
typename T_log_location, typename T_precision>
typename return_type<T_log_location, T_precision>::type
neg_binomial_2_log_log(const T_n& n,
const T_log_location& eta,
const T_precision& phi) {
typedef typename stan::partials_return_type<T_n, T_log_location,
T_precision>::type
T_partials_return;
static const char* function("stan::prob::neg_binomial_2_log_log");
using stan::math::check_finite;
using stan::math::check_nonnegative;
using stan::math::check_positive_finite;
using stan::math::value_of;
using stan::math::check_consistent_sizes;
using stan::math::include_summand;
// check if any vectors are zero length
if (!(stan::length(n)
&& stan::length(eta)
&& stan::length(phi)))
return 0.0;
T_partials_return logp(0.0);
check_nonnegative(function, "Failures variable", n);
check_finite(function, "Log location parameter", eta);
check_positive_finite(function, "Precision parameter", phi);
check_consistent_sizes(function,
"Failures variable", n,
"Log location parameter", eta,
"Precision parameter", phi);
// check if no variables are involved and prop-to
if (!include_summand<propto, T_log_location, T_precision>::value)
return 0.0;
using stan::math::multiply_log;
using stan::math::log_sum_exp;
using stan::math::digamma;
using stan::math::lgamma;
using std::exp;
using std::log;
// set up template expressions wrapping scalars into vector views
VectorView<const T_n> n_vec(n);
VectorView<const T_log_location> eta_vec(eta);
VectorView<const T_precision> phi_vec(phi);
size_t size = max_size(n, eta, phi);
OperandsAndPartials<T_log_location, T_precision>
operands_and_partials(eta, phi);
size_t len_ep = max_size(eta, phi);
size_t len_np = max_size(n, phi);
VectorBuilder<true, T_partials_return, T_log_location> eta__(length(eta));
for (size_t i = 0, size = length(eta); i < size; ++i)
eta__[i] = value_of(eta_vec[i]);
VectorBuilder<true, T_partials_return, T_precision> phi__(length(phi));
for (size_t i = 0, size = length(phi); i < size; ++i)
phi__[i] = value_of(phi_vec[i]);
VectorBuilder<true, T_partials_return, T_precision>
log_phi(length(phi));
for (size_t i = 0, size = length(phi); i < size; ++i)
log_phi[i] = log(phi__[i]);
VectorBuilder<true, T_partials_return, T_log_location, T_precision>
logsumexp_eta_logphi(len_ep);
for (size_t i = 0; i < len_ep; ++i)
logsumexp_eta_logphi[i] = log_sum_exp(eta__[i], log_phi[i]);
VectorBuilder<true, T_partials_return, T_n, T_precision>
n_plus_phi(len_np);
for (size_t i = 0; i < len_np; ++i)
n_plus_phi[i] = n_vec[i] + phi__[i];
for (size_t i = 0; i < size; i++) {
if (include_summand<propto>::value)
logp -= lgamma(n_vec[i] + 1.0);
if (include_summand<propto, T_precision>::value)
logp += multiply_log(phi__[i], phi__[i]) - lgamma(phi__[i]);
if (include_summand<propto, T_log_location, T_precision>::value)
logp -= (n_plus_phi[i])*logsumexp_eta_logphi[i];
if (include_summand<propto, T_log_location>::value)
logp += n_vec[i]*eta__[i];
if (include_summand<propto, T_precision>::value)
logp += lgamma(n_plus_phi[i]);
if (!is_constant_struct<T_log_location>::value)
operands_and_partials.d_x1[i]
+= n_vec[i] - n_plus_phi[i]
/ (phi__[i]/exp(eta__[i]) + 1.0);
if (!is_constant_struct<T_precision>::value)
operands_and_partials.d_x2[i]
+= 1.0 - n_plus_phi[i]/(exp(eta__[i]) + phi__[i])
+ log_phi[i] - logsumexp_eta_logphi[i] - digamma(phi__[i])
+ digamma(n_plus_phi[i]);
}
return operands_and_partials.to_var(logp, eta, phi);
}
template <typename T_n,
typename T_log_location, typename T_precision>
inline
typename return_type<T_log_location, T_precision>::type
neg_binomial_2_log_log(const T_n& n,
const T_log_location& eta,
const T_precision& phi) {
return neg_binomial_2_log_log<false>(n, eta, phi);
}
}
}
#endif
lgamma.hpp
stan::math::lgamma
fvar< T > lgamma(const fvar< T > &x)
Definition: lgamma.hpp:15
check_positive_finite.hpp
stan::math::value_of
T value_of(const fvar< T > &v)
Return the value of the specified variable.
Definition: value_of.hpp:16
digamma.hpp
stan::math::log
fvar< T > log(const fvar< T > &x)
Definition: log.hpp:15
stan::length
size_t length(const std::vector< T > &x)
Definition: length.hpp:10
stan::math::neg_binomial_2_log_log
return_type< T_log_location, T_precision >::type neg_binomial_2_log_log(const T_n &n, const T_log_location &eta, const T_precision &phi)
Definition: neg_binomial_2_log_log.hpp:33
binomial_coefficient_log.hpp
stan::math::OperandsAndPartials::to_var
T_return_type to_var(T_partials_return logp, const T1 &x1=0, const T2 &x2=0, const T3 &x3=0, const T4 &x4=0, const T5 &x5=0, const T6 &x6=0)
Definition: OperandsAndPartials.hpp:322
stan::math::log_sum_exp
fvar< T > log_sum_exp(const std::vector< fvar< T > > &v)
Definition: log_sum_exp.hpp:14
stan::math::include_summand
Template metaprogram to calculate whether a summand needs to be included in a proportional (log) prob...
Definition: include_summand.hpp:36
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: return_type.hpp:27
include_summand.hpp
multiply_log.hpp
stan::math::OperandsAndPartials::d_x1
VectorView< T_partials_return, is_vector< T1 >::value, is_constant_struct< T1 >::value > d_x1
Definition: OperandsAndPartials.hpp:253
check_nonnegative.hpp
stan::is_constant_struct
Metaprogram to determine if a type has a base scalar type that can be assigned to type double...
Definition: is_constant_struct.hpp:16
log_sum_exp.hpp
stan::partials_return_type
Definition: partials_return_type.hpp:16
stan::math::exp
fvar< T > exp(const fvar< T > &x)
Definition: exp.hpp:10
stan::math::OperandsAndPartials
A variable implementation that stores operands and derivatives with respect to the variable...
Definition: OperandsAndPartials.hpp:238
OperandsAndPartials.hpp
stan::max_size
size_t max_size(const T1 &x1, const T2 &x2)
Definition: max_size.hpp:9
VectorBuilder.hpp
grad_reg_inc_beta.hpp
stan::math::check_finite
bool check_finite(const char *function, const char *name, const T_y &y)
Return true if y is finite.
Definition: check_finite.hpp:62
stan::math::multiply_log
fvar< T > multiply_log(const fvar< T > &x1, const fvar< T > &x2)
Definition: multiply_log.hpp:15
stan::VectorBuilder
Definition: VectorBuilder.hpp:61
constants.hpp
stan::math::size
int size(const std::vector< T > &x)
Definition: size.hpp:11
stan::math::check_consistent_sizes
bool check_consistent_sizes(const char *function, const char *name1, const T1 &x1, const char *name2, const T2 &x2)
Return true if the dimension of x1 is consistent with x2.
Definition: check_consistent_sizes.hpp:31
stan::math::OperandsAndPartials::d_x2
VectorView< T_partials_return, is_vector< T2 >::value, is_constant_struct< T2 >::value > d_x2
Definition: OperandsAndPartials.hpp:256
stan::math::check_nonnegative
bool check_nonnegative(const char *function, const char *name, const T_y &y)
Return true if y is non-negative.
Definition: check_nonnegative.hpp:66
value_of.hpp
stan::VectorView
VectorView is a template metaprogram that takes its argument and allows it to be used like a vector...
Definition: VectorView.hpp:41
check_less.hpp
check_consistent_sizes.hpp
stan::math::check_positive_finite
bool check_positive_finite(const char *function, const char *name, const T_y &y)
Return true if y is positive and finite.
Definition: check_positive_finite.hpp:28
stan::math::digamma
fvar< T > digamma(const fvar< T > &x)
Definition: digamma.hpp:16

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