All Classes Namespaces Files Functions Variables Typedefs Enumerator Friends Macros
neg_binomial_log.hpp
Go to the documentation of this file.
#ifndef STAN_MATH_PRIM_SCAL_PROB_NEG_BINOMIAL_LOG_HPP
#define STAN_MATH_PRIM_SCAL_PROB_NEG_BINOMIAL_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_nonnegative.hpp>
#include <stan/math/prim/scal/err/check_positive_finite.hpp>
#include <stan/math/prim/scal/fun/constants.hpp>
#include <stan/math/prim/scal/fun/value_of.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/lbeta.hpp>
#include <stan/math/prim/scal/meta/length.hpp>
#include <stan/math/prim/scal/meta/is_constant_struct.hpp>
#include <stan/math/prim/scal/meta/VectorView.hpp>
#include <stan/math/prim/scal/meta/VectorBuilder.hpp>
#include <stan/math/prim/scal/meta/partials_return_type.hpp>
#include <stan/math/prim/scal/meta/return_type.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/fun/inc_beta.hpp>
#include <stan/math/prim/scal/meta/max_size.hpp>
#include <cmath>
namespace stan {
namespace math {
// NegBinomial(n|alpha, beta) [alpha > 0; beta > 0; n >= 0]
template <bool propto,
typename T_n,
typename T_shape, typename T_inv_scale>
typename return_type<T_shape, T_inv_scale>::type
neg_binomial_log(const T_n& n,
const T_shape& alpha,
const T_inv_scale& beta) {
typedef typename stan::partials_return_type<T_n, T_shape,
T_inv_scale>::type
T_partials_return;
static const char* function("stan::math::neg_binomial_log");
using stan::math::check_positive_finite;
using stan::math::check_nonnegative;
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(alpha)
&& stan::length(beta)))
return 0.0;
T_partials_return logp(0.0);
check_nonnegative(function, "Failures variable", n);
check_positive_finite(function, "Shape parameter", alpha);
check_positive_finite(function, "Inverse scale parameter", beta);
check_consistent_sizes(function,
"Failures variable", n,
"Shape parameter", alpha,
"Inverse scale parameter", beta);
// check if no variables are involved and prop-to
if (!include_summand<propto, T_shape, T_inv_scale>::value)
return 0.0;
using stan::math::multiply_log;
using stan::math::binomial_coefficient_log;
using stan::math::digamma;
using stan::math::lgamma;
using std::log;
using std::log;
// set up template expressions wrapping scalars into vector views
VectorView<const T_n> n_vec(n);
VectorView<const T_shape> alpha_vec(alpha);
VectorView<const T_inv_scale> beta_vec(beta);
size_t size = max_size(n, alpha, beta);
OperandsAndPartials<T_shape, T_inv_scale>
operands_and_partials(alpha, beta);
size_t len_ab = max_size(alpha, beta);
VectorBuilder<true, T_partials_return, T_shape, T_inv_scale>
lambda(len_ab);
for (size_t i = 0; i < len_ab; ++i)
lambda[i] = value_of(alpha_vec[i]) / value_of(beta_vec[i]);
VectorBuilder<true, T_partials_return, T_inv_scale>
log1p_beta(length(beta));
for (size_t i = 0; i < length(beta); ++i)
log1p_beta[i] = log1p(value_of(beta_vec[i]));
VectorBuilder<true, T_partials_return, T_inv_scale>
log_beta_m_log1p_beta(length(beta));
for (size_t i = 0; i < length(beta); ++i)
log_beta_m_log1p_beta[i] = log(value_of(beta_vec[i])) - log1p_beta[i];
VectorBuilder<true, T_partials_return, T_inv_scale, T_shape>
alpha_times_log_beta_over_1p_beta(len_ab);
for (size_t i = 0; i < len_ab; ++i)
alpha_times_log_beta_over_1p_beta[i]
= value_of(alpha_vec[i])
* log(value_of(beta_vec[i])
/ (1.0 + value_of(beta_vec[i])));
VectorBuilder<!is_constant_struct<T_shape>::value,
T_partials_return, T_shape>
digamma_alpha(length(alpha));
if (!is_constant_struct<T_shape>::value) {
for (size_t i = 0; i < length(alpha); ++i)
digamma_alpha[i] = digamma(value_of(alpha_vec[i]));
}
VectorBuilder<!is_constant_struct<T_shape>::value,
T_partials_return, T_inv_scale> log_beta(length(beta));
if (!is_constant_struct<T_shape>::value) {
for (size_t i = 0; i < length(beta); ++i)
log_beta[i] = log(value_of(beta_vec[i]));
}
VectorBuilder<!is_constant_struct<T_inv_scale>::value,
T_partials_return, T_shape, T_inv_scale>
lambda_m_alpha_over_1p_beta(len_ab);
if (!is_constant_struct<T_inv_scale>::value) {
for (size_t i = 0; i < len_ab; ++i)
lambda_m_alpha_over_1p_beta[i] =
lambda[i]
- (value_of(alpha_vec[i])
/ (1.0 + value_of(beta_vec[i])));
}
for (size_t i = 0; i < size; i++) {
if (alpha_vec[i] > 1e10) { // reduces numerically to Poisson
if (include_summand<propto>::value)
logp -= lgamma(n_vec[i] + 1.0);
if (include_summand<propto, T_shape, T_inv_scale>::value)
logp += multiply_log(n_vec[i], lambda[i]) - lambda[i];
if (!is_constant_struct<T_shape>::value)
operands_and_partials.d_x1[i]
+= n_vec[i] / value_of(alpha_vec[i])
- 1.0 / value_of(beta_vec[i]);
if (!is_constant_struct<T_inv_scale>::value)
operands_and_partials.d_x2[i]
+= (lambda[i] - n_vec[i]) / value_of(beta_vec[i]);
} else { // standard density definition
if (include_summand<propto, T_shape>::value)
if (n_vec[i] != 0)
logp += binomial_coefficient_log(n_vec[i]
+ value_of(alpha_vec[i])
- 1.0,
n_vec[i]);
if (include_summand<propto, T_shape, T_inv_scale>::value)
logp +=
alpha_times_log_beta_over_1p_beta[i]
- n_vec[i] * log1p_beta[i];
if (!is_constant_struct<T_shape>::value)
operands_and_partials.d_x1[i]
+= digamma(value_of(alpha_vec[i]) + n_vec[i])
- digamma_alpha[i]
+ log_beta_m_log1p_beta[i];
if (!is_constant_struct<T_inv_scale>::value)
operands_and_partials.d_x2[i]
+= lambda_m_alpha_over_1p_beta[i]
- n_vec[i] / (value_of(beta_vec[i]) + 1.0);
}
}
return operands_and_partials.to_var(logp, alpha, beta);
}
template <typename T_n,
typename T_shape, typename T_inv_scale>
inline
typename return_type<T_shape, T_inv_scale>::type
neg_binomial_log(const T_n& n,
const T_shape& alpha,
const T_inv_scale& beta) {
return neg_binomial_log<false>(n, alpha, beta);
}
}
}
#endif
lgamma.hpp
stan::math::binomial_coefficient_log
fvar< T > binomial_coefficient_log(const fvar< T > &x1, const fvar< T > &x2)
Definition: binomial_coefficient_log.hpp:16
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
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
return_type.hpp
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
VectorView.hpp
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
stan::partials_return_type
Definition: partials_return_type.hpp:16
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
partials_return_type.hpp
length.hpp
grad_reg_inc_beta.hpp
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
lbeta.hpp
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::log1p
fvar< T > log1p(const fvar< T > &x)
Definition: log1p.hpp:16
is_constant_struct.hpp
inc_beta.hpp
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
stan::math::neg_binomial_log
return_type< T_shape, T_inv_scale >::type neg_binomial_log(const T_n &n, const T_shape &alpha, const T_inv_scale &beta)
Definition: neg_binomial_log.hpp:39
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
max_size.hpp
stan::math::digamma
fvar< T > digamma(const fvar< T > &x)
Definition: digamma.hpp:16

[ Stan Home Page ] © 2011–2015, Stan Development Team.