laplace_latent_tol_neg_binomial_2_log_rng()

template<typename Eta , typename ThetaVec , typename Mean , typename CovarFun , typename CovarArgs , typename RNG , require_eigen_vector_t< ThetaVec > * = nullptr>

Eigen::VectorXd stan::math::laplace_latent_tol_neg_binomial_2_log_rng ( const std::vector< int > &  y, const std::vector< int > &  y_index, Eta &&  eta, Mean &&  mean, CovarFun &&  covariance_function, CovarArgs &&  covar_args, ThetaVec &&  theta_0, const double  tolerance, const int  max_num_steps, const int  hessian_block_size, const int  solver, const int  max_steps_line_search, RNG &  rng, std::ostream *  msgs  )

inline

In a latent gaussian model,.

theta ~ Normal(0, Sigma(phi)) y ~ p(y|theta,phi)

return a sample from the Laplace approximation to p(theta|y,phi). The Laplace approximation is computed using a Newton solver. In this specialized function, the likelihood p(y|theta) is a Negative Binomial with a log link. This function uses the second parameterization of the Negative Binomial.

Template Parameters

Eta	A type for the overdispersion parameter.
ThetaVec	A type inheriting from Eigen::EigenBase with dynamic sized rows and 1 column.
Mean	type of the mean of the latent normal distribution
CovarFun	A functor with an operator()(CovarArgsElements..., {TrainTupleElements...| PredTupleElements...}) method. The operator() method should accept as arguments the inner elements of CovarArgs. The return type of the operator() method should be a type inheriting from Eigen::EigenBase with dynamic sized rows and columns.
CovarArgs	A tuple of types to passed as the first arguments of CovarFun::operator()
RNG	A valid boost rng type

Parameters

[in]	y	Observed counts.
[in]	y_index	Index indicating which group each observation belongs to.
[in]	eta	Overdisperison parameter.
[in]	mean	The mean of the latent normal variable.
[in]	covariance_function	a function which returns the prior covariance.
[in]	covar_args	arguments for the covariance function.
[in]	theta_0	the initial guess for the Laplace approximation.
[in]	tolerance	controls the convergence criterion when finding the mode in the Laplace approximation.
[in]	max_num_steps	maximum number of steps before the Newton solver breaks and returns an error.
[in]	hessian_block_size	Block size of Hessian of log likelihood w.r.t latent Gaussian variable theta.
[in]	solver	Type of Newton solver. Each corresponds to a distinct choice of B matrix (i.e. application SWM formula): 1. computes square-root of negative Hessian. 2. computes square-root of covariance matrix. 3. computes no square-root and uses LU decomposition.
[in]	max_steps_line_search	Number of steps after which the algorithm gives up on doing a line search. If 0, no linesearch.
[in,out]	rng	Random number generator
[in,out]	msgs	stream for messages from likelihood and covariance

Definition at line 41 of file laplace_latent_neg_binomial_2_log_rng.hpp.