compute_s2()

template<typename F , typename Theta , typename AMat , typename Stream , typename... Args, require_eigen_vector_t< Theta > * = nullptr>

auto stan::math::laplace_likelihood::internal::compute_s2 ( F &&  f, Theta &&  theta, AMat &&  A, const int  hessian_block_size, Stream *  msgs, Args &&...  args  )

inline

The derivative of the log likelihood wrt theta evaluated at the mode.

Compute $s_2 = \Delta_{\theta} log \pi_G(y|\phi,\eta) = -\frac{1}{2} trace((K^{-1}+W)^{-1})$

Note

Equation 15 in https://arxiv.org/pdf/2306.14976

If Args contains var types then their adjoints will be calculated as a side effect.

Template Parameters

F	A functor with opertor()(Args&&...) returning a scalar
Theta	An Eigen Matrix
AMat	An Eigen Matrix
Stream	Type of stream for messages.
Args	Type of variadic arguments for likelihood function.

Parameters

f	Log likelihood function.
theta	Latent Gaussian variable.
A	Matrix storing initial tangents for higher-order differentiation (line 21 in Algorithm 4, https://arxiv.org/pdf/2306.14976)
hessian_block_size	If the Hessian of the log likelihood w.r.t theta is block diagonal, size of each block.
msgs	Stream for messages.
args	Variational arguments for likelihood function.

Definition at line 212 of file laplace_likelihood.hpp.