Compute the (concentrated) conditional log likelihood for a statespace system described by a model template.

This is an internal helper function, used by the function factory ll_FUN. For a more detailed documentation of the conditional log Likelihood, see ll. The conditional likelihood is computed for the initial state \(a_1\) given in the first column a[,1] of the matrix a.

Usage

cll_theta_STSP_cpp(
  th,
  y,
  skip,
  concentrated,
  pi,
  H_pi,
  h_pi,
  L,
  H_L,
  h_L,
  a,
  u,
  dU
)

Arguments

th: \((K)\) dimensional vector of "deep" parameters.
y: \((m,N)\) matrix with the observed outputs: \((y_1,y_2,\ldots,y_N)\).
skip: (integer), skip the first residuals, when computing the sample covariance of the residuals.
concentrated: (bool), if TRUE then the concentrated, conditional log Likelihood is computed
pi: \((m+s,m+s)\) matrix, is overwritten with the system matrix \([A,B | C,D]\).
H_pi: \((m+s)^2, K)\) matrix.
h_pi: \(((m+s)^2)\)-dimensional vector. Note that vec(pi) = H_pi*th + h_pi.
L: \((m,m)\) matrix. If (concentrated==FALSE) then L is overwritten with the left square of the noise covariance matrix L corresponding to the deep parameters th. However, if (concentrated==TRUE) then L is overwritten with sample covariance matrix of the computed residuals!
H_L: \((m^2, K)\) matrix.
h_L: \((m^2)\)-dimensional vector. Note that vec(L) = H_L*th + h_L.
a: \((s,N+1)\) matrix. This matrix is overwritten with the (computed) states: \((a_1,a_2,\ldots,a_N,a_{N+1})\). On input a[,1] must hold the initial state \(a_1\).
u: \((m,N)\) matrix. This matrix is overwritten with (computed) residuals: \((u_1,u_2,\ldots,u_N)\).
dU: \((mN,K)\) matrix or \((0,0)\) matrix. This matrix is overwritten with the directional derivatives of the residuals. However, if the matrix is empty then no derivatives are computed.

Value

(double) log Likelihood

Compute the (concentrated) conditional log likelihood for a statespace system described by a model template.

Usage

Arguments

Value

See also