This function computes the inverse of L matrix multiples the output vector, where the L matrix is the Cholesky decomposition of the correlation matrix. Instead of computing the Cholesky matrix, we compute it using the forward filtering algorithm.
Get_L_inv_y(GG,VV,Q,K,output)a list of matrices defined in the dynamic linear model.
a numerical value of the variance of the nugget parameter.
a vector defined in the dynamic linear model.
a matrix defined in the filtering algorithm for the dynamic linear model.
a vector of output.
A vector of the inverse of L matrix multiples the output vector, where the L matrix is the Cholesky decomposition of the correlation matrix.
Hartikainen, J. and Sarkka, S. (2010). Kalman filtering and smoothing solutions to temporal gaussian process regression models. Machine Learning for Signal Processing (MLSP), 2010 IEEE International Workshop, 379-384.
M. Gu, Y. Xu (2019), fast nonseparable gaussian stochastic process with application to methylation level interpolation. Journal of Computational and Graphical Statistics, In Press, arXiv:1711.11501.
Campagnoli P, Petris G, Petrone S. (2009), Dynamic linear model with R. Springer-Verlag New York.
Get_C_R_K_Q for more details about Q vector and K matrix.