VAR_Gauss: Vector auto-regressive model with GMRF represenation

In shazhe/mvst0: Multi-variate ST modelling on globe

Description

This function initialises a vector auto-regressive model and represents it as a Gaussian Markov Random Field with mean mu and precision matrix Q. This constructor differs from other GMRF constructors in that it takes function inputs to define temporally evolving characteristics. The default representation is

x_{k+1} = μ_k + A_kx_k + B_kβ_k + e_k

where e_k \sim \mathcal{N}(0,Q_k). Note that in addition to covariates, a known mean μ_k can be added, this can be omitted and replaced appropriately with entries in B_k. A multi-variate vector auto-regressive model can be speficied by letting A_fun and Qw_fun return matrices a multiple of the dimension of the underlying basis over which the GMRF is defined.

Usage

VAR_Gauss(mu_fun = function(k) return(matrix(0, 2, 5)), A_fun = function(k)
  return(Imat(2)), B_fun = function(k) return(emptySp()),
  Qw_fun = function(k) return(Imat(2)), t_axis = c(0:6), Qb = emptySp(),
  name = "none")

Arguments

mu_fun	function of time k, returns matrix of size n
A_fun	function of time k, returns sparse matrix of size n\times n
B_fun	function of time k, returns sparse matrix of size n\times m
Qw_fun	function of time k, returns sparse matrix of size n\times n
t_axis	time axis of process
Qb	prior precision matrix of β; sparse matrix of size m \times m
name	name of VAR

Value

Object of class VAR_Gauss which inherits from class GMRF.

Examples

require(Matrix)
t_axis <- 0:10
mu <- function(k) return(matrix(0,length(t_axis),1))
A <- function(k)  return(sparsediag(0.4))
B <- function(k)  cBind(Imat(1),k*Imat(1))
Q <- function(k)  return(sparsediag(1))
Qb = bdiag(Imat(1),Imat(1))
VAR <- VAR_Gauss( mu_fun = mu,A=A, B=B, Qw = Q,t_axis = t_axis,Qb=Qb,name="firstVAR")

shazhe/mvst0 documentation built on May 29, 2019, 9:20 p.m.