faprior<-function(y){

# This function estimates the mean (yb) and the background
# observable error covariance (c) of the prior distribution
# of y given by y~N(yb,c)
#
# USAGE: faprior(y)
#
# INPUT:
# y  -> n x q data matrix containing q observable time series
#
# OUTPUTS:
# yb -> 1 x q matrix containing the column means of y
# c  -> q x q observable state covariance matrix
#
# Authors: Caio Coelho <c.a.d.s.coelho@reading.ac.uk>
#          David Stephenson <d.b.stephenson@reading.ac.uk>
#



# Calculate column means of y and store in yb (1 x q)
yb <- t(apply(y, 2, mean))
#
#
# Estimates observable state covariance matrix (c) - biased estimate 1/N
#
c <- var(y)*(nrow(y)-1)/nrow(y)
list(yb = yb, c = c)
}