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Last update Apr 29, 2003 |
DESCRIPTION:Conjugated Kalman filter for Poisson data assuming identity link and partially specified linear latent process. The conjugate prior on the mean parameter is gamma. The specific model is
USAGE:ckal.fil.po.gam.id(ssm)
REQUIRED ARGUMENTS:
OPTIONAL ARGUMENTS:The following attributes of the ssm object might be needed:
VALUE:Returns an object of class ssm with the same attributes as the object in the call, but with attribute filtered updated with:
SIDE EFFECTS:None
DETAILS:This is the conjugate filter introduced for the class of dynamic generalized linear models by West, Harrison and Migon (1985). Instead of approximating the observational model with a Gaussian one like in the extended Kalman filter, the latent process guides the choice of the conjugate prior on the natural parameter.
REFERENCES:Klein, (2003), State Space Models for Exponential Family Data, Ph.D. Thesis, Department of Statistics, University of Southern Denmark.West & Harrison, (1997), Bayesian Forecasting and Dynamic Models, Springer Series in Statistics. West, Harrison & Migon, (1985),Dynamic Generalized Linear Models and Bayesian Forecasting (with discussion), Journal of the American Statistical association, 80, 73-97. EXAMPLES:# Specify a state space model # Latent process is local linear growth ss <- ssm(Ft = function(i,x,phi) {c(1,0)}, Gt = function(i,x,phi) {matrix(c(1,1,0,1),ncol=2,byrow=T)}, Wt = function(i,x,phi) {diag(2)/100}, m0 = c(15,0), C0 = diag(10,2), fam = "Poisson", link = "identity") # Simulate Poisson observations ss <- simulate.ssm(ss, n=50) # Apply the conjugated Kalman filter ss <- ckal.fil.po.gam.id(ss) plot(ss$filtered$mt[,1], ylab="mean", lty=1, type="l", ylim=c(0,max(ss$Yt))) lines(ss$simulated$theta[,1], lty=2) points(ss$Yt, pch=16) legend(0,max(ss$Yt),legend=c("Filtered mean", "Simulated mean","Yt"), lty=c(1,2,-1), marks=c(-1,-1,16)) title("Results from ckal.fil.po.gam.id") |