R/lgcpForecast.R

In lgcp: Log-Gaussian Cox Process

##' lgcpForecast function
##'
##' Function to produce forecasts for the mean field \eqn{Y}{Y} at times beyond the last time point in the 
##' analysis (given by the argument \code{T} in the function \code{lgcpPredict}).
##'
##' @param lg an object of class lgcpPredict
##' @param ptimes vector of time points for prediction. Must start strictly after last inferred time point.
##' @param spatial.intensity the fixed spatial component: an object of that can be coerced to one of class spatialAtRisk
##' @param temporal.intensity the fixed temporal component: either a numeric vector, or a function that can be coerced into an object of class temporalAtRisk
##' @param inclusion criterion for cells being included into observation window. Either 'touching' or 'centroid'. The former includes all cells that touch the observation window, the latter includes all cells whose centroids are inside the observation window.
##' @return forcasted relative risk, Poisson intensities and Y values over grid, together with approximate variance.
##' @references Brix A, Diggle PJ (2001). Spatiotemporal Prediction for log-Gaussian Cox processes. Journal of the Royal Statistical Society, Series B, 63(4), 823-841.
##' @seealso \link{lgcpPredict}
##' @export 

lgcpForecast <- function(lg,ptimes,spatial.intensity,temporal.intensity,inclusion="touching"){

    verifyclass(lg,"lgcpPredict")
    
    maxt <- max(lg$aggtimes)
   
    if(any(ptimes <=maxt)){
        stop("required prediction times must start strictly after last inferred time point.")
    }    
    
    if(!inherits(temporal.intensity,"temporalAtRisk")){
        temporal.intensity <- temporalAtRisk(temporal.intensity,tlim=range(ptimes))
    }
    temporalfit <- sapply(ptimes,temporal.intensity)

    MN <- dim(lg$EY.mean$grid[[1]])
    cellarea <- diff(lg$mcens[1:2])*diff(lg$ncens[1:2]) 

    tdiffs <- ptimes - maxt    
    n <- length(tdiffs) 
    gt <- 1 - exp(-2*tdiffs*lg$theta)

    spatial <- spatial.intensity
    if(!inherits(spatial.intensity,"spatialAtRisk")){
        spatial <- spatialAtRisk(spatial.intensity)
    }    
    spatialvals <- fftinterpolate(spatial,c(lg$mcens,lg$mcens[length(lg$mcens)]+diff(lg$mcens[1:2])+lg$mcens-lg$mcens[1]),c(lg$ncens,lg$ncens[length(lg$ncens)]+diff(lg$ncens[1:2])+lg$ncens-lg$ncens[1]),ext=lg$ext)[1:lg$M,1:lg$N]   
    if(inclusion=="centroid"){
        cellInside <- matrix(as.numeric(inside.owin(x=rep(lg$mcens,lg$N),y=rep(lg$ncens,each=lg$M),w=lg$xyt$window)),lg$M,lg$N)
    }    
    else if(inclusion=="touching"){
        cellInside <- matrix(as.numeric(touchingowin(x=lg$mcens,y=lg$ncens,w=lg$xyt$window)),lg$M,lg$N)
    }
    else{
        stop("Invlaid choice for argument 'inclusion'.")
    }    
    spatialvals <- spatialvals*cellInside
    spatialvals <- spatialvals / (cellarea*sum(spatialvals)) 
    
    ymats <- list()
    yvars <- list()
    rr <- list()
    rr.var <- list()
    intens <- list()
    intens.var <- list()  		
    for(j in 1:n){ 
        ymats[[j]] <- at(tdiffs[j],lg$mu,lg$theta)+bt.scalar(tdiffs[j],lg$theta)*lg$y.mean$grid[[length(lg$y.mean$grid)]]
        yvars[[j]] <- (bt.scalar(tdiffs[j],lg$theta)^2)*lg$y.var$grid[[length(lg$y.var$grid)]] + gt[j]*lg$sigma^2 
        rr[[j]] <- exp(ymats[[j]])
        rr.var[[j]] <- exp(ymats[[j]]-yvars[[j]]/2) 
        intens[[j]] <- cellarea*temporalfit[j]*spatialvals*rr[[j]]
        intens.var[[j]] <- (cellarea*temporalfit[j]*spatialvals)^2*rr.var[[j]]
    }
    
    return(list(relrisk=lgcpgrid(rr,xvals=lg$mcens,yvals=lg$ncens,zvals=lg$aggtimes),
                relrisk.var=lgcpgrid(rr.var,xvals=lg$mcens,yvals=lg$ncens,zvals=lg$aggtimes),
                intensity=lgcpgrid(intens,xvals=lg$mcens,yvals=lg$ncens,zvals=lg$aggtimes),
                intensity.var=lgcpgrid(intens.var,xvals=lg$mcens,yvals=lg$ncens,zvals=lg$aggtimes),
                y.mean=lgcpgrid(ymats,xvals=lg$mcens,yvals=lg$ncens,zvals=lg$aggtimes),
                y.var=lgcpgrid(yvars,xvals=lg$mcens,yvals=lg$ncens,zvals=lg$aggtimes),
                mcens=lg$mcens,
                ncens=lg$ncens))
    
}