lgcpPredictSpatial: lgcpPredictSpatial function

In lgcp: Log-Gaussian Cox Process

lgcpPredictSpatial function

Description

The function lgcpPredictSpatial performs spatial prediction for log-Gaussian Cox Processes

Usage

lgcpPredictSpatial(
  sd,
  model.parameters = lgcppars(),
  spatial.covmodel = "exponential",
  covpars = c(),
  cellwidth = NULL,
  gridsize = NULL,
  spatial.intensity,
  spatial.offset = NULL,
  mcmc.control,
  output.control = setoutput(),
  gradtrunc = Inf,
  ext = 2,
  inclusion = "touching"
)

Arguments

sd	a spatial point pattern object, see ?ppp
model.parameters	values for parameters, see ?lgcppars
spatial.covmodel	correlation type see ?CovarianceFct
covpars	vector of additional parameters for certain classes of covariance function (eg Matern), these must be supplied in the order given in ?CovarianceFct
cellwidth	width of grid cells on which to do MALA (grid cells are square) in same units as observation window. Note EITHER gridsize OR cellwidthe must be specified.
gridsize	size of output grid required. Note EITHER gridsize OR cellwidthe must be specified.
spatial.intensity	the fixed spatial component: an object of that can be coerced to one of class spatialAtRisk
spatial.offset	Numeric of length 1. Optional offset parameter, corresponding to the expected number of cases. NULL by default, in which case, this is estimateed from teh data.
mcmc.control	MCMC paramters, see ?mcmcpars
output.control	output choice, see ?setoutput
gradtrunc	truncation for gradient vector equal to H parameter Moller et al 1998 pp 473. Default is Inf, which means no gradient truncation. Set to NULL to estimate this automatically (though note that this may not necessarily be a good choice). The default seems to work in most settings.
ext	integer multiple by which grid should be extended, default is 2. Generally this will not need to be altered, but if the spatial correlation decays slowly, increasing 'ext' may be necessary.
inclusion	criterion for cells being included into observation window. Either 'touching' or 'centroid'. The former, the default, includes all cells that touch the observation window, the latter includes all cells whose centroids are inside the observation window.

Details

The following is a mathematical description of a log-Gaussian Cox Process, it is best viewed in the pdf version of the manual.

Let \mathcal Y(s) be a spatial Gaussian process and W\subset R^2 be an observation window in space. Cases occur at spatial positions x \in W according to an inhomogeneous spatial Cox process, i.e. a Poisson process with a stochastic intensity R(x), The number of cases, X_{S}, arising in any S \subseteq W is then Poisson distributed conditional on R(\cdot),

X_{S} \sim \mbox{Poisson}\left\{\int_S R(s)ds\right\}

Following Brix and Diggle (2001) and Diggle et al (2005) (but ignoring temporal variation), the intensity is decomposed multiplicatively as

R(s,t) = \lambda(s)\exp\{\mathcal Y(s,t)\}.

In the above, the fixed spatial component, \lambda:R^2\mapsto R_{\geq 0}, is a known function, proportional to the population at risk at each point in space and scaled so that

\int_W\lambda(s)d s=1.

Before calling this function, the user must decide on the parameters, spatial covariance model, spatial discretisation, fixed spatial (\lambda(s)) component, mcmc parameters, and whether or not any output is required. Note there is no autorotate option for this function.

Value

the results of fitting the model in an object of class lgcpPredict

References

1. Benjamin M. Taylor, Tilman M. Davies, Barry S. Rowlingson, Peter J. Diggle (2013). Journal of Statistical Software, 52(4), 1-40. URL http://www.jstatsoft.org/v52/i04/

2. Brix A, Diggle PJ (2001). Spatiotemporal Prediction for log-Gaussian Cox processes. Journal of the Royal Statistical Society, Series B, 63(4), 823-841.

3. Diggle P, Rowlingson B, Su T (2005). Point Process Methodology for On-line Spatio-temporal Disease Surveillance. Environmetrics, 16(5), 423-434.

4. Wood ATA, Chan G (1994). Simulation of Stationary Gaussian Processes in [0,1]d. Journal of Computational and Graphical Statistics, 3(4), 409-432.

5. Moller J, Syversveen AR, Waagepetersen RP (1998). Log Gaussian Cox Processes. Scandinavian Journal of Statistics, 25(3), 451-482.

See Also

lgcpPredict KinhomAverage, ginhomAverage, lambdaEst, muEst, spatialparsEst, thetaEst, spatialAtRisk, temporalAtRisk, lgcppars, CovarianceFct, mcmcpars, setoutput print.lgcpPredict, xvals.lgcpPredict, yvals.lgcpPredict, plot.lgcpPredict, meanfield.lgcpPredict, rr.lgcpPredict, serr.lgcpPredict, intens.lgcpPredict, varfield.lgcpPredict, gridfun.lgcpPredict, gridav.lgcpPredict, hvals.lgcpPredict, window.lgcpPredict, mcmctrace.lgcpPredict, plotExceed.lgcpPredict, quantile.lgcpPredict, identify.lgcpPredict, expectation.lgcpPredict, extract.lgcpPredict, showGrid.lgcpPredict

lgcp documentation built on Oct. 3, 2023, 5:08 p.m.