A function to deliver fully Bayesian inference for a multitype spatial log-Gaussian Cox process.
lgcpPredictMultitypeSpatialPlusPars(
formulaList,
sd,
typemark = NULL,
Zmat = NULL,
model.priorsList,
model.initsList = NULL,
spatial.covmodelList,
cellwidth = NULL,
poisson.offset = NULL,
mcmc.control,
output.control = setoutput(),
gradtrunc = Inf,
ext = 2,
inclusion = "touching"
)an object of class formulaList, see ?formulaList. A list of formulae of the form t1 ~ var1 + var2 etc. The name of the dependent variable must correspond to the name of the point type. Only accepts 'simple' formulae, such as the example given.
a marked ppp object, the mark of interest must be able to be coerced to a factor variable
if there are multiple marks, thrun the MCMC algorithm for spatial point process data. Not for general purpose use.is sets the name of the mark by which
design matrix including all covariate effects from each point type, constructed with getZmat
model priors, a list object of length the number of types, each element set using lgcpPrior
list of model initial values (of length the number of types). The default is NULL, in which case lgcp will use the prior mean to initialise eta and beta will be initialised from an oversispersed glm fit to the data. Otherwise use lgcpInits to specify.
list of spatial covariance functions (of length the number of types). See ?CovFunction
the width of computational cells
A list of SpatialAtRisk objects (of length the number of types) defining lambda_k (see below)
MCMC paramters, see ?mcmcpars
output choice, see ?setoutput
truncation for gradient vector equal to H parameter Moller et al 1998 pp 473. Default is Inf, which means no gradient truncation, which seems to work in most settings.
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.
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.
an object of class lgcpPredictMultitypeSpatialPlusParameters
See the vignette "Bayesian_lgcp" for examples of this code in use.
We suppose there are K point types of interest. The model for point-type k is as follows:
X_k(s) ~ Poisson[R_k(s)]
R_k(s) = C_A lambda_k(s) exp[Z_k(s)beta_k+Y_k(s)]
Here X_k(s) is the number of events of type k in the computational grid cell containing the point s, R_k(s) is the Poisson rate, C_A is the cell area, lambda_k(s) is a known offset, Z_k(s) is a vector of measured covariates and Y_i(s) where i = 1,...,K+1 are latent Gaussian processes on the computational grid. The other parameters in the model are beta_k , the covariate effects for the kth type; and eta_i = [log(sigma_i),log(phi_i)], the parameters of the process Y_i for i = 1,...,K+1 on an appropriately transformed (again, in this case log) scale.
We recommend the user takes the following steps before running this method:
Compute approximate values of the parameters, eta, of the process Y using the function minimum.contrast. These approximate values are used for two main reasons: (1) to help inform the size of the computational grid, since we will need to use a cell width that enables us to capture the dependence properties of Y and (2) to help inform the proposal kernel for the MCMC algorithm.
Choose an appropriate grid on which to perform inference using the function chooseCellwidth; this will partly be determined by the results of the first stage and partly by the available computational resource available to perform inference.
Using the function getpolyol, construct the computational grid and polygon overlays, as required. As this can be an expensive step, we recommend that the user saves this object after it has been constructed and in future reference to the data, reloads this object, rather than having to re-compute it (provided the computational grid has not changed).
Decide on which covariates are to play a part in the analysis and use the lgcp function getZmat to interpolate these onto the computational grid. Note that having saved the results from the previous step, this is a relatively quick operation, and allows the user to quickly construct different design matrices, Z, from different candidate models for the data
If required, set up the population offset using SpatialAtRisk functions (see the vignette "Bayesian_lgcp"); specify the priors using lgcpPrior; and if desired, the initial values for the MCMC, using the function lgcpInits.
Run the MCMC algorithm and save the output to disk. We recommend dumping information to disk using the dump2dir function in the output.control argument because it offers much greater flexibility in terms of MCMC diagnosis and post-processing.
Perform post-processing analyses including MCMC diagnostic checks and produce summaries of the posterior expectations we require for presentation. (see the vignette "Bayesian_lgcp" for further details). Functions of use in this step include traceplots, autocorr, parautocorr, ltar, parsummary, priorpost, postcov, textsummary, expectation, exceedProbs and lgcp:::expectation.lgcpPredict
Benjamin M. Taylor, Tilman M. Davies, Barry S. Rowlingson, Peter J. Diggle. Bayesian Inference and Data Augmentation Schemes for Spatial, Spatiotemporal and Multivariate Log-Gaussian Cox Processes in R. Submitted.
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/
Brix A, Diggle PJ (2001). Spatiotemporal Prediction for log-Gaussian Cox processes. Journal of the Royal Statistical Society, Series B, 63(4), 823-841.
Diggle P, Rowlingson B, Su T (2005). Point Process Methodology for On-line Spatio-temporal Disease Surveillance. Environmetrics, 16(5), 423-434.
Wood ATA, Chan G (1994). Simulation of Stationary Gaussian Processes in [0,1]d. Journal of Computational and Graphical Statistics, 3(4), 409-432.
Moller J, Syversveen AR, Waagepetersen RP (1998). Log Gaussian Cox Processes. Scandinavian Journal of Statistics, 25(3), 451-482.
linkchooseCellWidth, getpolyol, guessinterp, getZmat, addTemporalCovariates, lgcpPrior, lgcpInits, CovFunction lgcpPredictSpatialPlusPars, lgcpPredictAggregateSpatialPlusPars, lgcpPredictSpatioTemporalPlusPars, ltar, autocorr, parautocorr, traceplots, parsummary, textsummary, priorpost, postcov, exceedProbs, betavals, etavals