R: Computation of log likelihood ratios for Markov point process models.

pathsampling.mpp {MppMLE}

R Documentation

Computation of log likelihood ratios for Markov point process models.

Description

Log likelihood ratios for Markov point processes are computed using path sampling and importance sampling.

Usage

pathsampling.mpp=function(inhompar0,interactpar0,inhompar1,interactpar1,interactradii,nogrid,smpsize,space,data,border,model,torus=F)

Arguments

`inhompar0, interactpar0, inhompar1, interactpar1, interactradii`	parameters for Markov point processes, see details on models
`nogrid`	number of quadrature points in trapezoidal approximation of inner integral in pathsampling formula
`smpsize`	size of MCMC sample used for estimation of score and observed information
`space`	specifies subsampling of birth-death Markov chain
`data`	a `ppp` `spatstat` object.
`border`	border correction. The reduced observation window is obtained by trimming off a margin of width `border` from the observation window of the data pattern. If zero, no border correction is used.
`torus`	if true, toroidal edge correction is used.

Details

This function computes log likelihood ratios corresponding to two sets of parameters for a Markov point process model. Note same interaction radii is used for both sets of parameters. The computational methods are pathsampling and importance sampling, see Moeller and Waagepetersen (2003) for details.

data

The observation window must be of type rectangular

models

0 is the multiscale process. In this case interactradii[1] specifies the maximal interaction range and interactionradii[2] specifies the number of intervals (of same length) with different interaction parameters. The interaction parameters are given in interactpar. The vector inhompar should have one component: the first order interaction potential (AKA the chemical activity).

1 implements the overlap process used for Norwegian spruces data in Moeller and Waagepetersen (2003). In this case interactradii[0] specifies the factor for computing influence zones.

2 is a multitype (0 or 1) Strauss process where inhompar contains coefficients for a fourth-order polynomial in the y coordinate while interactpar contains 3 interactionparameters for interactions between type 0 points, between type 0 and type 1 points, and between type 1 points. The interaction radius is given in interactradii.

3 is as 2 but only one interactionparameter is used regardless of type of the points.

4 is the hierarchical model used for ants's nests in Moeller and Waagepetersen (2006).

Value

A list with components: loglikeratio, loglikeratioimp (log likelihood ratios computed using pathsampling and importance sampling, respectively), part (parameter values along path), and integrand (values of integrand for inner integral in pathsampling formula evaluated at quadrature points).

Author(s)

Rasmus Waagepetersen rw@math.aau.dk http://www.math.aau.dk/~rw

References

Moeller, J. and Waagepetersen, R. (2003) Statistical inference and simulation of spatial point processes. Chapman & Hall/CRC Press, Boca Raton.

Moeller, J. and Waagepetersen, R. (2006) Modern statistics for spatial point processes. (prepared as a discussion paper for Scandinavian Journal of Statistics).