NScluster-package {NScluster}

Simulation and Estimation of the Neyman-Scott Type Spatial Cluster Models

Description

NScluster involves the maximum Palm likelihood estimation procedure for Neyman-Scott cluster point process models and their extensions with parallel computation using OpenMP technology. The maximum Palm likelihood estimates (MPLEs for short) are those that maximize the log-Palm likelihood function. The computation of MPLEs is implemented by simplex maximization with parallel computation via OpenMP. Together with the likelihood estimation procedure, NScluster also provides a simulation procedure for cluster point process models.

Details

The documentation 'A Guide to NScluster: R Package for Maximum Palm Likelihood Estimation for Cluster Point Process Models using OpenMP' is available in the package vignette using the vignette function (e.g., vignette("NScluster")).

The package NScluster comprises of four tasks: simulation, parameter estimation (MPLE), confidence interval estimation, and non-parametric and parametric Palm intensity comparison.

• Simulation:

  The sim.cppm function simulates the five cluster point process models: the Thomas and Inverse-power type models, and the extended Thomas models of type A, B, and C.

• Parameter estimation (MPLE):

  The mple.cppm function improves the given initial parameters using the simplex method to maximize the log-Palm likelihood function.

  The expensive calculation of the estimation for calculating the parameters can be parallelized to reduce calculation time. The package is implemented to employ OpenMP, which is a simple framework for shared memory parallel computation.

• Confidence interval of parameter estimates:

  The boot.mple function carries out the bootstarp replicates for an object generated by mple.cppm and computes confidence intervals and standard errors.

• Palm intensity comparison:

  The package can depict non-parametric and parametric normalized Palm intensity function of the five cluster point process models using the palm.cppm function.

References

Tanaka, U., Ogata, Y. and Katsura, K. (2008) Simulation and estimation of the Neyman-Scott type spatial cluster models. Computer Science Monographs 34, 1-44. The Institute of Statistical Mathematics, Tokyo. https://www.ism.ac.jp/editsec/csm/

Tanaka, U., Ogata, Y. and Stoyan, D. (2008) Parameter estimation and model selection for Neyman-Scott point processes. Biometrical Journal 50, 43-57.

Tanaka, U., Saga, M. and Nakano, J. (2021) NScluster: An R Package for Maximum Palm Likelihood Estimation for Cluster Point Process Models Using OpenMP. Journal of Statistical Software, 98(6), 1-22. doi:10.18637/jss.v098.i06.