Description Details Getting Started Bayesian computational methods Objects in sppmix External dependencies Use the help pages and please report errors! License Information Citation Author(s) References

This help page contains a summary of the features of
the R package `sppmix`

.

The main page for the package is at

http://faculty.missouri.edu/~micheasa/sppmix/index.html

including the package vignettes and R code with examples for each function of the package.

The `sppmix`

package implements classes and methods
for modeling spatial point process data using
Poisson point processes, where the intensity
surface is assumed to be a multiple of a finite
additive mixture with normal components.

Comprehensive accounts on modeling spatial point processes can be found in the books by Illian et al. (2008), Gelfand et al. (2010), Diggle (2014), and Baddeley, Rubak and Turner (2015).

The idea of using mixtures of normals for the intensity function is not entirely new (e.g., Thomas processes or Poisson cluster processes). However, the Bayesian framework (DAMCMC) for general mixtures for a fixed number of components were recently presented by Chakraborty and Gelfand (2010), and for a fixed or random number of components in the context of marked point processes, by Micheas (2014) (both DAMCMC and BDMCMC). In Zhou et al. (2015), the authors entertained space-time models based on Poisson point processes with mixture intensity surfaces.

The addition of marks and the introduction of time to a point pattern,
leads to general Marked Space-Time Poisson point processes, and
such models will be investigated in
future versions of the `sppmix`

package.

We recommend that you run the basic demos
in order to get a first taste of the capabilities
of `sppmix`

. Simply run

`Demo_sppmix(#)`

in order to view the available demos and
tutorials (vignettes), by choosing an appropriate
number #. A call `Demo_sppmix()`

will bring up
a browser with all the available vignetters of the package.
The following demos are available:

1) Defining, generating, working with and basic plotting of sppmix objects.

2) Plotting in the sppmix package.

3-6) How to perform model fitting for a Poisson point process with intensity surface assumed to be a mixture of normals. There are 4 cases discussed: fixed or random number of components and edge effects are considered or not considered.

7) Model checking in the sppmix package.

8) Perform model fitting for a (discrete) marked Poisson point process with ground (locations process) intensity surface assumed to be a mixture of normals.

Data Augmentation MCMC (DAMCMC by Diebolt and Robert, 1994,
function `est_mix_damcmc`

)
and Birth-Death MCMC (BDMCMC by Stephens, 2000, function `est_mix_bdmcmc`

)
are the two main MCMC methods we have implemented
for estimating the parameters of the Poisson intensity surface, in
a Bayesian framework. The intensity surface consists
of a parameter `lambda`

, interpreted as the
average number of points over the window of observation
and the mixture component parameters, including
the component probabilities `ps`

, the component means `mus`

, and
the component covariances `sigmas`

. See the details
section of the function `rsppmix`

. The
latter function is used for sampling a point pattern from the Poisson point process.

`sppmix`

We introduce an object of class `normmix`

for
handling 2d mixtures of bivariate normal components. This
helps us build the Poisson point process
intensity surface as an object of class `intensity_surface`

.

The DAMCMC and BDMCMC functions, return objects `damcmc_res`

and
`bdmcmc_res`

, respectively, representing the fitted model
parameters, as well as, a plethora of information. The functions
`plot`

and `summary`

can then be applied to these objects
to obtain additional information. See
`plot.damcmc_res`

,
`plot.bdmcmc_res`

,
`summary.damcmc_res`

, and
`summary.bdmcmc_res`

, for more details.

We link and require several R packages, including
`spatstat`

, `rgl`

,
`ggplot2`

,
`Rcpp`

, `RcppArmadillo`

, `fields`

,
and `mvtnorm`

.

In particular, we utilize the `ppp`

and `owin`

classes
from the `spatstat`

package in order to
describe a point pattern.

The MCMC algorithms are implemented in C++ using
`Rcpp`

and `RcppArmadillo`

, and were
optimized after extensive testing, meaning that this approach
is significantly faster than some other implementations of 2d mixture models.

Plotting is accomplished using the `rgl`

package in order to create 3d plots of the
intensity surfaces. In addition, the `fields`

and `ggplot2`

packages were used for 2d plots.

There are many examples in the help pages of
each and every function in the `sppmix`

package. You will find all the answers you need there,
in the demos and in the vignettes.

But just in case we missed something, or if you find a typo, or a mistake or have any other suggestions feel free to contact the package maintainer Sakis Micheas.

All code in this package is copyright Sakis Micheas and Jiaxun Chen and is released under the MIT license (https://cran.r-project.org/web/licenses/MIT).

Furthermore, a lot of our examples utilize the `PlotUSAStates`

function
which requires the Cartographic Boundary Shapefiles (boundary data) provided by the
USA Census Bureau at https://www.census.gov/geo/maps-data/data/tiger-cart-boundary.html.
To our knowledge there is no special license required to use this data.

If you use the `sppmix`

package in your research, we would appreciate a citation.

In order to cite the `sppmix`

package in publications
please use:

Micheas, A., and Chen, J. (2017): sppmix-Modeling spatial Poisson and related point processes using normal mixture models. R package. Package website: http://faculty.missouri.edu/~micheasa/sppmix/index.html.

Jiaxun Chen (Author and Creator) chenjiaxun9@hotmail.com.

Athanasios (Sakis) Christou Micheas (Author and Maintainer) micheasa@missouri.edu

Significant contributions on the package skeleton creation, plotting functions and other code by Yuchen Wang ycwang0712@gmail.com

Diebolt, J., and Robert, C. P. (1994). Estimation of Finite Mixture Distributions through Bayesian Sampling. Journal of the Royal Statistical Society B, 56, 2, 363-375.

Stephens, M. (2000). Bayesian analysis of mixture models with an unknown number of components-an alternative to reversible jump methods. The Annals of Statistics, 28, 1, 40-74.

McLachlan, G., and Peel, D. (2000). Finite Mixture Models. Wiley-Interscience.

Jasra, A., Holmes, C.C. and Stephens, D. A. (2005). Markov Chain Monte Carlo Methods and the Label Switching Problem in Bayesian Mixtures. Statistical Science, 20, 50-67.

Illian, J., Penttinen, A., Stoyan, H. and Stoyan, D. (2008) Statistical Analysis and Modelling of Spatial Point Patterns. Wiley.

Chakraborty, A., and Gelfand, A.E. (2010). Measurement error in spatial point patterns. Bayesian Analysis, 5, 97-122.

Gelfand, A.E., Diggle, P.J., Fuentes, M. and Guttorp, P., editors (2010) Handbook of Spatial Statistics. CRC Press.

Diggle, P.J. (2013) Statistical Analysis of Spatial and Spatio-Temporal Point Patterns, Third edition. Chapman and Hall/CRC.

Micheas, A. C. (2014). Hierarchical Bayesian Modeling of Marked Non-Homogeneous Poisson Processes with finite mixtures and inclusion of covariate information. Journal of Applied Statistics, 41, 12, 2596-2615.

Zhou, Z., Matteson, D.S., Woodard, D.B., Henderson, S.G., and Micheas, A.C. (2015). A Spatio-Temporal Point Process Model for Ambulance Demand. Journal of the American Statistical Association, 110, 509, 6-15.

Baddeley, A., Rubak, E. and Turner, R. (2015) Spatial Point Patterns: Methodology and Applications with R. Chapman and Hall/CRC Press.

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