# Statistical analysis of environmental space-time processes

### Description

EnviroStat provides functions for spatio-temporal modeling of environmental processes and designing monitoring networks for them based on an approach described in Le and Zidek (2006).

### Details

The modeling approach offered by this package has a number of features:

Conditional on knowing the process parameters the environmental process is assumed to have (after a suitable transformation if necessary) to be a Gaussian random field (GRF).

At every spatial location, the process can yield a multiplicity of random responses such as air pollutant concentrations.

The approach used in the package lies within a Bayesian hierarchical modeling framework However for computational expediency empirical shortcuts are made at higher levels of the hierarchical setup. Thus for example most hyperparameters are fitted using a type II maximum likelihood approach, eliminating the need for the the user to specify them. Thus the package can handle large fields of monitoring networks, say with 600 or more spatial sites.

The approach does not assume a stationary GRF. Instead it takes a nonparametric approach where the spatial covariance matrix is left completely unspecified and instead endowed with a prior distribution with a hypercovariance matrix that can be modeled at level two of the hierarchy, making the method quite robust against non-stationarity in the random field.

It presents a approach for designing monitoring networks based on the well-known warping method of Sampson and Guttorp (1992) as developed with Wendy Meiring.

It allows for missing data, providing that these data are missing in blocs of time, which after a regional trend is fitted, then become exchangeable. For then the blocs of residuals can be permuted the get a decreasing or increasing staircase pattern in the data matrix something that is required in the approach.

It has been empirically assessed in a number of major applications and found to yield well calibrated prediction intervals. For example, a 95% interval will cover their predictands about 95% of the time.

### Author(s)

Nhu Le, Jim Zidek, Rick White, and Davor Cubranic.

Fortran code for Sampson-Guttorp estimation authored by Paul D. Sampson, Peter Guttorp, Wendy Meiring, and Catherine Hurley.

Maintainer: Davor Cubranic <cubranic@stat.ubc.ca

### References

Le, Nhu D. and James V. Zidek. Statistical Analysis of Environmental Space-Time Processes. Springer, New York, 2006.

### See Also

See the package vignette for a guided example of complete analysis using the package and the manual for details of individual functions.