# cope: Coverage Probability Excursion (CoPE) Sets In maxsommerfeld/cope: Coverage Probability Excursion (CoPE) Sets

## Description

The package cope computes and plots CoPE sets defined in Sommerfeld, Sain and Schwartzman (2015) for 2D functions. CoPE sets for a real-valued target function μ(s) on a two-dimensional domain are designed to bound the excursion set {μ(s) >= c} from above and below with a predefined probability. The target function can be a parameter in spatially indexed linear regression Y(s)=X*b(s)+ ε(s), where s is the spatial location, X is a known n by p design matrix, ε(s) is an error field and Y(s) is the observed data.

## Major functions

• `ComputeCope` Computes CoPE sets for 2D data.

• `PlotCope` Plots CoPE sets.

## Toy example functions

• `ToySignal` Generates a toy signal.

• `ToyNoise1`, `ToyNoise2`, `ToyNoise3` Generates realizations of toy noise fields.

## References

M. Sommerfeld, S. Sain and A. Schwartzman. Confidence regions for excursion sets in asymptotically Gaussian random fields, with an application to climate. Preprint, 2015.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12``` ```# An example using the ToySignal and the Toy Noise1 of this package. # Set sample size. n = 30 # Generate n realizations of the toy noise field. Data = ToyNoise1(n = n) # Add the toy signal to the noise. Data\$z = Data\$z + rep(ToySignal()\$z, n) # Compute the CoPE sets. CopeSet = ComputeCope(Data,level=4/3, mu=ToySignal()\$z) # Plot the result. PlotCope(CopeSet) ```

maxsommerfeld/cope documentation built on May 21, 2017, 11:15 p.m.