# sim.dpp.modal.nystrom: Draw samples from the conditional DPP design emulator using... In demu: Optimal Design Emulators via Point Processes

## Description

sim.dpp.modal.nystrom() uses the DPP-based design emulator of Pratola et al. (2018) to draw a sample of the n-run optimal design for a Gaussian process regression model with stationary correlation function r(x,x^\prime), where the entries of R are formed by evaluating r(x,x^\prime) over a grid of candidate locations. This function uses a grid-based Nystrom approximation based on the passed matrix X to avoid constructing a large correlation matrix if dimension ngrid^p and its subsequent eigendecomposition.

## Usage

 1 sim.dpp.modal.nystrom(Xin,rho,n=0,ngrid=NULL,method="Nystrom") 

## Arguments

 Xin A initial n\times p matrix of points. rho The p\times 1 parameter vector for the Gaussian correlation model. n Size of the design to sample from the candidate grid. ngrid Size of the candidate grid will be ngrid^p. method Type of approximation to use. Currently only supports “Nystrom”.

## Details

For more details on the method, see Pratola et al. (2018). Detailed examples demonstrating the method are available at http://www.matthewpratola.com/software.

## Value

A list containing the candidate points constructed and the points selected as the design sites from this candidate set as well as their indices.

## References

Pratola, Matthew T., Lin, C. Devon, and Craigmile, Peter. (2018) Optimal Design Emulators: A Point Process Approach. arXiv:1804.02089.

demu-package sim.dpp.modal sim.dpp.modal.nystrom.kmeans
  1 2 3 4 5 6 7 8 9 10 11 12 13 library(demu) # Starting design X=matrix(runif(10*2),ncol=2) rho=rep(0.01,2) n=10 ngrid=11 samp=sim.dpp.modal.nystrom(X,rho,n,ngrid) samp$design # Could plot the result: # plot(samp$X,xlim=c(0,1),ylim=c(0,1)) # points(samp$X[samp$pts,],pch=20)