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How can we produce kappa and delta in the following model using Matlab?

Ask Time:2012-09-23T09:33:07         Author:

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I have a following stochastic model describing evolution of a process (Y) in space and time. Ds and Dt are domain in space (2D with x and y axes) and time (1D with t axis). This model is usually known as mixed-effects model or components-of-variation models

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I am currently developing Y as follow:

%# Time parameters
T=1:1:20; % input
nT=numel(T);

%# Grid and model parameters
nRow=100;
nCol=100;


[Grid.Nx,Grid.Ny,Grid.Nt] = meshgrid(1:1:nCol,1:1:nRow,T);

xPower=0.1;
tPower=1;
noisePower=1;
detConstant=1;

deterministic_mu = detConstant.*(((Grid.Nt).^tPower)./((Grid.Nx).^xPower));

beta_s = randn(nRow,nCol); % mean-zero random effect representing location specific variability common to all times

gammaTemp = randn(nT,1);

for t = 1:nT
    gamma_t(:,:,t) = repmat(gammaTemp(t),nRow,nCol); % mean-zero random effect representing time specific variability common to all locations
end

var=0.1;% noise has variance = 0.1
for t=1:nT
    kappa_st(:,:,t) = sqrt(var)*randn(nRow,nCol);
end

for t=1:nT
    Y(:,:,t) = deterministic_mu(:,:,t) + beta_s + gamma_t(:,:,t) + kappa_st(:,:,t);
end

My questions are:

  1. How to produce delta in the expression for Y and the difference in kappa and delta?
  2. Help explain, through some illustration using Matlab, if I am correctly producing Y?

Please let me know if you need some more information/explanation. Thanks.

Author:,eproduced under the CC 4.0 BY-SA copyright license with a link to the original source and this disclaimer.
Link to original article:https://stackoverflow.com/questions/12549056/how-can-we-produce-kappa-and-delta-in-the-following-model-using-matlab
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