I have some simulated experiments where I generate some samples with an exponential correlation function. I am assuming a spatial grid whose variables form a multivariate gaussian distribution with an exponential correlation function and range r. I am assuming the mean of the gaussian is u.
Now if I add some noise to each of the observations like lets say noise with difference variances to each variable. Also suppose I also shift the mean by adding some noise in the mean as well.
How can I estimated the actual underlying values from these noisy observations using gaussian process.
In the case where I add the gaussian white noise, I could just plot the semi variogram fit a model and get the nugget parameter to know the amount of noise. But what in the case where I add noise with different variances to each variable.
Adding different noise levels will definitely make the observations non homogeneous.