Gaussian process Definition and 11 Threads

Hello, I am better studying the theory that is the basis of Bayesian optimization with a Gaussian Process and the acquisition function EI. I would like to expose what I think I understand and ask you to correct me if I'm wrong. The aim is to find the best ##\theta## parameters for a parametric...

I am looking at a surface where the height is described by a zero-mean gaussian process with cov(h_1,h_2)=\sigma^2\exp[-0.5\frac{(x_1-x_2)}{a^2}]. Given that h(x=0) = 0, what is the probability that a surface realization will go above the black line going from x=0 to infinity in the figure...

Hi, I remember seeing a few months ago, at a lecture about statistical signal processing, something which looked similar to commutation relations, only with a gaussian, instead of a delta function. Basically, it looked like this: $$\left[\phi(x),\phi(y)\right] = ie^{-\alpha(x-y)^2}$$ This...

Given a Gaussian process X(t), identify which of the following , if any, are gaussian processes. (a)X(2t) solution said that X(2t) is not gaussian process, since and similarly Given Poisson process X(t) (a) X(2t) soultion said that X(2t) is not poisson process, since same reason above...

written as title, 1. If X(t) is gaussian process, then Can I say that X(2t) is gaussian process? of course, 2*X(t) is gaussian process 2. If X(t) is poisson process, then X(2t) is also poisson process?

Hi guys, I have run multiple simulations on networks that are all slightly perturbed from each other. They produce slightly different curve outputs onto an x-y graph which I need to now analyse (it has been about 5 years since I did statistical analysis hence why I am here). A couple of the...

Hi everybody Any ideas how to simulate a Gaussian stationary process in R language using predefined variance and mean? I have a uni-variate normal distribution for my real life process Thank you

X = (Y(t))^2 where Y(t) is zero mean Gaussian process and correlation function R_YY = exp(-λ|τ|) i want to check if X is weakly stationary.So i guess for the first part, i checked if mean is constant σ^2=R_YY = exp(-λ|0|) = 1 E(X^2) = μ^2+ σ^2 = 1 since μ is zero and σ = 1 I wanted to check if...

Hi I have a stationary gaussian process { X_t } and I have the correlation function p(t) = Corr(X_s, X_(s+t)) = 1 - t/m, where X_t is in {1,2,..,m}, and I want to simulate this process. The main idea is to write X_t as sum from 1 to N of V_i, X_t+1 as sum from p+1 to N+p V_i and so on, where...

This is probably a stupid question, but here goes: based on the covariance function of some (centered, stationary) Gaussian process - how can one determine non-degeneracy (here I mean for any choice of a finite number of sampling times, the resulting RV is AC). Ideas?

How to prove the output of Linear Filtering a Gaussian Process is still Gaussian? It has been stated in many books I read, but none of them actually prove it. One even stated that "The technical mechinery to prove this property is beyond the scope of this book..." By definition, a Gaussian...