Lecture 1

Question 1

What does assuming the correlation is a function of distance allow us to do with the individual correlations

Answer 1

It lets us replace it with a function of distance

corr(|x1,x2|) = f(|x1-x2|)

Question 2

What are the steps for making a Gaussian Process

Answer 2

i) Assume (xi) have a multivariate normal distribution
ii) Gives a mean vector of mu and a variance matrix \Sigma
iii) Assume we have constant variance \sigma^2 and we then make the correlation a function of distance
iv) Interpolate points intbetween the data using mean and covariance and n tends to infinity, replacing the correlation matrix with the correlation function

Question 3

Define a Gaussian Process

Answer 3

A continuous Stochastic Process defined by
a) a mean function mu(x)
b) Covariance function sigma(x1,x2)
c) x is a vector
d) All marginal, conditional and joint distributions are Gaussian