# E9. To be completed after lesson 25¶

## Exercise 9.1¶

Discuss the relationship between these two statements.

\begin{align} &1.\quad f \sim \text{GP}(m(\mathbf{x}), k(\mathbf{x}, \mathbf{x}';\theta_k)), \\[1em] &2.\quad \mathbf{f} \sim \mathrm{MultiNorm}(\mathbf{m}(\mathbf{X}), \mathsf{K}), \\[1em] \end{align}

where the entries in $$\mathsf{K}$$ are given by $$K_{ij} = k(\mathbf{x}_i, \mathbf{x}_j';\theta_k)$$.

## Exercise 9.2¶

Are Gaussian processes useful for extrapolation? That is, say we measured $$y$$ values on an interval $$[x_\mathrm{start}, x_\mathrm{end}]$$. Could we use a Gaussian process to estimate what values of $$y$$ we might get for $$x > x_\mathrm{end}$$?

## Exercise 9.3¶

When we have a GP prior and a Normal likelihood, there are some really fortuitous consequences. What are they?

## Exercise 9.4¶

Write down any additional questions you have.