Estimating the thing that is always given to you by oracles in statistics homework assignments. The meat of Gaussian process regression. A complement to Gaussian process simulation. Loosely speaking, if your stochastic distribution has only 2 free parameters and you can do mean and covariance estimation, you've done the whole thing.

To consider:

- relation to PCA.
- simulation of a field with a given covariance

Estimating the covariance, precision, concentration matrices of things. Turns about to be a lot more involved than estimating means in various ways and at various times. Long story.

- -matrix methods.

## Bayesian

Wishart priors.

## Sandwich estimators

For robust covariances of vector data. AKA Heteroskedasticity-consistent covariance estimators. Incorporating Eicker-Huber-White sandwich estimator, Andrews kernel HAC estimator, Newey-West and others.

https://eeecon.uibk.ac.at/~zeileis/papers/DAGStat-2007.pdf

## Parametric covariance functions

For spatial statistics or other Cartesian-ish indexed random fields. I am told I should look up Matérn covariance matrices for a parametric covariance field.

## To read

- Basic inference using Inverse Wishart by having a very basic “process model” that increases uncertainty of the covariance estimate as some convenient monotonic function of time, i should be able to get this one.
- general moment combination tricks
- John Cook's version

## Refs

- DiNe93: C. R. Dietrich, G. N. Newsam (1993) A fast and exact method for multidimensional gaussian stochastic simulations.
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*Journal of the Royal Statistical Society. Series B (Methodological)*, 15(1), 125–139. - Gray06: Robert M. Gray (2006) Toeplitz and Circulant Matrices: A Review.
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