Extend new data processing tools to handle the high-dimensional output covariance structures from EKP

[odunbar]

Issue

Given an ObservationSeries how can we integrate this into the CES pipeline from the EKP?

Scope for Solution

I believe there are several items to address

• Scalable types and Dim reduction: Looking at Observations.jl of EKP We see that the observational covariances may be of different types Notably SVDplusD. We should investigate how to handle and use such compact matrix types in Emulator particularly if these must be used in the dimension reduction procedures.
• Minibatching from EKP: different data samples, with fixed obs_noise_cov If we assume fixed obs. covariance, but have many data, this currently is passed into MCMC as a vertor of data. Should be a quick change to instead take in the observation series.
• Minibatching from EKP: different data samples and obs_noise_cov's This is a more challenging problem for data processing... I Imagine a solution would require first whitening each EKP iteration with it's respective noise cov, for training the emulator in a unified space, then during sampling, whitening each data sample with their respective noise in the likelihood.
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