new predict method API, and reduced sampling in input space

[odunbar]

Purpose

-Closes #400

To-do

• unit testing, [NB Reverse diff becomes very slow with encoding]
• example testing (Works on Sinusoid example)
• Docstrings on new get functions

Content

• For the predict() for both Emulator and ForwardMapWrapper
  • Added deprecation notice to transform_to_real=false kwarg
  • Added add_obs_noise_cov=false kwarg to predict. when set true, this adds the regularization to the machine learning tool
  • Added encode=nothing to the predict method, when set to "in", "out", "in_and_out" it will take in / push out encoded/decoded outputs.
  • When encoding inputs, with ForwardMapWrapper, samples are decoded into the output space before application

I add samples from the orthogonal complement of the LIS where necessary by drawing x ~ prior and then performing x_perp = x-D(E(x)) using the encoder-decoder pair

• this is used to go from reduced->full posterior samples
• this is also used used to evaluate the forward map wrapper on the reduced samples

Current settings: full (F) vs reduced (R) space

• Emulator space (R)
• MCMC: initial conditions (R)
• MCMC: computing likelihood (R)
• MCMC: stored prior distribution (F)
• MCMC: computing logpdf(prior,x) (F) (decoding current sample of subspace)
• MCMC: output posterior samples (F) (decoding each posterior sample + add orth complement)

Misc

• Bugfix for arguments of _predict , , -> ;

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• I have read and checked the items on the review checklist.