Diagnostics and plots for Pushforward of prior

[odunbar]

Issue

When leaving settings of perfect model-data pairings it is common to have prior or model misspecification. Catching these early, (i.e. before the algorithm iterates) would save users some time.

Suggestions

The user creates the EKP setting, generates and runs the initial ensemble.

• We could add recipes that plot the following lines: (1) y,G(\theta_i) with ribbondiag(\Gamma) (2) \Gamma^{-1/2}y, \Gamma^{-1/2}G(\theta)_i) with ribbon I. This could be extended to any iteration, for example, plot_pushforward(ekp,i) for plotting the pushforward of iteration i.
• Some quick diagnostic to evaluate the consistency of the truth and prior.
• ...