Hidden Dynamics (ex Decision Making) T2 E3/E4 suggestion

[JesseLivezey]

In E2, we assume that the hidden state is changing and we don't have new observations and we look at how our estimate of our latent state gets worse over time.

Currently in E3, we go back to assuming a fixed hidden state and look at how incorporating observations changes things. I think this setup is a bit counter-intuitive for T2 since the model naturally has changing hidden states so this setup investigates a case that is more similar to T1. It is also difficult to compare E3 to E2 for this reason.

Suggestion:

• Make E3 forward inference in a model with changing latent states. Visualize a single trial and its estimate.
• E4 could visualize inference using the posterior for a single trial, then plot the summary plot like in current E3 except just plot accuracy for the changing hidden state rather than P(x=0).