Vignette demonstrating inference via pathfinder and Laplace

[athowes]

To include:

• Showing how you would use pathfinder and Stan's Laplace method rather than NUTS
• A comparison of the inference results using pathfinder, Laplace, and NUTS for a small number of data sets (which ones? Ebola?)
• Suggestions about when you would and wouldn't want to use pathfinder or Laplace over NUTS

Edit: updated.

[athowes]

As of March 18 both pathfinder and some type of Laplace approximation are supported: paul-buerkner/brms#1591

[athowes]

Discussion with @kgostic and @seabbs:

• Evaluation once per delay rather than once per individual could speed things up, but would require quite significant model changes
• To what extent do we have model fitting times issues? Suggestion that we do have issues

[athowes]

Discussion with @seabbs:

• brms also enables within-chain multi-threading
• If evaluating methods to speed up inference we should consider looking at this as it is an option which shouldn't have approximation error.