Material on relative vs. absolute tolerances (for tests and optimizers)

[jlperla]

Maybe in the optimizer/solver section

• Explain why it is sometimes tricky to pick tolerances due to scaling, etc.
• In tests, stick with defaults if possible and copy many numbers. Tell them how to get a printout of more digits
• The reason you can't test the comparison to 0 without an atol

Then in the style guide:

• Use defaults where possible, and not to clutter the interface. Probably better than you would pick

[Nosferican]

I don't think we use convolutional tolerance, but if we doing some material on the topic it might be worthwhile to mention it.

[jlperla]

I don't know about convolutional tolerances. Where do these things come up?

[Nosferican]

The basic idea is quite natural. For example, an algorithm for maximizing log-likelihood might use the difference or track the progress in relative terms rather than an absolute change.

Δ = abs(ℓℓ₀ - ℓℓ₁) / ℓℓ₀

a pretty simple concept that can help tune up convergence steps. It relates to the ambiguity of the scales or deciding what is good enough.

[jlperla]

Neat. We definitely should add that if we end up putting more structural estimation/etc. stuff in the course.

[Nosferican]

For long-term, I could contribute a GLM section if that would be beneficial.

[jlperla]

I think we should consider those in the spring. But my worry is that a major scope creep from "quantitative" economics towards empirical and statistics may be spread things too thin. I threw in a few basic examples in one of the lectures so that people could do basic statistics and data as part of the more general models, but I am not sure we want to go much further quite yet.

That said, I think a course/online set of lectures on econometrics and statistics in Julia would be amazing starting in about a year (when the AD, optimization, MCMC, etc. libraries have caught up to their potential).