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Research

ppsds answers one question from two sides: how well can a system you only partly know be predicted? The ceiling is a property of a system you know exactly; the floor is what a predictor can guarantee over a set of systems you are willing to admit. These are the papers the package implements.

Paper Venue Question On this site
Probabilistic Predictability of Stochastic Dynamical Systems Automatica How well could any predictor do on a system known exactly? Paper · Experiment · Example
Distributionally Robust Probabilistic Prediction for Stochastic Dynamical Systems IEEE Transactions on Automatic Control What can a predictor guarantee when the system is known only through an ambiguity set? Paper · Experiment · Example

Two things to take away

  1. A predictor does not become better by having a worse model. What decides how well this works is the declaration you write, not how accurate your model is.
  2. The guarantee is conditional, and the condition is that declaration. Nothing in the library can check it for you. diagnose() can tell you what your residuals look like; it cannot tell you whether the set you wrote down contains the system you are actually running.

Before the papers

Both papers assume the same small vocabulary. In brief:

  • A probabilistic prediction is a distribution over the next state, judged by a scoring rule.
  • An ambiguity set is the set of systems you are willing to admit. The worst case ranges over that set and nothing else.
  • There are two different pairs of bounds: one pair sits inside a single ambiguity set, the other compares a system known exactly against one known only through a set.
  • The guarantee is conditional on the declaration. Every limit follows from that.

The full treatment, written for a reader who has not opened either paper, is Preliminaries. Each paper page then takes one side and goes all the way down.

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