I really like this, particularly how the conceptual splits lead to the appropriate mitigations.
The best taxonomy of uncertainty I’ve ever seen is this great paper by some physicists reflecting on the Great Recession. It’s ordinal and gives a bit more granularity to the stats (“Opaque”) branch of your tree, and also has a (half-serious) capstone category for catching events beyond reason:
1. “Complete certainty”. You are in a Newtonian clockwork universe with no residuals, no observer effects, utterly stable parameters. So, given perfect information, you yield perfect predictions.
2. “Risk without uncertainty”. You know a probability distribution for an exhaustive set of outcomes. No statistical inference needed. This is life in a hypothetical honest casino, where the rules are transparent and always followed. This situation bears little resemblance to financial markets.
3. “Fully Reducible Uncertainty”. There is one probability distribution over a set of known outcomes, but parameters are unknown. Like an honest casino, but one in which the odds are not posted and must therefore be inferred from experience. In broader terms, fully reducible uncertainty describes a world in which a single model generates all outcomes, and this model is parameterized by a finite number of unknown parameters that do not change over time and which can be estimated with an arbitrary degree of precision given enough data. As sample size increases, classical inference brings this down to level 2.
4. “Partially Reducible Uncertainty”. The distribution generating the data changes too frequently or is too complex to be estimated, or it consists in several nonperiodic regimes. Statistical inference cannot ever reduce this uncertainty to risk. Four sources:(1) stochastic or time-varying parameters that vary too frequently to be estimated accurately; (2) nonlinearities too complex to be captured by existing models, techniques, and datasets; (3) non-stationarities and non-ergodicities that render useless the Law of Large Numbers, Central Limit Theorem, and other methods of statistical inference and approximation; and (4) the dependence on relevant but unknown and unknowable conditioning information...
5. “Irreducible uncertainty”. Ignorance so complete that it cannot be reduced using data: no distribution, so no success in risk management. Such uncertainty is beyond the reach of probabilistic reasoning, statistical inference, and any meaningful quantification. This type of uncertainty is the domain of philosophers and religious leaders, who focus on not only the unknown, but the unknowable.
This is great, thanks for sharing!