Quantifying uncertainty
The primary way to quantify uncertainty is to use probability. Subject to certain axioms that aim to capture common-sense rules for quantifying uncertainty, probability theory is essentially the only way. (This is Cox's theorem.)
Other methods, such as fuzzy logic, may be useful, though they must violate common sense (at least as defined by Cox's theorem) under some circumstances. They may be still useful when they provide approximately the results that probability would have provided and at less effort and stay away from edge cases that deviate too far from common sense.
There are various kinds of uncertainty, principally epistemic uncertainty (lack of knowledge) and aleatory uncertainty (randomness), and various philosophies for how to apply probability. One advantage to the Bayesian approach is that it handles epistemic and aleatory uncertainty in a unified way.
Blog posts related to quantifying uncertainty:
- How loud is the evidence?
- The law of small numbers
- Example of the law of small numbers
- Laws of large numbers and small numbers
- Plausible reasoning
- What is a confidence interval?
- Learning is not the same as gaining information
- What a probability means
- Irrelevant uncertainty
- Probability and information
- False positives for medical papers
- False positives for medical tests
- Most published research results are false
- Determining distribution parameters from quantiles
- Fitting a triangular distribution
- Musicians, drunks, and Oliver Cromwell