Understanding Uncertainty (2006)
- There are some things that you know to be true, and others that you know to be false; yet, despite this extensive knowledge that you have, there remain many things whose truth or falsity is not known to you. We say that you are uncertain about them. You are uncertain, to varying degrees, about everything in the future; much of the past is hidden from you; and there is a lot of the present about which you do not have full information. Uncertainty is everywhere and you cannot escape from it.
- Preface. p. xi
- Generally there is Stigler’s law of eponymy that says that a scientific notion is never attributed to the right person; in particular, the law is not due to Stigler.
- Prologue. p. xv
- Uncertainty is a personal matter; it is not the uncertainty but your uncertainty.
- 1. Introduction. p. 1
- It is not surprising that in talking about uncertainty we should lean heavily on facts, just as the court of law does when interrogating witnesses. Facts form a sort of bedrock on which we can build the shifting sands of uncertainty.
- 2. Stylistic Questions. p. 19
- Utility is the emotion pleading to be let into the house of pure reason and thereby enriching it.
- 2. Stylistic Questions. p. 20
- There is much evidence that people are not rational, in the economist’s sense; nor do they take into account expectation, in the precise interpretation of that word. As a result economic theory often does not correspond with what happens in the market. Some would argue that we need descriptive economics. I would argue that all should be taught about probability, utility, and MEU (maximization of expected utility) and act accordingly.
- 2. Stylistic Questions. p. 22
- In my opinion, it helps enormously to know why something is true, rather than being told it is true, for why should you believe me? Never believe anything on the authority of a single person but seek confirmation — and reason is the best confirmation.
- 2. Stylistic Questions. p. 24–25
- It is dangerous to attach probability zero to anything other than a logical impossibility.
- 5. The Rules of Probability. p. 64
- The grand assertion is that you must see the world through probability and that probability is the only guide you need.
- 5. The Rules of Probability. p. 66
- Whatever way uncertainty is approached, probability is the only sound way to think about it.
- 5. The Rules of Probability. p. 71
- It is not merely a question of calculating with probabilities but also one of relating the ingredients of your probability statements to reality. You do not need to think only about p(E|K) but also about the precise nature of E and K.
- 5. The Rules of Probability. p. 78
- In teaching there can be too much emphasis on certainty and a proper appreciation of uncertainty is to be encouraged.
- 6. Bayes Rule. p. 81
- Consider the case of a person who holds a view with probability 1. Then coherence says that it is no use having a debate with them because nothing will change their mind.
- 6. Bayes Rule. p. 91
- Almost all thinking people agree that you should not have probability 1 (or 0) for any event, other than one demonstrable by logic, like 2 x 2 = 4.
- 6. Bayes Rule. p. 91