Peter L Bernstein - Collected Quotes

"A normal distribution is most unlikely, although not impossible, when the observations are dependent upon one another - that is, when the probability of one event is determined by a preceding event. The observations will fail to distribute themselves symmetrically around the mean." (Peter L Bernstein, "Against the Gods: The Remarkable Story of Risk", 1996)

"All the law [of large numbers] tells us is that the average of a large number of throws will be more likely than the average of a small number of throws to differ from the true average by less than some stated amount. And there will always be a possibility that the observed result will differ from the true average by a larger amount than the specified bound." (Peter L Bernstein, "Against the Gods: The Remarkable Story of Risk", 1996)

"But real-life situations often require us to measure probability in precisely this fashion - from sample to universe. In only rare cases does life replicate games of chance, for which we can determine the probability of an outcome before an event even occurs - a priori […] . In most instances, we have to estimate probabilities from what happened after the fact - a posteriori. The very notion of a posteriori implies experimentation and changing degrees of belief." (Peter L Bernstein, "Against the Gods: The Remarkable Story of Risk", 1996)

"Probability theory is a serious instrument for forecasting, but the devil, as they say, is in the details - in the quality of information that forms the basis of probability estimates." (Peter L Bernstein, "Against the Gods: The Remarkable Story of Risk", 1996)

"So we pour in data from the past to fuel the decision-making mechanisms created by our models, be they linear or nonlinear. But therein lies the logician's trap: past data from real life constitute a sequence of events rather than a set of independent observations, which is what the laws of probability demand. [...] It is in those outliers and imperfections that the wildness lurks." (Peter L Bernstein, "Against the Gods: The Remarkable Story of Risk", 1996)

"Under conditions of uncertainty, both rationality and measurement are essential to decision-making. Rational people process information objectively: whatever errors they make in forecasting the future are random errors rather than the result of a stubborn bias toward either optimism or pessimism. They respond to new information on the basis of a clearly defined set of preferences. They know what they want, and they use the information in ways that support their preferences." (Peter L Bernstein, "Against the Gods: The Remarkable Story of Risk", 1996)

"Under conditions of uncertainty, the choice is not between rejecting a hypothesis and accepting it, but between reject and not - reject. You can decide that the probability that you are wrong is so small that you should not reject the hypothesis. You can decide that the probability that you are wrong is so large that you should reject the hypothesis. But with any probability short of zero that you are wrong - certainty rather than uncertainty - you cannot accept a hypothesis." (Peter L Bernstein, "Against the Gods: The Remarkable Story of Risk", 1996)

"Until we can distinguish between an event that is truly random and an event that is the result of cause and effect, we will never know whether what we see is what we'll get, nor how we got what we got. When we take a risk, we are betting on an outcome that will result from a decision we have made, though we do not know for certain what the outcome will be. The essence of risk management lies in maximizing the areas where we have some control over the outcome while minimizing the areas where we have absolutely no control over the outcome and the linkage between effect and cause is hidden from us." (Peter L Bernstein, "Against the Gods: The Remarkable Story of Risk", 1996)

"We can assemble big pieces of information and little pieces, but we can never get all the pieces together. We never know for sure how good our sample is. That uncertainty is what makes arriving at judgments so difficult and acting on them so risky. […] When information is lacking, we have to fall back on inductive reasoning and try to guess the odds." (Peter L Bernstein, "Against the Gods: The Remarkable Story of Risk", 1996)

"Whenever we make any decision based on the expectation that matters will return to 'normal', we are employing the notion of regression to the mean." (Peter L Bernstein, "Against the Gods: The Remarkable Story of Risk", 1996)