## Friday, April 23, 2010

### Two interpretations of probability

To many of my readers this will be old hat; I wrote about the topic only a short time ago in "Plight of the Fortune Tellers: two views of probability." But let’s have another go at it anyway. Terje Aven in Misconceptions of Risk distinguishes between the frequentist and the subjective (which he upgrades to the knowledge-based) views of probability.

A frequentist probability is the percentage of “successes” if an experiment is repeated an infinite number of times. Since this definition defies empirical replication we need to estimate the probability. We do this with standard statistical calculations. Yet even here, Aven argues, “the estimation error is expressed by confidence intervals and the use of second-order knowledge-based probabilities.” (p. 31) That is, knowledge-based probabilities (even if at a meta-level) are an integral part of calculating frequency-based probabilities.

We don’t have to agonize unduly over sullying frequentist theories of probability with the intrusion of meta-order gunk since they never adequately explained Wall Street action in the first place. So on to the subjective view of probability. Here “probability is a measure of uncertainty about future events and consequences, seen through the eyes of the assessor and based on some background information and knowledge.” (p. 32) Uncertainty is the fundamental concept, probability a tool used to express this uncertainty. Probability is a measure of our best guesses based on available knowledge.

The problem is that our available knowledge may be flawed or woefully incomplete, our assumptions may be off base, and we may not have noticed that black swan swimming in the pond. Probability assignments often camouflage uncertainties. To take Aven’s example, assume that the management of an offshore oil installation is concerned about leakages and undertakes a special maintenance regime. The risk assessor, after compiling background information on the effectiveness of this maintenance program, assigns a leakage probability of 10%. This number, however painstakingly derived, masks a host of hidden uncertainties about corrosive forces at work that could result in unpleasant surprises. If we focus exclusively on the probability assignment we will not have captured the essence of risk. In Aven’s words, “It is common to define and describe risk using probabilities and probability distributions. However, . . . the estimated or assigned probabilities are conditioned on a number of assumptions and suppositions. They depend on background knowledge. Uncertainties are often hidden in such background knowledge, and restricting attention to the estimated or assigned probabilities could camouflage factors that could produce surprising outcomes. By jumping directly into probabilities, important uncertainty aspects are easily truncated, meaning that potential surprises could be left unconsidered.” (p. 31) Uncertainty, Avens contends, should be the pillar of risk, not probability.