In my previous post, Nassim Nicholas Taleb Explains It All, I noted the feeling that Taleb had something important to tell me, but I was having a hard time figuring out the practical implications of what he was trying to tell me.
I have gone back to his web site a few times and looked at random items for which he has links. True to the very randomness he has been describing, I suddenly and unexpectedly came across an item that has taken me to the next level of understanding.
His link Mandelbrot Makes Sense points to a document that contains two articles by Taleb. The article titles are “Mandelbrot Makes Sense: A Book Review Essay A discussion of Benoit Mandelbrot’s The (Mis)Behavior of Markets” and “Fat Tails, Asymmetric Knowledge, and Decision Making Nassim Nicholas Taleb’s Essay in honor of Benoit Mandelbrot’s 80th birthday.”
The best teaser that I can come up with are a few paragraphs from a few sections of the second article.
The central problem of uncertainty
What I call the central epistemological problem of uncertainty is summarized as follows: we do not observe probability distributions, only random draws from an unspecified generator. So we need data to figure out the probability distribution. How do we gauge the sufficiency of the size of the sample? Well, from the probability distribution. If at the same time one needs data to figure out the probability distribution, and the probability distribution to figure out if we have enough data, then we have a severe circular epistemological problem.
When, many years ago, I first came across the explanation of measuring the error in statistical sampling I thought I had gained a great insight into some of the mysteries of statistics. I might have felt queasy about the reasoning for a moment, but the skepticism had been beaten out of me enough to put aside the realization of the circular reasoning involved.
Finally he did discuss, in a way that was finally understandable to me, what to do with his insights into the flaws of applying inappropriate models of the statistics of stock markets.
An easier solution
As an operator first and last, I believe that there are, however, far more elementary (and practical) ways to deal with this problem, or at least to protect ourselves from its ill effects. How? I propose two approaches.
First, consider Pascal’s wager. We can change our payoff structure to accommodate what absence of knowledge we suffer from, and with respect to which moments of the distribution. For instance, if the data has “infinite” (or undefined) variance, one can avoid exposure to such infinite tail by clipping the sensitivity to the offending part of the distribution. Purchasing a simple derivative(say, an extremely out-of-themoney call), if it such product is available, may provide a solution. Our doubt can be targeted and remedied by transactions. Tout simplement.
I am not saying that I understand everything he is saying as much as I would like to, but the dawn is starting to dawn on me.
When I talk about skepticism being beaten out of me, I refer to a quite few incidents in my engineering career. The more I think about mentioning them, the more I realize that there are so many that I will have to select just one.
The first half of my career revolved around the support and development of software to simulate the behavior of integrated circuits and the processes that were used to manufacture those circuits. I was in regular contact with several of the leading academics in this field. At one point, one of these academics tried to sell me on the latest research of his students. He was promoting the statistical analysis of behavior of circuits and processes. I never could feel comfortable with how this could work in practice. It was quite uncomfortable to play the part of the persistent skeptic who kept asking for a satisfactory proof that was beyond what the purveyors of the techniques were quite willing to accept as proof for themselves.
A second thing that really hit home about what Taleb was saying harks back to an incident in Freshman year at MIT. I was trying to get ideas for a paper I had to write about Plato. I asked a friend what he was going to write about. He particularly liked the part in the book where the logic says that if A implies B and B implies C and C implies A, then A, B, and C must be true. I told him that this was circular reasoning and there was nothing about the truth of A, B, and C that one could glean from their implied relationships. He did not take my advice to find something else to write about. I chose to write about my frustration at the logical Sophistry used in the book.
When the professor handed out the graded papers, my paper got a D, the highest grade I had ever received in this class. Not only did my friend get an A, but the professor chose to read to the class the very section of his paper that I had cautioned him about.
I still tell this story when the occasion arises. I still believe my friend and the professor where both wrong. What amazes me about what I read in Taleb’s papers was that I had failed to consciously come to grips with the circular reasoning in some of the mathematics that I had come to accept over the years. I emphasize “consciously”, because I think my gut always made me nervous about these ideas when I thought enough about their derivation.