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A Few Notes on Probability Theory, The Logic of Science

Posted in Big Ideas

Because economics and financial markets lack mature theoretical (deductive) foundations, these fields involve largely empirical (inductive) work. The principal mathematical tools in this pursuit derive from probability and statistics. In his 2003 book Probability Theory, The Logic of Science, E.T. Jaynes presents in textbook form his own evolutionary growth in the understanding of probability theory. His approach is Bayesian, in that he views probabilities as conceptually distinct from frequencies of occurrence and probability theory as synonymous with the process of inductive inquiry. He emphasizes iterative “plausible reasoning” as the kernel of probability theory. He offers a few summarizing points relevant to equity investors/traders, as follows:

From pages 128-129:

“…[T]he new information that a scientist gets is not that an experiment did in fact yield this result, with adequate protection against error. It is that some colleague has claimed that it did. The information that we get from the TV evening news is not that a certain event actually happened in a certain way; it is that some news reporter has claimed that it did.

“Scientists can reach agreement quickly because we trust our experimental colleagues to have high standards of intellectual honesty and sharp perception to detect possible sources of error. And this belief is justified because, after all, hundreds of new experiments are reported every month, but only about once in a decade is an experiment reported that turns out later to have been wrong. So our prior probability for deception is very low; like trusting children, we believe what the experimentalists tell us.

“In politics, we have a very different situation. Not only do we doubt a politician’s promises, few people believe that news reporters deal truthfully and objectively with economic, social or political topics. …[W]e cannot trust anyone to tell us the truth, because we perceive that everyone who wants to talk about it is motivated either by self-interest or by ideology…our prior probability of deception is very high…”

In most ways, stock market experts and financial reporters are like politicians and news reporters, rather than scientists and science writers. The probability of encountering deceptive (or delusional) models of stock market behavior is relatively high.

From pages 233-234:

“It seems likely…that the ‘turbulence’ of individual variations in economic behavior is the engine that drives macroeconomic change in the direction of the equilibrium envisioned by Adam Smith. The existence of this turbulence was recognized by John Maynard Keynes, who called it ‘animal spirits’ which cause people to behave erratically…

“…Adam Smith’s equilibrium is never actually attained in the real world because of what a physicist would call ‘external perturbations’ and what an economist would call ‘exogenous variables’ which vary on the same time scale. That is, wars, droughts, taxes, tariffs, bank reserve requirements, discount rates and other disturbances come and go on about the same time scale as would the approach to equilibrium in a perfectly ‘calm’ society.

“The effect of small disturbances may be far greater than one might expect… That is, a very slight influence may be able to pull many seemingly independent agents into phase with each other so they generate large organized waves instead of small ripples…

“…[T]hese are the basic reasons why economic data are very difficult to interpret; even if relevant and believable data were easy to gather, the rules of the game and the conditions of play are changing constantly. But…the conditions for instability should be predictable…, just as they are in physics, meteorology, and engineering.”

The author believes that economies and financial markets are very complex but fundamentally predictable, not intrinsically random.

Finally, from page 312:

“…[T]he human mind has a predilection for rampant, uncontrolled induction, and it requires much education to overcome this. …[T]he reasoning of those without training in any mental discipline — who are therefore unfamiliar with either deductive logic or probability theory — is mostly unjustified induction.

“…As we observe constantly in news commentaries and documentaries, the untrained mind never hesitates to interpret every observed correlation as a causal influence, and to predict its recurrence in the future.”

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