Andrew Gelman recently ran a post title “Why waste time philosophizing?” My answer is that different philosophies dramatically affect how, and how well, we get answers from probabilities. This is illustrated with an example from Finance.
Nominally this post is about the importance of Statistical power. In reality it answers the immortal, but often neglected question: “why everyone in Quantitative Finance should be a Bayesian and love the Cauchy Distribution?” (more…)
In some cases, no. For example, 95% Confidence Intervals for physical constants are known to have coverage rates noticeably less than 95%. But this is far from the only use of statistics in physics. There are the various Ensembles of Statistical Mechanics which yield accurate predictions. Are these correct in a Frequentist sense? (more…)
Here is a simple challenge for the Frequentists out there. How do you include information about the range of a mean when estimating it from a series of measurements? (more…)
There is a long and sordid history of trying to use thermodynamic analogies in Economics. Everyone senses thermodynamics is relevant somehow, but no one’s able to make the notion specific, true, and useful. The latest effort comes from Andrew Gelman, who speculates on “Free Energy” in Economics. Ironically, “Free Energy” occurs all the time in Gelman’s field of Statistics; a fact which gives clues to its profitable use in Economics.
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Tyler Cowen’s The Great Stagnation claims progress is slowing leading to a kind of stagnation. Cowen’s pamphlet spells out the what and the why, while many have added debate. My favorite anecdote is the graph of per capita GDP growth, which shows a decline impervious to taxes, spending, elections, and everything else that matters. It certainly suggests diminishing returns from some prior successes, whatever they were: (more…)
It appears to be a quite general principle that, whenever there is a randomized way of doing something, then there is a non-randomized way that delivers better performance but requires more thought.
This remark by E. T. Jaynes will be illustrated with the Metropolis-Hastings algorithm. (more…)
Imagine a medical researcher is conducting a drug trial on 1000 people and wishes to compare it to a placebo. The researcher randomly assigns 500 to the placebo group and the rest to the treatment group. The hope is that if there is some unknown variable influencing the efficacy of the drug, then it will evenly split between the two groups, allowing the statistician to say if the drug worked. Unfortunately, the belief that randomization removes the problem of unknown factors or influences is false. (more…)
The peculiar philosopher John Derbyshire once wrote :
Practically all conspiracy theories are false … You will likely get through life with your mind’s serenity undisturbed if you dismiss without investigation every conspiracy theory that comes to your attention. I do so reflexively.
How to choose probability models to avoid over fitting data? Below I show how for Maximum Entropy models, but the results are more general than this special case. There is even a connection to melting ice, but you have to read to the end to see it.
Warren Buffett brazenly discounts cash flows using risk free rates. This effrontery is excused by claiming his predictions are so good as to be without risk; a view hard to square with Buffett’s occasional losses. This post outlines a better, or at least more useful, explanation using financial economics. (more…)
Much blood, sweat, and beer has been spilled understanding insurgencies. Having none of these in excess, however, I’m forced to use simpler methods. What follows is low tech, but it gets results. (more…)
You’re a student of volatility. You wrote the book on volatility. You probably invented volatility and would rather find out you’re adopted than be accused of unlawful calculation. Nevertheless, you’re getting it wrong. (more…)
This blog is about my adventures in Physics, Economics, and allied disciplines with some Marine Corps sorties thrown in for color. The thread connecting these exploits is “Probability”; which, as everyone knows, is the language used to ameliorate uncertainty.
