Advent of Alpha Day 19: Bayesian Thinking One Offs

I’m not a statistician by training, I got into this by problem solving through code. However, when I first read about Bayesian statistics, it made me excited in an intuitive way that frequentist statistics just didn’t.

Most people learn frequentist stats at school: given a set of observations, figure out some properties that tell you about the shape of those observations (mean, mode, median, variance, and so on), and use those numbers to help make some sort of analytical model that can help you predict ranges in which future observations should fall.

What about one-off events though, like elections? You can’t run those thousands of times (although if you remember the hanging chads in 2000, you’ll feel like that did actually happen). How do you model them?

Bayesian statistics basically says “have a prior hypothesis as to what the value is, and update your value as new data arrives”. This sits at the heart of electoral forecasting (which now has a bad rep, for reasons I think are unrelated to the statistics), and is more suitable for calibrating, particularly when the number of data points is limited, or where you’re trying to update a hypothesis based on subsets of data like polling.

Another way of describing Bayes stats is that it provides us with maths to update subjective beliefs as new data arises, and to describe probability as a measure of confidence you may have about an event.

Frequentist statistics throws belief away and makes statements about confidence intervals in a way that requires large sample numbers to support.

The question I have is: isn’t every event a one-off?

No two football matches are the same. Or horse races, cricket matches or elections. They’re all one-offs, and while previous results might give you some indication of ranges or some probabilities in certain conditions, I have a hard time describing these numbers as predictive. At least with Bayes I’m being honest: I’m choosing data to interpret, and I’m modelling confidence accordingly.

You can go a long way using frequentist statistics. I’m confident that as Twain once said that “History doesn’t repeat, but it does rhyme”, and that distributions of certain events tend to hold. I just don’t think you can understand how a particular market is evolving in front of you with nothing but frequentist statistics.

On Day 8 I talked about Markov Chains and using a frequentist approach to model price action to predict a sequence of events. A more mature approach would be to use that approach to create some priors, but update your priors as a market evolves in front of you, as you can then better model outliers, or even deal with an event that is shaping in a way unlike anything in your sample set.

Use frequentist statistics as a creator of priors, but maybe think about Bayes to adjust.

Sometimes history doesn’t rhyme, because it can’t, or doesn’t do so in a way that is useful to you in a market. Understanding Bayes and having a way to incorporate it into a model that is purely frequentist will likely plug some leaks and perhaps add some alpha.

Or it may not. Only testing it will tell you.