Why your probability tribe matters
How we think about probability affects how we practice probability
In my article The Two Schools of Probability, I argue that despite all the squabbling, there isn’t actually that much difference between the various approaches to thinking about probability; and those differences have more to do with temperament than actual mathematics. All the same, those temperamental differences can make a substantial difference to the way you practice probability.
If you believe that probability is exclusively defined by the statistics of long sequences of repeatable trials (frequentism) then you will want to wait with an analysis till you have enough data to establish those statistics with a specific level of confidence. You will be sure your analysis is objective and robust, but you will walk away from a lot of analysis because the data aren’t good enough. You also need the future to look like the past and, actually, you need that uniformity to extend far enough into the past to include all the data you need to use and far enough into the future to cover everything you want to forecast.
If you believe that probability is nothing more than subjective belief about the plausibility of events (subjective Bayesianism), then you will be much more willing to rush in where frequentists fear to tread. You will have no illusion that your method is objective, but you will argue that your analysis is at least rational relative to what you believe. You will enjoy the huge reductions in uncertainty that are the natural provenance of the transition from no data to even just a few data and you will be more inclined to conjecture causal models that allow for more efficient use of available data to reduce uncertainty at the expense of uncertainty about the models themselves. You are very much at the mercy of the agenda, bias, heuristics and probabilistic ineptitude of the experts who furnish your subjective probabilities.
If you are one of the happy few that believe that probability is, indeed, a quantitative measure of the plausibility of events, but that there is an objectively correct probability for a given set of data (objective Bayesianism, Pragmatism) then you will also be bold in the face of frequentist fear. You may resort to subject matter experts and conjectural causal models, but you will treat both with the skepticism and humility they require. You will account for structural uncertainty in your decision-making by allowing for multiple models, and you will make every effort to triangulate those models with data and expert opinion, relative to the decisions you have to make and the objectives you want to achieve.
If you’ve ever thought about calibrating probability assessments, then you are an objective Bayesian, because the very act of calibration pre-supposes a correct probability against which to calibrate.
