October 25, 2020
The original article can be found here.
How to Think Like an Epidemiologist
Don’t worry, a little Bayesian analysis won’t hurt you.
There is a statistician’s rejoinder — sometimes offered as wry criticism, sometimes as honest advice — that could hardly be a better motto for our times: “Update your priors!”
In stats lingo, “priors” are your prior knowledge and beliefs, inevitably fuzzy and uncertain, before seeing evidence. Evidence prompts an updating; and then more evidence prompts further updating, so forth and so on. This iterative process hones greater certainty and generates a coherent accumulation of knowledge.
In the early pandemic era, for instance, airborne transmission of Covid-19 was not considered likely, but in early July the World Health Organization, with mounting scientific evidence, conceded that it is a factor, especially indoors. The W.H.O. updated its priors, and changed its advice.
This is the heart of Bayesian analysis, named after Thomas Bayes, an 18th-century Presbyterian minister who did math on the side. It captures uncertainty in terms of probability: Bayes’s theorem, or rule, is a device for rationally updating your prior beliefs and uncertainties based on observed evidence.
Reverend Bayes set out his ideas in “An Essay Toward Solving a Problem in the Doctrine of Chances,” published posthumously in 1763; it was refined by the preacher and mathematician Richard Price and included Bayes’s theorem. A couple of centuries later, Bayesian frameworks and methods, powered by computation, are at the heart of various models in epidemiology and other scientific fields
As Marc Lipsitch, an infectious disease epidemiologist at Harvard, noted on Twitter, Bayesian reasoning comes awfully close to his working definition of rationality. “As we learn more, our beliefs should change,” Dr. Lipsitch said in an interview. “One extreme is to decide what you think and be impervious to new information. Another extreme is to over-privilege the last thing you learned. In rough terms, Bayesian reasoning is a principled way to integrate what you previously thought with what you have learned and come to a conclusion that incorporates them both, giving them appropriate weights.”