Bayes’ Theorem and policing

Professor Ken Pease, former Home Office Researcher, discusses the contribution of Bayesian analysis.

Forty-seven years ago I started work in the Home Office Research Unit and I have spent all the intervening years researching crime and justice, in one secure hospital, two national ministries and several police forces. The gulf between crime research and crime policy and practice remains wide. In this blog I will write only about policing, though the same argument applies to other criminal justice agencies.

I spent last week in ride alongs with police in a northern city, admiring the skill and sensitivity of almost all of them. Their skill had nothing to do with knowing any research results, but that valuable commodity: professional experiential judgement.

The primary task of the academic is, as Jason Roach and I have written elsewhere, to help practitioners morph experience into the best possible evidence. That’s why I am keen to support EMPAC.

The key change involves starting from practitioner mindset rather than from a carefully crafted academic hypothesis comparing two ‘treatments’, both of which are likely to be sub- optimal. This starting point flies under various flags, experiential learning, user experience design and the like. In statistics, it is enshrined in Bayesian analysis, whereby the aspiration is to become less and less wrong in the light of experience rather than reach truth by comparing two or more ways of doing something (which in any case will drift over time after the evaluators have left).

The core of the Bayesian approach is ridiculously simple. It is to state in advance what you believe will happen after you (or someone else) has acted in a particular way. You see how things turn out and insofar as that differs from what you anticipated, say what you think will happen after the action is tweaked, see what happens, predict, revise, predict until you become as near right as you will get. Keep checking because the context will change so if you stick with the same beliefs, your performance will drift. Bayesians in their Sunday best prose speak of prior and posterior probabilities, but at its core the method is just how we improve our skills, from DIY to horseriding. The process needs formalising because we all, including police officers, are better at hindsight than foresight. We need to state our belief in advance and take things from there.

The best simple introduction to Bayesian thought is Chapter 8 of Nate Silver’s book ‘The Signal and the Noise’ where he uses the expert gambler to illustrate the process. It’s apt because for the gambler foresight (prior probability) is tangible. It’s called a bet! The good gambler bets and changes beliefs when she loses money. For all its simplicity at the point of use there is a vast and sophisticated statistical underpinning to Bayesian analysis which has led to its adoption in a wide range of hard science settings. To use a metaphor, this plane is a masterpiece of complex design but is really easy to fly. Its virtues have led to its adoption in very many science contexts from heart surgery to through cancer diagnosis to archaeological dating and estimation of rail passenger satisfaction .

Bayes is all about probabilities and how these are dynamically moving just as life is around you. It helps you think rationally about the best things to do; it doesn’t promise ‘facts’ or everlasting solutions, simply because in an everchanging world with highly diverse contexts it can be misleading to search for ‘static and universal truths’. Policing knows this already, so I believe there is potential here for ‘real world’ use.

You can see a short visual explanation of Bayes on Youtube, courtesy of Ian Osolov of City University, New York at

The reason I believe Bayes offers us a better, rational and scientific approach – yet in a real world context – is that we are in danger of promoting single methodological approaches, as Malcolm Sparrow (2012) and Ray Pawson (2006) have argued. Policing ought to be using the best available evidence processes, and this means evidence that is tied to the dynamic context and is a tool for use in such a dynamic world. Police decision makers can’t really wait years for insight into choosing option A or B and the public quite rightly won’t want to be waiting for, what is at its core, an emergency service to protect people.

The College of Policing website Research Map offers a great opportunity to collate and promote policing research. I would advocate a broader illustration of different research forms beyond RCTs, including the ethnomethodological for example, and some promotion of Bayesian analysis.

The benefit of Thomas Bayes is a close alignment to the national decision making cycle and the reflective practitioner model that have been built into police training for some time. The notion of having a working hypothesis, a working strategy, with objectives, is very familiar to a firearms commander for example. The contribution of Bayes is that this fits into an operational application, rather than being a form of remote enquiry that has to be then ‘translated’ back into contemporary practice. Bayes then offers us a dynamic research model to constantly improve professional practice and we should use more of it.