Bayesian thinking and the importance of applying a base rate when interpreting

Decision-Making

The core of Bayesian thinking (or Bayesian updating, as it can be called) is this: given that we have limited but useful information about the world, and are constantly encountering new information, we should probably take into account what we already know when we learn something new. As much of it as possible. Bayesian thinking allows us to use all relevant prior information in making decisions. Statisticians might call it a base rate, taking in outside information about past situations like the one you’re in.

Consider the headline “Violent Stabbings on the Rise.” Without Bayesian thinking, you might become genuinely afraid because your chances of being a victim of assault or murder are higher than it was a few months ago. But a Bayesian approach will have you putting this information into the context of what you already know about violent crime. You know that violent crime has been declining to its lowest rates in decades. Your city is safer now than it has been since this measurement started. Let’s say your chance of being a victim of a stabbing last year was one in 10,000, or 0.01%. The article states, with accuracy, that violent crime has doubled. It is now two in 10,000, or 0.02%. Is that worth being terribly worried about? The prior information here is key. When we factor it in, we realize that our safety has not really been compromised.

One complaint last month. Two this month. Complaints have doubled.

Nine hundred and ninety-eight customers remain silent, but someone gives the percentage a headline and an enormous red arrow. Another person proposes an urgent redesign.

Now reverse the scale. Ten thousand complaints become twenty thousand. The same word—doubled—describes an operational emergency. From the percentage, you learn the direction and proportion of change. From the base numbers, you learn which world you occupy.

The team rebuilds the decision paper around four entries: current count, population at risk, usual range and evidence that this case differs from previous ones. The result is less dramatic and harder to misuse.

A new regulation, product or failure mode can make yesterday’s average a poor guide. The team has to state the difference and estimate its effect. In this review, “this time is different” needs a number before anyone accepts it.

The team replaces the urgent redesign with a two-week investigation. Support reads the two complaints. Both concern the same broken browser version. Engineering can reproduce the fault.

The red arrow was melodramatic; the defect is real. Fixing it costs two days. The team keeps the investigation open because next month’s denominator will be larger. Everyone involved now knows the difference between two complaints and twice as many complaints.

Excerpt from

Great Mental Models, Volume 1: General Thinking Concepts

by Shane Parrish and Rhiannon Beaubien

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Base-rate neglect

We focus on vivid specifics and ignore the wider statistical odds.

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Bayesian thinking and the importance of applying a base rate when interpreting

Behavioural ideas at play in this post

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