“The problems come when we don’t update,” said David Spiegelhalter, a statistician and chair of the Winton Centre for Risk and Evidence Communication at the University of Cambridge. “You can interpret confirmation bias, and so many of the ways in which we react badly, by being too slow to revise our beliefs.”
There are techniques that compensate for Bayesian shortcomings. Dr. Spiegelhalter is fond of an approach called Cromwell’s law. “It’s heaven,” he said. In 1650, Oliver Cromwell, Lord Protector of the Commonwealth of England, wrote in a letter to the Church of Scotland: “I beseech you, in the bowels of Christ, think it possible you may be mistaken.”
In the Bayesian world, Cromwell’s law means you should always “keep a bit back — with a little bit of probability, a little tiny bit — for the fact that you may be wrong,” Dr. Spiegelhalter said. “Then if new evidence comes along that totally contradicts your main prior belief, you can quickly ditch what you thought before and lurch over to that new way of thinking.”
“In other words, keep an open mind,” said Dr. Spiegelhalter. “That’s a very powerful idea. And it doesn’t necessarily have to be done technically or formally; it can just be in the back of your mind as an idea. Call it ‘modeling humility.’ You may be wrong.”
A lot of audiophile thinking seems to be to be based on either outdated information (priors that need updating) or just plain rumor. Update your priors!
And, you know, “the bowels of Christ” – why don’t we say things like that anymore?