Bayesian Shangri-La Diet

In July, a Cambridge UK programmer named John Aspden wanted to lose weight. He had already lost weight via a low-carb (no potatoes, rice, bread, pasta, fruit juice) diet. That was no longer an option. He came across the Shangri-La Diet. It seemed crazy but people he respected took it seriously so he tried it. It worked. His waist shrank by four belt notches in four months. With no deprivation at all.

Before he started, he estimated the odds (i.e., his belief) of three different outcomes predicted by three different theories. What would happen if he drank 300 calories (2 tablespoons) per day of unflavored olive oil (Sainsbury’s Mild Olive Oil)? Aspden considered the predictions of three theories.

I called my three ideas of what would happen [= three theories that make different predictions] if I started eating extra oil Willpower, Helplessness and Shangri-La. (1) Willpower (W) is the conventional wisdom. If you eat an extra 300 calories a day you should get fatter. This was the almost unanimous prediction of my friends. Your appetite shouldn’t be affected. (2) Helplessness (H) was my own best guess. If you eat more, it will reduce your appetite and so you’ll eat less at other times to compensate, and so your weight won’t move. Whether this appetite loss would be consciously noticeable I couldn’t guess. This was my own best guess. (3) Shangri-La (S) is your theory. The oil will drop the set point for some reason, and as a result, you should see a very noticeable loss of appetite.

More about these theories. His original estimate of the likelihood of each prediction being true: W 39%, H 60%, S 1%. He added later, “I think I was being generous with the 1%”. After the prediction of the S theory turned out to be true, the S theory became 50 times more plausible, Aspden decided.

I like this a lot. Partly because of the quantification. If you were a high jumper in a world without exact measurement, people could only say stuff like “you jumped very high.” It would be more satisfying to have a more precise metric of accomplishment. It is a scientist’s dream of making an unlikely prediction that turns out to be true. The more unlikely, the more progress you have made. Here is quantification of what I accomplished. Although Aspden could find dozens of online reports that following the diet caused weight loss, he still believed that outcome very unlikely. Given that (a) the obesity epidemic has lasted 30-odd years and (b) people hate being fat, you might think that conventional wisdom about weight control should be assigned a very low probability of being correct.

I also like this because it is the essence of science: choosing between theories (including no theory) based on predictions. The more unlikely the outcome, the more you learn. You’d never know this from 99.99% of scientific papers, which say nothing about how unlikely the actual outcome was a priori — at least, nothing numerical. I can’t say why this happens (why an incomplete inferential logic, centered on p values, remains standard), but it has the effect of making good work less distinguishable from poor work. Maybe within the next ten years, a wise journal editor will begin to require both sorts of logic (Bayesian and p value). You need both. In Aspden’s case, the p value — which would indicate the clarity of the belt-tightening — was surely very large. This helped Aspden focus on the Bayesian aspect — the change in belief. This example shows how much you lose by ignoring the Bayesian aspect, as practically all papers do. In this case, you lose a lot. Anyone paying attention understands that the conventional wisdom about weight control must be wrong. Here is guidance towards a better theory. If not mine, you at least want a theory that predicts this result.