Using Bayes to update odds

The NY Times science section rarely publishes an article about math, and when they do, it is so confused that I wonder if anyone learns anything. Here is the latest, its most emailed story for the day:

Now Bayesian statistics are rippling through everything from physics to cancer research, ecology to psychology. Enthusiasts say they are allowing scientists to solve problems that would have been considered impossible just 20 years ago. And lately, they have been thrust into an intense debate over the reliability of research results.

When people think of statistics, they may imagine lists of numbers — batting averages or life-insurance tables. But the current debate is about how scientists turn data into knowledge, evidence and predictions. Concern has been growing in recent years that some fields are not doing a very good job at this sort of inference. In 2012, for example, a team at the biotech company Amgen announced that they’d analyzed 53 cancer studies and found it could not replicate 47 of them.

Similar follow-up analyses have cast doubt on so many findings in fields such as neuroscience and social science that researchers talk about a “replication crisis”

It is a problem that major cancer studies cannot be replicated, but the suggestion here is that Bayesianism solves the problem by avoiding lists of numbers and using more computing power. That is nonsense.

It quotes Andrew Gelman as a prominent Bayesian gurn, but he disavows much of the article, including nearly all the opinions attributed to him. Still, he says that it is a good article, because he expects dumb journalists to screw up the content anyway.

A big example is the Monty Hall problem:

A famously counterintuitive puzzle that lends itself to a Bayesian approach is the Monty Hall problem, in which Mr. Hall, longtime host of the game show “Let’s Make a Deal,” hides a car behind one of three doors and a goat behind each of the other two. The contestant picks Door No. 1, but before opening it, Mr. Hall opens Door No. 2 to reveal a goat. Should the contestant stick with No. 1 or switch to No. 3, or does it matter?

A Bayesian calculation would start with one-third odds that any given door hides the car, then update that knowledge with the new data: Door No. 2 had a goat. The odds that the contestant guessed right — that the car is behind No. 1 — remain one in three. Thus, the odds that she guessed wrong are two in three. And if she guessed wrong, the car must be behind Door No. 3. So she should indeed switch.

This is too confusing to be useful. There are some hidden assumptions about how Mr. Hall opens the door, or the problem cannot be solved. It says "odds" instead of "probability". Furthermore, it doesn't really require Bayesianism because other approaches give the same answer.

The article is really about Bayesian probability, an increasingly popular interpretation of probability. The interpretation has a cult-like following, where followers insist that it is the most scientific way to look at data.

Bayesianism has its merits, but it is just an interpretation, and is not provably better than others. There are some subtle points here, as some of the confusion over quantum mechanics is rooted in confusion over how to interpret probability. The NY Times should have asked Gelman to review the article for accuracy before publication, but the paper considers that unethical.

The same newspaper reports:

All five research groups came to the conclusion that last year’s heat waves could not have been as severe without the long-term climatic warming caused by human emissions.

“When we look at the heat across the whole of Australia and the whole 12 months of 2013, we can say that this was virtually impossible without climate change,” said David Karoly, a climate scientist at the University of Melbourne who led some of the research.

It seems obvious that if you take a computer model of the Earth's climate, and subtract out some human-attributed warming, then the model will show the Earth not as warm. Or that if you observe some extreme weather, you can attribute it to climate change.

What's missing here is some showing of a net worsening of the climate. Maybe some extreme cold waves were avoid. And what's also missing is a showing that the human influence is significant. Maybe humans made the heat waves worse, but only slightly, and not enuf for anyone to care.

The research papers probably address these points. I get the impression that the NY Times staff wants to convince everyone of various evironmental causes associated to global warming, but I don't think these explanations help.