Instead of “confidence interval,” let’s say “uncertainty interval”

因为有了统计
我可以把天上的星星重新梳理

Because of statistics
I can rearrange the stars in the skies above

Indeed. Especially so when the PSF is broad and the stars overlap.

(via)

“Why I don’t like Bayesian Statistics”

- Andrew Gelman

Oh, alright, here’s one:

I can’t keep track of what all those Bayesians are doing nowadays–unfortunately, all sorts of people are being seduced by the promises of automatic inference through the “magic of MCMC”–but I wish they would all just stop already and get back to doing statistics the way it should be done, back in the old days when a p-value stood for something, when a confidence interval meant what it said, and statistical bias was something to eliminate, not something to embrace.

And before you panic, note the date.

Over the years I’ve had many strong likes and dislikes for the various parts our subject. At different times I have confidently asserted this or that topic to be useless, wrong-headed, stupid, superficial, impossible, inappropriate, irrelevant, phony, boring, or finished. I’ve been in love with sufficiency and hated cluster analysis. I thought the theory of games was elegant, while that of linear models lacked style. Group theory and invariance were fascinating to me, while maximum likelihood seemed mundane. Coordinate-free was the way to go, explicit parameters were to be avoided. Brownian theory was hot, sampling theory was not. The Markov property was natural, the mixing property artificial. Category theory was pure, applied probability wasn’t applied. Rao-Blackwellizing was cool, the delta method left me cold. Exact results were good, approximate ones bad. Scientific applications were beautiful, technological applications were ugly. Frequentist inference was objective, Bayesian inference subjective. And so it went on. My view was that means were to be avoided; extremes were the place to be.

I’ve noticed another trend over my career. For decades I have jealously watched other people work on fascinating, complicated things — data, questions, contexts, models, methods and theory — leading them to fame and fortune, while I have been working on uninteresting, simple things, condemning myself to obscurity and poverty. I hasten to add that my things are always very interesting to me, and sometimes quite complicated too, just not to others. But the strange thing is that as time passed, many of those dimly-recalled, fascinating, complicated things from the past that others worked on, turn out to be just what I needed in order to answer a question at a later date. I’ve been behind the times, but, at least in some cases, I’ve caught up eventually.

[Once I quoted an article by Prof. Terry Speed in IMS Bulletin: Data-Doctors. Reading his columns in the IMS Bulletin provides me an opportunity to reflect who I am as a statistician and some guidance for treating data. Although his ideas were not from astronomy or astronomical data analysis, I often find his thoughts and words can be shared with astronomers.]

“What’s the question (this model is supposed to help us answer)?” I want to shout. More politely, Samuel Karlin once said “The purpose of models is not to fit the data but to sharpen the question”. Or, John Tukey: “Our focus should be on questions, not models…Models can – and will – get us in deep trouble if we expect them to tell us what the unique proper questions are.

We’ve all heard George Box’s quaqua-versal quotation “All models are wrong, some models are useful”, and I agree with the second half. But where do we find out which models are useful and which aren’t, which are appropriate and which aren’t? You’d think there must be lots of examples; do you know one?