How Statisticians Could Help Find That Missing Plane | Hacker News Reader

How Statisticians Could Help Find That Missing Plane

fivethirtyeight.com

68 pointsThrymr34 comments

it sounds like the strength of the bayesian model is completely dependant on the ability of experts to provide accurate statistical guesses

Bayesian inference is definitely only as good as the quality of the chosen prior, if the number of samples is low.

I don't think this is technically correct - as Bernstein-Von Mises guarantee under certain conditions that the posterior is independent of the prior after sufficient data is observed.

http://en.m.wikipedia.org/wiki/Bernstein%E2%80%93von_Mises_t...

It was actually "technically correct" - he said "if the number of samples is low".

You're correct about the general case, of course.

The previous comment was edited - the comment I replied to said something along the lines of 'especially when the number of samples are low'

In fairness, I actually edited my reply for clarity, what I had in mind were small samples where the prior ends up dominating.

But what's the alternative? The same experts making the same guesswork with the same information.

I'd like to disagree with that. If your priori are particularly bad then you should expect your estimates to change quickly based on new evidence.

Completess of the state space seems relevant.

And unfortunately 4-dimensional. They could have landed the plane, taken it apart and melted it for scrap, killed all the passengers and crew, and burned the bodies by now.

Unless of course, they have a lot more data than they're saying. My chief worry here is that this was a dress rehearsal for how to make a jet disappear. If so, then the media is doing a fantastic job enumerating the mistakes they made so they can refine the technique so down the road they can make it last just enough to ram a bunch of jets into skyscrapers again. Sigh...

Consider an ideal black spherical 777, hilarity ensues...

But seriously, the strength of Bayes is in coping with an initially craptastic prior by updating probabilities (the posteriors) as (potentially noisy) evidence comes in. Now based on that data as it arrives, build an evolving model for the location with confidence intervals and probabilities.

Now refine your search to emphasize locations with both emerging high probability and high variance and hope the noise in the data isn't so pathological as to make the process worthless.

It's worth a shot.

While technically true, another way to say the same thing is "Bayesian reasoning helps you draw reasonable conclusions if the number of samples is low, while converging on the objective solution as the number of samples grows". Which has an entirely different ring to it.

For any model of statistical analysis, it's difficult for an inference to be accurate if the data are poor.

It probably helps, but having experts may not be necessary in all cases.

http://en.wikipedia.org/wiki/The_Wisdom_of_Crowds

By Submarine in the 1960's, he's referring to Dr. John Craven's methodology for finding the USS Scorpion using Bayesian search theory. It was interesting to read the back story in Blind Man's Bluff, although I did get the feeling it was punched up a bit for drama.

James Surowiecki also tells the story of the search for the Scorpion in his book The Wisdom of Crowds, where I first read about it.

The Wikipedia article [0] gives a basic account, and the article on Bayesian search theory [1], in addition to describing the procedure quite well, mentions several other searches in which the method proved successful.

0. http://en.wikipedia.org/wiki/USS_Scorpion_(SSN-589)#Search:_...

1. http://en.wikipedia.org/wiki/Bayesian_search_theory

If this is the case, let's see it in action. There is a great deal of information about this event that has been released to the public so I am curious to see if the experts in this field can generate probable locations of the aircraft and when the aircraft is found take a look and see if following the recommendations would have found the aircraft more quickly.

I think they need actual data - GPS coordinates, search areas, precise search methodology and a whole slew of other hard data that, afaik, is not available to the public.

a great deal that has proven to be inaccurate later

I would guess that the authorities already have some stats guys working on it.

What are the odds?

Last I heard they recruited a witch.

From the sounds of it he recruited himself. Malaysia has denied involvement.

http://www.washingtonpost.com/news/morning-mix/wp/2014/03/13...

Thanks for pointing that out.

FTA:

>Despite the widespread use of Bayesian methods in searches, not every airline or government uses them — there’s no evidence the Malaysian government nor Malaysia Airlines has in the current search, though they are getting help from a team of French government investigators who worked on the Air France hunt. (The Malaysian embassy in Washington, D.C., didn’t immediately respond to an emailed request for comment, and calls to the embassy on Monday yielded an automated reply that the office was closed because of snow.)

>“I suspect that they just guess, like professional baseball managers used to do before ‘Moneyball,’” said Peter Thall, a biostatistician at MD Anderson Cancer Center in Houston.

I was thinking yesterday that there are not _that_ many jets the size of the 777 in the world, and the location of most of them can probably be detected by U.S. military satellites. If that satellite data were correlated with data from the airlines on the location of their planes, some much smaller set should emerge that consists of planes whose location does not have an official explanation.

Commercial satellites are ok for seeing planes for that matter. It's knowing where and when to look that's important. I don't think that even the US military constantly monitors vast tracts of empty ocean on the off chance that a plane might crash there.

https://maps.google.com/maps?q=35%C2%B003%E2%80%B234%E2%80%B...

For instance, these two maps are pretty similar in scale (I couldn't make Maps do the exact same scale though)

https://maps.google.com/?ll=44.527843,13.227539&spn=14.14170...

https://maps.google.com/?ll=-32.509762,80.991211&spn=16.6984...

That's a "whole lot of nothin'".

I don't think that even the US military constantly monitors vast tracts of empty ocean on the off chance that a plane might crash there.

https://en.wikipedia.org/wiki/SOSUS

Lines (chains, as per your article) have a "lot less area" than rectangles do, though. In other words, it's way, way easier to answer "what has crossed this line, at what time?" than "is there a needle in this haystack as large as Europe?", especially when the rectangle in question is basically of zero interest 99.9999% of the time, and you're tying up resources that could be pointed at China, North Korea, Russia, Iran, San Marino or other more 'interesting' places.

Furthermore, as your article mentions, they decommissioned some of that because it was too expensive and didn't serve much purpose with the end of the cold war. Even those guys' budgets are not unlimited.

Pardon my ignorance, but why is San Marino in that list?

You never know what the Sammarinesi are plotting up there on that rock! Mostly just to see if anyone was paying attention :-)

Yeah, I was thinking specifically of the case where the plane is still intact and on the ground somewhere. If it has crashed into the sea this technique wouldn't be useful. And it could also be foiled by hiding the plane, which would be a large but not impossible task.

Seemed like a pretty clear (if low level) explanation of Bayes theorem.

so, October Sky 2014?

Reply on news.ycombinator.com