Interesting Links for 3-10-2011

[andrewducker]

• This is how they gerrymander homeless children
  (tags: uk homeless housing politics)


• Why the world envies Mr Osborne
  (tags: GeorgeOsborne finance politics uk)


• Rick Perry's hunting ranch is called....Niggerhead.
  (tags: usa RickPerry racism politics)


• Homemade GPS Receiver
  (tags: GPS Electronics)


• Judge rules against Bayesian probability
  (tags: statistics law uk)


• Why This Year's Doctor Who Finale Was (Mostly) Better than Last Year's
  (tags:)


• The Pinboard people talk about the fallout from how badly Delicious fucked up.
  (tags: avos bookmarking fanfiction del.icio.us pinboard taxonomy)


• Cameron wants to scrap the Human Rights Act but Clegg won't let him
  (tags: libdem Conservatives politics rights uk)


• Historians Politely Remind Nation To Check What's Happened In Past Before Making Any Big Decisions
  (tags: TheOnion satire funny history)


• USA now assassinating its own citizens without due process
  (tags: usa law assassination murder)


• How cat videos get onto the internet
  (tags: cats videos youtube funny comic)

Comments

[supergee]

Perry really is stupider than Dubya.

[major-clanger.livejournal.com]

That story on legal statistics is depressingly misleading - I'd hoped for better from Guardian - as the ruling said nothing at all about whether Bayes' Theorem was right or not. Rather, the court expressed concern about how valid its application was given issues about the assumed probability distributions.

The actual judgment, which again I am disappointed to see that the story doesn't refer to, is available at BAILII. It's redacted to protect T's identity, but the full discussion of statistics and evidence is all there.

[steer.livejournal.com]

I must say I 100% agree with you here. The Guardian article misuses statistical terms horribly so it's impossible to tell what is going on. In particular confusing Bayes' theorem and Bayesian methods is a horrible mistake.

[momentsmusicaux.livejournal.com]

Also, they say a theorem is 'invented'. Theorems are *discovered*. Grumble grumble.

[steer.livejournal.com]

I guess that would depend on the mathematical school of philosophy that you subscribe to surely? A realist or platonist would discover not invent. Not so sure about an empiricist or a formalist though.

[momentsmusicaux.livejournal.com]

What you do with or to a proof is more open to debate I think.
But a theorem was true all along, even before anyone knew about it.

[andrewducker]

Aren't theorem's mostly "proven"?

[momentsmusicaux.livejournal.com]

Yes, but the method of the proof itself. Eg, there are tons of proofs of Pythagoras. Each has been invented, I would say. There's only one theorem, which has always been true.

[naath.livejournal.com]

Greg Egan wrote a nice short story based on the notion that that is not actually the case :)

[simont]

Two short stories! There's a sequel in a more recent collection.

[steer.livejournal.com]

Something strictly is only a conjecture until it's proven but this is not always adhered to. Fermat's last theorem was an interesting case because it remained "claimed proven" (but most mathematiciancs now doubt it ever was proven by Fermat) until very recently. Now it is proven. Should it really have been Fermat's last conjecture?

[andrewducker]

Fermat's last guess? Fermat's last blind stab in the dark? Fermat's last assumption? Fermat's last joke?

[steer.livejournal.com]

I am not sure a "formalist" would agree with "true all along" but instead that a particular theorem is (and always was) a consistent result of manipulation of strings of characters beginning with a set of axioms and rules of inference. However, it is a result of picking the axioms and inference rules. This sits comfortably with, for example, the fact that some statements in mathematics are only "true" for the type of mathematics you choose. For example Zermelo's theorem is "true" in ZF set theory with the axiom of choice but not true in ZF set theory without. In Euclidean geometry Pythagorus is true but not in elliptic geometry.

Given that the mathematician is free to choose the axioms and inference rules he or she works with, is "discovered" the correct word? I'm not wholly sure. Most people would feel uncomfortable saying that Charles Dickens "discovered" the sequence of letters, spaces and punctuation that made The Tale of Two Cities.

[0olong.livejournal.com]

Of course, you could argue that all inventions are discovered...

[andrewducker]

They're just sitting out there in phase space, after all :->

[undeadbydawn.livejournal.com]

the Guardian talking complete crap about something important.

who'd have thought?

[purplecthulhu.livejournal.com]

Interesting...

The key thing about Bayesian statistical inference is that it should be the case that the data and the prior are explicitly stated, so that arguments about the prior - eg. the number of a certain kind of running shoe sold in the UK - specifically address one term in the equation. Of course council might not wish to present things as clearly as that, if they don't understand the method or if they want to muddy the waters.

Am beginning to think we should be offering consultancy for lawyers on such things...

[philmophlegm.livejournal.com]

I was interviewed by a journalist looking to dig up some dirt about George Osborne on Saturday. I'll post about it if I get the chance tomorrow.

[andrewducker]

I shall look forward to it!

[steer.livejournal.com]

Seriously that guardian article about statistics and the courtroom is extremely annoying. It completely confuses Bayes Theorem (uncontroversial established fact) with Bayesian statistics (controversial way of doing things where the outcome relies on your prior belief). I looked a the judgement made which actually seems to be about Bayesian statistics not about Bayes Theorem -- hard to tell as it is highly redacted.

But the guardian article... nightmare. It talks about two things, one 100% correct the other 100% contravesial and doesn't realise they are different because they have very similar names.

[spacelem.livejournal.com]

I don't know if it's all that controversial. You're just substituting uncertainty after the calculation for uncertainty before the calculation. The actual maths is pretty much the same, you're just being upfront about what you don't know.

[steer.livejournal.com]

If you look at the letters page in the Royal Society of Statisticians newsletter you'll find it is pretty controversial. One leading professor called for people to stop calling it Bayesian as he did not beleive Bayes would have agreed with it and called such methods "abominations performed in his name". The Frequentist versus Bayesian wrangling gets pretty vituperative.

[spacelem.livejournal.com]

I think a professor probably understands it better than I do, but that (the whole putting the uncertainty up front rather than having confidence in the result) is how it was described when I was taught Bayesian statistics, and Bayes' theorem is the core of the whole discipline.

[steer.livejournal.com]

Bayes Theorem is core to both Bayesian and Frequentist statistics. It's unfortunate that Bayes Theorem and Bayesian statistics have the same name as people then muddle the two things (like that Guardian article does).

I don't wish to suggest that a Bayesian approach to statistics is obviously dead wrong. It's just that there is a big split within statistics between Bayesian and Frequentist and the whole thing is rather contentious. A competent statistician will produce "good science" using either method but working statisticians usually have a strong preference for one and suspicion of the other.

[purplecthulhu.livejournal.com]

This all gets interesting when you're not in a position to have a parent population to draw your sample from. That's why Bayesianism has taken over cosmology - we only have the one universe.

I'm now working in a nest of Bayesians and what it says about priors and posteriors makes a lot of sense to me. But maybe that's the indoctrination :-)

[steer.livejournal.com]

Heh... yes, it puts frequentists in an awkward philosophical position but it's not actually uncommon. For example, in road transport work, due to the nature of the systems you really don't want to repeat an experiment (for example the "experiment" you are studying is a massive road closure -- you only get one). So philosophically a frequentist is more troubled by the notion of talking of the probability of an event which has definitely happened in a one off unrepeatable experiment... but the mathematics still works even if the philosophy is broken. I'm extremely uncomfortable with the notion of the prior distribution -- especially as the notion of an "uninformative prior" is completely inconsistent for many situations (anywhere where there's no symmetry in your outcomes).

In a legal situation (which is where this started) you might be feeding into your model a prior probability of guilt (or a prior probability of the blood sample being the defendants). Now obviously a competent statistician checks that the prior does not greatly affect the posterior. Nonetheless it could lead to some awkward situations. I agree that mathematically the whole situation makes sense -- indeed the mathematics is uncontroversial once the prior is asserted (OK, it can get rough and you need sampling but I'm 100% fine with that). However, I'm not at all comfortable with asserting an ex nihilo belief and then that being an important part of the model.

[purplecthulhu.livejournal.com]

Indeed, the prior is where I've had philosophical and technical issues with Bayesianism. But where there is good reason for a prior (a previous set of data for example), or where a variety of uniform priors don't affect the posterior, then I don't have a problem. They are in effect representing your ignorance of the system.

The prior, likelihood, posterior approach also explains why the same set of data can be taken as evidence for utterly different conclusions - eg. tea partyists and liberals. They're working from utterly different priors, which are there no matter what. Even if you're a frequentist.

[steer.livejournal.com]

is good reason for a prior (a previous set of data for example)

Where did that get its prior? :-)

here there is good reason for a prior (a previous set of data for example), or where a variety of uniform priors don't affect the posterior, then I don't have a problem

Absolutely -- in a symmetrical situation (the ball is under one of three cups) a uniform prior is perfect.

They're working from utterly different priors, which are there no matter what. Even if you're a frequentist.

Sure -- but having different outcomes from the same set of data (depending on prior) would not happen in frequentist analysis (and, a good Bayesian would say that the conclusions are not meaningful unless there was a reason to prefer one prior).

[purplecthulhu.livejournal.com]

You might be interested in this discussion on Prof Peter Coles' blog...

http://telescoper.wordpress.com/2011/10/06/bayes-in-the-dock/#entry

[steer.livejournal.com]

Interesting -- thanks for that.

My reading of the original redacted court document was that it was Bayesian statistics, not Bayes Theorem which the judge ruled against. The Guardian article muddies the water completely by using the two interchangably. The original court document is heavily redacted so it's unclear.

If the Prof you link to is right, it's a stupid ruling but I *think* he's working from the Guardian article not the court document. The rest of his column is interesting though.

[purplecthulhu.livejournal.com]

Do comment on Peter's blog if you wish - he likes to have new people visit!

[andrewducker]

Cheers, that was fascinating. And the conversation between you and Steer, likewise.

[undeadbydawn.livejournal.com]

The Onion:

continually pointing out that The Stupid is there, but really doesn't have to be.
i find the closing statement particularly poignant.

and speaking of which, I haven't checked how BP's legal action against Halliburton is going. That whole 'hire the worlds most incompetent contractor to oversee site safety' thing didn't work out too well.

[momentsmusicaux.livejournal.com]

Just about any fiction with time travel ends up inventing a sort of meta-time.

Eg, the Cybermen are in the year 1800 and the Doctor is in the present. Stuff happens in one timeline that progressively affects the current one. Hence there's a meta-time that changes to the timeline take place in...