The pale cast of thought

October 7, 2007

Discovered a great new blog last week – the AstroStat Slog. It reminded me how Astronomy has some things in common with social science. Pause for spluttering by hard nosed physical scientists. What I have in mind is that its hard to do controlled experiments. You have to let Nature do the experiments for you, and then work out whats going on. This causes all sorts of problems, but in particular you often need to be good at statistics, to stop yourself being a sucker for all those fascinating flukes.

Even worse, often you don’t even know the underlying probability distributions of your variables. Assuming everything is a Gaussian is a dangerous mistake. Cue non-parametric statistics. Years back in the 80s chum Martin turned me on to the Mann-Whitney U-test, the Spearman rank correlation co-efficient, and other delights. I was hooked. Martin’s secret weapon was a book called “Non parametric statistics for behavioural scientists” by Sidney Siegel. It was full of arcane secrets but still written in plain English. Impressive. An updated version with John Castellan is available.

Why is doing statistical analysis so addictively satisfying ? I see it as a kind of merger of thought and action.

As an Experimental Scientist, you need to think hard and slow; to be absurdly rigorous and avoid the traps set by sloppy thought; to root out the assumptions you didn’t realise you were making; to experiment and test in a carefully controlled manner, and conclude only when you are sure. Don’t jump in. Stop, Think, Test.

The Busy Executive (or the Neolithic Hunter..) laughs. Pause and you are dead. Sicklied o’er wi’ the pale cast of thought you do not want to be. Sure, you don’t want to be dumb. But over the years, you build up your experience, knowledge, and instinct. It waits inside you, a coiled spring, ready for release when you need a Decision. Even if you have plenty of time, you never have all the information you need. Assemble what you have, run it through your judgement mill, and go for the best bet.

The Astronomer’s instinct is to be just like the experimental scientist but its impossible. You just can’t do the experiments you want. You have to make do with the ragbag of facts Nature has provided. Like the executive you need to take a decision with incomplete information, but you want it to be somehow impartial and rigorous. Well tough. You can’t absolutely and safely decide. You just can’t. But given any possible decision, you CAN say how likely it is you are being fooled. I can’t tell you which horse will win, but I can tell you whether I will accept that wager.

I’d better stop now or I am in danger now of drifting into the sticky morass that is the Frequentist-Bayesian debate.

Once I almost read a paper called “Are probabilities propensities ?” but it was lunchtime so I decided not to.