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November 16, 2009

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Richard Mann

I'm not sure its valid to say Pd|s = 1 - Pd|f. Probabilities should sum to 1 in the argument, not the condition. But other than that a very illuminating argument

Chris Williams

I'm not a probability theorist, but I can tell you that the British Empire casualties in WW1 reached a very high level in the last four months of 1918. And we know how that one turned out. The Battle of Berlin resulted in more than 200,000 soviet casualties too.

Whatever the merits of Bayesian analysis, this crude McNamarism as an index of anything much needs to be looked at very critically, if at all. I'd pick a better example next time, were I you, Chris D.

David Heigham

I half remember an ancient example (from the 1920s or 30s, I think)illiustrating the appliction of Bayes theorem to a roughly analagous situation. It ran something like this:
There are disturbances in a colony. The government sends in troops to pacify the area. The trend in the number of fatalities from violence is an indicator of whether the policy is succeeding or not. That is to say, in the absense of other indicators a decline in the number of fatalites from period to period indicates that the likelihood that the policy will succeed is rising from period to period. The other side of that coin is that a rising trend in fatalities indicates a declining likelihood of the policy succeeding.

The message I remeber from the example was that even if your prior (here for the likelihood of success) was not quantified, you could tell the direction in which it wes changing by looking at the evidence.

Jackart

D-day was the bloodiest day of the war as far as British military casualties were concerned. The more effort you make, the more casualties you take. In Afghanistan for example the Italians were thought to have stayed in base, buying peace with a taliban Danegeld. The French, taking over were not informed about the payments, and took casualtis as a result. The US and British forces (and latvians, Danes and others who are also fighting hard) are taking casualties, whilst fighting for the aim

War is a risky business, and I think, like Chris Williams, you should pick a better, more tasteful example.

chris

@ Chris, Jackart. Your examples do not invalidate the use of Bayes theorem. Quite the opposite.
The question: are high casualties a sign of success or failure? is surely important.
In the case of D-day, casualties were high because the operation was a high-stakes, high pay-off one. They were not, therefore, a sign of failure: in my example, Pd|s was high.
All Bayes theorem does is force us to ask this question.
I would have thought that when lives were at stake, it is more important to think properly.
It is precisely because war is a risky business that we need Bayesianism, as it is a huge part of how to think about risk.

CharlieMcMenamin

Chris,
you've got to help us non mathematical types who can't count passed 10 without removing our socks on this one.

I've read this post and the previous one with interest and I note that one link goes to a Wiki list of of cognitive biases which include 'Déformation professionnelle — the tendency to look at things according to the conventions of one's own profession, forgetting any broader point of view.'

So, forgive me, but do we have anything more here than an economist used to calculating risk probabilities telling us that politicians should routinely use a risk management technique?

You accept Bayes can't tell you what success is, just, it seems, measure it if you first agree that there is a cut off point of possible non optimal results/ consequences you're not prepared to accept.

Quite often, though, things in politics aren't like that at all. Some policies are not about results or consequences per se, but about keeping together invariable fissurous coalitions, each element of which will have a different point of Bayesian non optimal return on different issues. Scoring this sort of thing is very complex and, to be frank, hard to see the point of.

Isn't this exactly an example of 'Déformation professionnelle? Or am I just being very, very slow?

jameshigham

Note that I am not saying that Bayes’ theorem is sufficient.

Thank goodness for that.

BG

Chris,

Thanks for the interesting example. Not quite sure that the math works entirely though. As Richard points out, I don't really see why you would have Pd|s + Pd|f = 1. The rest seems fine, but that relationship doesn't have to hold I think (if d and s / f were independent for instance,that would imply that Pd = 0.5 no matter what, which doesn't really sound right).

Keith

Is this not an example of the misuse of Maths along the line criticised by J S Mill? Some things do not admit of numerical methods as they involve Judgement of a qualitative kind. To use numbers is an attempt to give a spurious certainty to uncertain prospects. Any adventure by Bush was obviously a bad idea. Since the Neocons are a bunch of Right wing lunies who think history is on their side; rather like other extremists. History however is not on any side. History is an ex post construct.

chris

@ Charlie - I don't think this is an example of deformation professionnelle. Bayes theorem is a way of thinking, used by many science professionals. In my example it explicitly invites us to draw upon another area of expertise, as only military expertise can tell us Ps and Ps|d.
You're right that politics is also about building coalitions as well. But surely knowing the (changing) probability of the success of a project matters.
@ Keith - this would be misusing maths, if it were used to generate a spurious certainty (or even a certainty about probabilities). But it's not. We can input ranges into the theorem, or use the theorem backwards ("You think the Afghan mission will be a success. What values of Ps and Ps|d generate this view, with what degree of certainty?)Or we could use it just as a reminder to update our views in light of evidence.

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