Interesting spam

I usually don’t like spam, but this message I got the other day from Ed Tranham was pretty good:

If A is half of B why can’t I conclude that B is two times A?

Suppose you known that, on average, 50% of the trucks that start out in a military campaign are fully operational at the end. Then you would be correct in deducing that, if you start with 100 trucks you will end up, on average, with 50 that are fully operational. But, what if you know that you ended a campaign with 50 operational trucks. Then is it correct to assume that, on average, you started with 100? This was a simplified version of a real problem that one of Agena’s clients had to tackle and the answer (surprisingly to them) was NO. This has everything to do with the way we reason with prior assumptions (this reasoning lies at the heart of the so-called Bayesian approach to probability).

Click here for the full article, which is one of a series looking at probability puzzles and fallacies. You can see more here.

They seem to be advertising some sort of software.

3 thoughts on “Interesting spam

  1. An interesting problem with an awful delivery. In particular, no one would put the uncertainty of the outcome of passed students that high. Even with an obscenely uninformative prior distribution on p = "does a student pass the class?", with 50 passes and 50 fails, that's still basically a p|y ~ Beta(50,50), with 1/(p|y) = 2.01. So with reasonable assumptions, it's still only 100.5 students on average who started.

    I'd normally agree that someone's selling something with this, but the fact that the page was cosponsored by a university makes me wonder about their grossly exaggerated result.

  2. In response to Andrew Thomas's offensive comments I have posted the following message on the blog that he links to. At time of writing my posting is 'being reviewed':

    **************************************

    I am the author of the original article and a colleague of mine alerted me to your posting on Andy Gellman's blog. You said (about my article):

    "An interesting problem with an awful delivery."

    You also said:

    "I'd normally agree that someone's selling something with this, but the fact that the page was cosponsored by a university makes me wonder about their grossly exaggerated result."

    For a start it would not have been too difficult for you to have found out who I was since my name is very clearly stated at the bottom of the article, and the web site provides full information about me. So it would have been nice for you to raise the concerns you have about the article with me directly rather than through the use of insulting comments on a third party web site.

    As to the substance of your criticisms, you seem to have misunderstood the particular problem and context and have produced a different model, that does not address the very real example that we had to deal with. You say that

    "The original authors … make a profound overestimation of the average of starting students, choosing a "posterior" distribution that yields a class size of 150."

    This is not what I did at all. I made it clear that the crucial assumption was the prior average class size. To illustrate the problem I chose an example in which the prior average was deliberately high, 180. The fact that this gives a posterior average class size of about 153 when the 50 passes is observed is exactly the point I wanted to emphasize. Your comment about us making a "profound overestimation" is quite simply nonsense. Part of the fallacy was to assume that the class size of 100 in the specific example was in any way representative of the average class size.

    I suggest you read the article again and pay particular attention to the (real) vehicle example at the end. The model that I produced EXACTLY represented the real data.

    You should also be aware that the aim of my probability puzzles/fallacies web page is to raise awareness of probability (and in particular Bayesian reasoning) to as broad an audience as possible. While I am pleased if other professional statisticians read it, it is not they who are the target. This means having to use a language and presentation style that does not fit with the traditional academic approach.

    In fact, one thing I have discovered over the years is that too many academic statisticians tend to speak only to other like-minded academic statisticians. The result is that in practice (i.e. in the real world) potentially powerful arguments have been ‘lost’ or simply ignored due to the failure to present them in a way in which lay people can understand. I have seen this problem extensively first hand in work as an expert witness. For example, in a recent medical negligence case the core dispute was solved by a very straightforward Bayesian argument. However, this had been presented to the defence lawyers and expert physicians in the traditional formulaic way. Neither the lawyers nor the physicians could understand the argument, and the QC was adamant that he could not present it in court. We were brought in to check the validity of the Bayesian results and to provide a user-friendly explanation that would enable the lawyers and doctors to understand it sufficiently well to present it in court. The statisticians simply did not realise that what is simple to them may be incomprehensible to others, and that there are much better (visual) ways to present these arguments. We used a decision tree and all the parties understood it immediately because it was couched in term of real number of patients rather than abstract probabilities. Had we not been involved the (valid) Bayesian argument would simply have never been used.

    Norman Fenton
    Professor of Computer Science
    Head of RADAR (Risk Assessment and Decision Analysis Research)
    Computer Science Department
    Queen Mary (University of London)
    London E1 4NS.
    Email: [email protected] http://www.dcs.qmul.ac.uk/research/radar/ http://www.dcs.qmul.ac.uk/~norman/
    Tel: 020 7882 7860

    CEO
    Agena Ltd http://www.agena.co.uk
    London Office:
    32-33 Hatton Garden
    London EC1N 8DL
    Tel: +44 (0) 20 7404 9722
    Fax: +44 (0) 20 7404 9723

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