Tuesday, 19 August 2014

Highest Bayesian probability of Megrahi guilt 23 per cent

[Two highly important articles have recently been posted on the website Three Sides to Every Story. The first is headed Why the Lockerbie bomb was loaded at Heathrow and Megrahi was innocent. The first two paragraphs and the last paragraph of the lengthy piece read as follows:]

It is slightly shocking that Morag Kerr's book, which gives the first ever convincing, evidence-based reconstruction of the Lockerbie bombing, has not been reviewed in a major UK-wide newspaper since coming out in December.

She completely rebuts the case which was pressed by the Crown and accepted by the Camp Zeist court against the late Abdelbaset al-Megrahi, a Libyan agent, who served [8] years in prison in Scotland after conviction.  She also shows how the crime was really committed: not by Megrahi loading the suitcase with the bomb at Malta, to be transferred at Frankfurt onto the plane to Heathrow that was set to go on to New York City, before detonating over Scotland, but rather by persons unknown spiriting the suitcase onto the plane at Heathrow by placing it in a luggage shed ready to go directly on board Pan Am 103 to New York City. (...)

You will have to read the book and judge the forensic complexities for yourself.  For my part, I am convinced that Kerr is the first person to accurately reconstruct the Lockerbie bombing.  It was a crime perpetrated at Heathrow, and an innocent man suffered for it.  It is a textbook case of a miscarriage of justice, featuring leads missed by the police, unfeasible reconstructions of events and incompetent experts, as well as misconstrued, unreliable evidence both material and eye-witness.  The judges constructed a circumstantial case by irrationally explaining away key exculpatory evidence.  Kerr's book is not only a triumph of critical, evidence-based investigation, but also an instructive example of how a miscarriage of justice can occur.

[The second article is headed Bayesian probability analysis of the guilty verdict against Megrahi for the Lockerbie bombing. The first two paragraph read as follows:]

In my first post about the Lockerbie bombing, I discussed Morag Kerr's book reconstructing the commission of the Lockerbie bombing and demonstrating the innocence of the convicted man, Abdelbaset al-Megrahi.  In common with most humanistic reasoning, neither the verdict that condemned him nor Kerr's argument for his exoneration deployed any arithmetic of probability in analysing the evidence.  I think the widespread lack of arithmetical analysis of evidence is a serious weakness in fields like criminal law and history.

In this, I am following Richard Carrier in his book Proving History.  I am persuaded by him that we ought not just to use adjectives like "possible" and "probable" when we debate which theories best explain the evidence before us on a contentious historical or forensic question.  Additionally, we should use Bayes' Theorem: using numbers to express our opinions, and multiplying and dividing them according to Bayes' formula in order to calculate our reckoning of which theory explains the evidence the best.  The three main virtues of Bayes' Theorem are that it forces the analyst of evidence to specify clearly how good they think a theory is at explaining the evidence; it enables them to put all the evidence together in a mathematically sound way; and, above all, it forces them to look for evidence that supports their theory better than alternative theories, thus helping them to overcome the common failure to give alternatives due consideration.  Of course, different people can have different opinions about probabilities: the virtue of Bayes is that it brings out exactly what people agree and disagree about, and thus focuses their debate productively on crucial areas of disagreement.

[The author then subjects the evidence against Megrahi to Bayesian probability analysis and concludes that the highest probability of guilt that the judges should have arrived at was 23% and concludes:]

The judges failed to use Bayesian reasoning, which would have shown them that, far from a series of improbabilities adding up to a proof of Megrahi's guilt, they should have multiplied them out to a much greater sense of doubt.  They failed to appreciate that the crime was such an unlikely one on principle, that iron-clad evidence of Megrahi's guilt was required to overcome the prior improbability: extraordinary claims require extraordinary evidence.  A circumstantial case built on improbabilities does not cut it.

If the judges had applied correct probabilistic reasoning to the facts they did have about an unaccompanied bag from Warsaw, then this would have neutralised the evidence of an unaccompanied bag coming from Malta.

Of course, if we included the evidence explained yesterday, and considered how probable it was, on a hypothesis of Megrahi's guilt, that a mysterious suitcase answering to the description of the bomb-case would be seen by a baggage-handler at Heathrow before the feeder flight from Frankfurt had even arrived, then it would only be fair to divide the 23% we have come to here by maybe 10 times, if not more.  Include all the evidence, and the probability of guilt is minimal.

Moreover, include a more realistic expectation of the probability of getting the bomb into the baggage system at Malta, and the probability drops again to a minuscule number.

In sum, even without the new understanding born of Kerr's investigation, Megrahi should not have been found guilty. With it, his innocence is proven.

Thus the worst mass-murder in British history, the killing of 270 people, should be regarded as an unsolved crime.


  1. All,

    Precisely how and why three Scottish High Court eminences managed to lapse into the Twilight Zone, as they appear to have done at Kamp van Zeist, or what variety of medication they had been prescribed at the time, is an open question.

    Without question, Kerr has, ripped the whole process to shreds, fig leaves have now become in extremely short supply indeed!

    In a moderate degree of detailed criticism, however, Kerr's work was publicised by the 'Scottish Sunday Express' (editor: Ben Borland and journo Greg Christison). The fact that the like of Linklater etc have chosen to castigate us (JFM) as fun loving criminals is something you must direct at him his ilk and or his nether regions.

    The bottom line is that they (government, COPFS and etc) are now cornered facing a total of 9 allegations of criminality, accompanied by a major crime investigation sanctioned by Sir Stephen House (Chief Constable of Police Scotland), PE1370, and a third appeal against conviction.

    I hope they have some pick-axes handy, cos they are going to need some serious weaponry to dig themselves out of the deep-freeze of their own making!

    Pip, pip.

  2. Robert, Borland and Christison don't get it. I practically had to write the article for them, they were so clueless. And Borland has since stated categorically on television that he believes Megrahi put the bomb on board at Malta.

    However Heather Mills wrote a good review in Private Eye and Jennifer May did an even better one in the Big Issue Ireland. (I don't believe it was picked up by the Scottish edition though.)

    I was however rudely rebuffed by the Herald despite the interest the paper has taken in the case, and I think the author has a point about the book being ignored by the mainstream quality press.

  3. Dear Mr Black, I don't know about "highly important" but thank you for your recommendation. Hopefully my analysis will help ppl to understand the miscarriage of justice.

  4. It is very interesting to apply statistics/probability theory to court trial matters.

    Did I miss a link somewhere? I'd really like to see the report.

    I general, such an application is unfortunately too riddled with uncertainties and limitations to have any real value in the determination of guilt. Rather, it tends to mislead.

    The world is so complex that when math is applied it can only be done under an extreme amount of assumptions. Famous is the 'ceteris paribus' in economics.

    - - -

    As an example of the troubles, the amount of circumstantial evidence it completely dependent on how much effort was provided to bring it forward.

    There will always be quite a bit. A man is accused of poison-murdering his wife for the thrill of it.

    After heavy search the police finds:
    - that he 10 years ago bought a novel, "Bye, Darling", where a man gets away with murdering his wife. There are similarities with the actual murder at certain points.

    - he has been googling for various types of poison within the last 2 years.

    - a friend of his whom he meet now and then is found to have the not too uncommon type of poison in his cellar where he experiment with biochemistry.

    Hmm, interesting, isn't it? Evidence. Well, yes...

    Could we have questioned Megrahi's closest friend he might have told us that Megrahi one day had said "Damned Americans. One day soon somebody just might teach them a lesson they will not forget" and that Megrahi afterwards 'had looked like he was keeping some kind of secret'.

    The point is, that similar evidence will exists for all of us, lots of it, for any case, if you just dig deep enough.

    The parameter "How, and how hard was the evidence searched for, and by who" should be in somewhere.

    Milosevic had 500,000 of pages against him submitted by the prosecution. Can we then not conclude that he must be guilty of something?

    Will statistics help?

    - - -

    Even very simple considerations (from a strictly mathematical point of view) can be complicated.

    The probability of a number of independent events all happening is the product of the probabilities of each of them happening. One of the few intuitive and easy ones from that world. 10% that your wife serves the food you like best? 10% chance that Ipswich beats Man U? Well, the chance that both happens at the same day is 1%.

    So at Sally Clark's trial Professor Sir Roy Meadow stated, that that the chance of two children from an affluent family suffering cot death was 1 in 73 million.

    He calculated, from statistics, the chance of one child suffering cot death to be 1/8500, and, for two deaths, squared it.

    This argument was the main reason of the conviction of Sally Clark.

    The press even reported that 'The chance that Clark was innocent was one in 73 million".

    It's a long story. The argument does not hold, that is for sure. But it is impossible to evaluate to what extent it may apply.


    There are other cases, maybe the best known one is the one of Luca de Berk, where the application of math failed badly.

    It would now be easy to say “But that was math applied wrongly”.
    Yes, but then comes the question of determining when it was applied correctly.
    There will always be a thousand arguments against it.


  5. - - -

    "It just can't be a coincidence..."
    The whole process of thought is so riddled with traps, "fallacies", that it can make your head spin.

    At times one single piece of evidence is enough. Two or more pieces, that alone would allow for a conclusion is of course even better

    N pieces of non-conclusive evidence - no matter the size of N - will much more rarely allow for a guilty verdict 'beyond reasonable doubt' than most people would ever imagine.

    I'd say, at the time Megrahi was a reasonable suspect.

    But the question: “Can we conclude that it could not easily have been anyone else that we just don't know about?” could never be answered with a “no” at the end of the trial.
    But this they did.

    I am afraid that math wouldn't really help us. But much looking forward to maybe seeing this report.

  6. I wrote: "'Can we conclude that it could not easily have been anyone else that we just don't know about?' could never be answered with a “no” at the end of the trial.
    But this they did."

    Did you spot it? The "no" should be replaced with a "yes". (I was just testing if you paid attention.)

  7. The full text of the Bayesian probability article can be found by clicking on its title in the blogpost. But maybe this isn't the "report" you were referring to, sfm?

  8. Dear SFM,

    I think the point is, that since one must inevitably make assumptions, test theories, assign probabilities, all implicitly -- then one may as well do it in a mathematically sound way.

    It is difficult to know what probabilities to assign, but if you assign higher probabilities than you really think, then you get a maximum final probability, and hence your argument works "a fortiori". I.e. "whatever more realistic probabilities you care to apply, you won't get a higher final probability than x."

  9. All,

    Never been dreadfully bright academically, and especially with numbers. Damn, I've only got ten fingers to count with after all! Having said that though, I do have a lot of time for Émilie du Châtelet, Niels Bohr and Lisa Meitner.

    Baset was stitched up, end of. I and the gang like to call it triangulation, some may prefer the term strangulation. There is 1370, 9 allegations of criminality and a 3rd appeal active. Cornered! Let's see how Mulhooligan blags himself out of that firing line! Chambers Street has a choice: 'Dig yourselves deeper into the deep-freeze or come out without blood on your hands'. We are the 'Nice Guys', we seek no punishment only resolution.

    And, by the way, Rolfe, don't bite the hands that feed you.


  10. When the "hand" goes on TV and openly declares that the bomb was loaded at Malta and Megrahi being there at the time is highly incriminating, I start to feel somewhat famished.