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Miscalculating the odds

imageI used the non-specific words “wildly implausible” directed at commenter John here on this forum to described his speculation on various fraud scenarios in Hawaii.  I actually did a calculation once on the probability that Obama was born in Kenya, given the fact that his literary agent said otherwise in a brochure of biographical information about several authors. (I came up with a generous 0.000007.)

Well that crazy Christopher “Lord” Monckton has crunched his own numbers on whether Obama’s long form birth certificate is legitimate, reports WorldNetDaily. His answer is 0.0000000000000000000016.

Monckton’s argument basically assumes probabilities for various anomalies in the long form PDF, and then multiplies them all together. Monckton obviously is not a mathematician (his college degree is in Classics) because he makes some obvious mistakes. I spotted two right off the bat: his numbers are wrong and his math is wrong.

First, unless two outcomes are independent (not correlated), you can’t simply multiply the probabilities. My article (linked above) actually shows how correlated events are properly treated. Let me give an example: what is the probability that someone is a male freemason. I’ll just make up the individual probabilities and say that the chances that someone is a man is .5 and the chance that someone is a freemason is .0001. You can’t multiply those probabilities and get .00005 because all freemasons are men (the two are correlated).

The second big mistake is to assign a probability to certain characteristics of the certificate PDF. For example, Monckton says that the chance that the registrar date stamp is in a separate clipping region is 1 in 100. This is a made up number. In fact given the hardware and software combination, the chances should be 1 or 0 for a given document since the process is algorithmic.

The big fallacy, and I don’t know a formal name for it, is to take any event that already happened and then assign a probability to it having happened. Say the winning lottery number is 1 4 6 9 18 21 22 5 7. It makes no sense to say that the odds against that number coming up were a zillion to one and conclude that the lottery must be rigged.

Monckton is fairly unfamiliar with the facts, for example, he assigns a 1 in 25 chance to the certificates being out of sequence (numbers matching birth order) in “error.” However, we know that the certificates were not in sequence for anybody. If anything they were in alphabetic order by last name, and Obama’s number is correct. The neonatal death is the only one out of alphabetic sequence (much higher). He also assigns a probability to Obama’s father’s birth date being wrong, but Obama Sr. put different birth dates on a host of government forms.

Monckton’s analysis is just pseudomathematical gobbledygook, perfect for birthers.

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38 Responses to Miscalculating the odds

  1. avatar
    donna September 26, 2012 at 9:46 pm #

    the non-lord was the republicans’ only witness at a climate change hearing in 2010

    GOP Chooses Non-Scientist Lord Monckton as Sole Expert Witness at Climate Change Hearing

    http://www.huffingtonpost.com/brendan-demelle/gop-chooses-lord-hitler-y_b_565126.html

    he gets around

  2. avatar
    Squeeky Fromm, Girl Reporter September 26, 2012 at 10:08 pm #

    Well synchronicity strikes again. I have just finished one on this, too. What are the odds of that happening???

    Squeeky Fromm
    Girl Reporter

  3. avatar
    Andrew Vrba, PmG September 26, 2012 at 10:39 pm #

    Anyone else find it humorous that a man who falsely uses the title “Lord”, despite not being a member of the House of Lords, has the balls to call someone else a phony?

  4. avatar
    Dave B. September 26, 2012 at 10:50 pm #

    Monckton in motion! (down at the bottom of the page).
    http://inversesquare.wordpress.com/2011/07/19/send-in-the-clowns-upper-class-twit-edition/

  5. avatar
    Slartibartfast September 26, 2012 at 11:04 pm #

    OMG! Squeeky is really Doc C! The probability of this is definitely 1 (or 0… I forget which ;-) ).

    Squeeky Fromm, Girl Reporter:
    Well synchronicity strikes again. I have just finished one on this, too. What are the odds of that happening???

    Squeeky Fromm
    Girl Reporter

  6. avatar
    Paul September 26, 2012 at 11:15 pm #

    Ok, I’ve seen this guy quoted on FauxNews and the WingNut Interwebs. But seriously, who the F#*K is “Lord Monkton”, and why the F#*K should any of us care what the F#*K he thinks?!

  7. avatar
    brygenon September 27, 2012 at 12:06 am #

    Technically astute, as usual, Dr. C, but I think there are yet bigger sources of error.

    Even independent and correct probabilities multiplied together are not the net probability of the default hypothesis. Any particular observable outcome has a probability less than one, so it’s a one-way trip arbitrarily close to zero whether the document is authentic or not.

    When we go looking for anything we can always find something. When we look in many places for the unusual, we will usually find it. See the recent ig Nobel prize winner, “Neural Correlates of Interspecies Perspective Taking in the Post-Mortem Atlantic Salmon: An Argument For Proper Multiple Comparisons Correction”. Birthers fail to apply proper multiple comparison correction around their dead fish.

    Perhaps the neatest refutation is to turn the method around and use it asses the probability that Obama’s long form birth certificate is fake. What percentage of fake birth certificates are linked by the state authority that produces real ones with the description “a certified copy of his original Certificate of Live Birth”?
    http://hawaii.gov/health/vital-records/obama.html

  8. avatar
    Greenfinches September 27, 2012 at 1:20 am #

    There are many people with the title ‘Lord’, who are not members of the House of Lords – but Monckton is at fault for claiming he is a member of that House, when he isn’t.

    As I recall there is a copy of a letter to him from the authorities at the House of Lords on their website, so that people will be able to see that Monckton knows he lies…..

    He talks a lot of nonsense about many things that he knows nothing of – climate change for one. Why, I don’t know. Follow the money????

  9. avatar
    Slartibartfast September 27, 2012 at 1:53 am #

    If you’d like to see what a real expert has to say about an algorithm being used to generate the LFBC image, check out this article at John Woodman’s site:

    http://www.obamabirthbook.com/2012/09/genuine-world-class-computer-expert-evaluates-obamas-birth-certificate-pdf/

  10. avatar
    Dr. Conspiracy September 27, 2012 at 2:00 am #

    Well, given that we probably get our ideas from similar sources, it’s not all that remarkable.

    However, there can be some really crazy arguments made that everything that happens is wildly improbable. One might quote a really tiny probability that a team of 100 monkeys with keyboards will reproduce the works of William Shakespeare in a year; however, they will produce something and that something is no more probable than anything else.

    Squeeky Fromm, Girl Reporter: Well synchronicity strikes again. I have just finished one on this, too. What are the odds of that happening???

  11. avatar
    Squeeky Fromm, Girl Reporter September 27, 2012 at 2:37 am #

    Dr. C:

    I guess you are right. I was real excited for a while because I thought I discovered a new mathematical thingie. Which is if you have 2 sets of 5 cards each, and 3 cards in each set is a face card, then what are the odds you can draw 1 card from each set and get a face card???

    Which is 3/5 X 3/5 = 9/25. But, if you have 10 cards and 6 of them are face cards, and you draw twice, then you should have 6/10 x 5/9 = 30/90 or 1/3. But 9/25 is MORE than 1/3, which would take 27 on bottom. Sooo I got to thinking maybe I had found all that missing stuff in the universe???

    But I didn’t.

    Squeeky Fromm
    Girl Reporter

  12. avatar
    Slartibartfast September 27, 2012 at 3:25 am #

    Squeeky,

    I just think it’s good that you were excited when you thought you had discovered a new mathematical thingy—I felt exactly the same way when I thought I had figured out how to trisect an angle in high school geometry class.

    Squeeky Fromm, Girl Reporter:
    Dr. C:

    I guess you are right. I was real excited for a while becauseI thought I discovered a new mathematical thingie.Which is if you have 2 sets of 5 cards each, and 3 cards in each set is a face card, then what are the odds you can draw 1 card from each set and get a face card???

    Which is 3/5 X 3/5 = 9/25. But, if you have 10 cards and 6 of them are face cards, and you draw twice, then you should have 6/10 x 5/9 = 30/90 or 1/3. But 9/25 is MORE than 1/3, which would take 27 on bottom. Sooo I got to thinking maybe I had found all that missing stuff in the universe???

    But I didn’t.

    Squeeky Fromm
    Girl Reporter

  13. avatar
    The Magic M September 27, 2012 at 4:32 am #

    > The big fallacy, and I don’t know a formal name for it, is to take any event that already happened and then assign a probability to it having happened. Say the winning lottery number is 1 4 6 9 18 21 22 5 7. It makes no sense to say that the odds against that number coming up were a zillion to one and conclude that the lottery must be rigged.

    That’s basically the same fallacy as the assumption that because the chances that the initial conditions of the universe resulted in life coming to existence are so mathematically small, it cannot have happened without outside interference (“God”).

    Squeeky Fromm, Girl Reporter: But 9/25 is MORE than 1/3

    … because there is a difference between having two independent sets and having a single (self-dependent) set.

    Drawing one face card from the 10 card set reduces your chances of drawing another face card (60% to 55.5…%) whereas with the 5 card sets, the chance for the second draw remains the same, regardless of what you draw from the first.

    I think this can be related to the famous Monty Hall problem which is also about (the illusion of) independent choice.

    Also, you might try to calculate the number of balls in the Ross-Littlewood paradox if you have an afternoon to spare. ;)

    But these things remind me why I never took a statistics course when I studied math. My girlfriend at the time did, and I had a hard time understanding the stuff because I cannot switch off my intuition (and statistics is pretty often very counter-intuitive). I have no problems visualizing curves in tangent bundles over bounded manifolds, but statistics is my kryptonite.

  14. avatar
    Keith September 27, 2012 at 5:43 am #

    The Magic M: I think this can be related to the famous Monty Hall problem which is also about (the illusion of) independent choice.

    Oh yes, please lets go off on the Monty Hall Problem.

    Because the MSM (Main Street Mathematicians) have it wrong and are all complicit in a giant conspiracy to make us believe that a 50-50 choice is really a one third v two third choice after one third of the choices have been removed.

    Its a conspiracy I tell you! I’m right and the MSM are all ignorant ignoramuses.

  15. avatar
    Slartibartfast September 27, 2012 at 5:50 am #

    The Magic M:
    > The big fallacy, and I don’t know a formal name for it, is to take any event that already happened and then assign a probability to it having happened. Say the winning lottery number is 1 4 6 9 18 21 22 5 7. It makes no sense to say that the odds against that number coming up were a zillion to one and conclude that the lottery must be rigged.

    I don’t know that there is a name for it—it’s kind of like a cross between the Texas Sharpshooter fallacy and the probabilistic analog of lies, damn lies, and statistics. Formally, while the odds that a particular number came up were small, the odds that some number would come up were 1.

    That’s basically the same fallacy as the assumption that because the chances that the initial conditions of the universe resulted in life coming to existence are so mathematically small, it cannot have happened without outside interference (“God”).

    Yeah, the birthers often use the same tactics favored by creationists… (they like God of the gaps arguments as well).

    … because there is a difference between having two independent sets and having a single (self-dependent) set.

    Drawing one face card from the 10 card set reduces your chances of drawing another face card (60% to 55.5…%) whereas with the 5 card sets, the chance for the second draw remains the same, regardless of what you draw from the first.

    I think this can be related to the famous Monty Hall problem which is also about (the illusion of) independent choice.

    Yes—the Monty Hall problem is the extreme case (fewest number of choices). You are given the choice of three doors—behind one of which is a prize. After you choose, Monty (the host of the game show “Let’s Make a Deal” which operated this way) would open a door that didn’t contain the prize and offer to let you switch. Mathematically, you should always switch (you have a 50% chance of winning instead of a 33% chance). Psychologically, people are very biased towards going with their original choice (Mythbusters found that all of 20 people tested stayed with their first choice), and functionally, Monty said that (a) he knew where the prize was; and (b) he didn’t have to offer a deal (he could just open up the door and show you that you lost). When you consider the fact that he was a master at reading people, his suggestion that if you were offered money to switch (which he would sometimes do), you should go for the bird in the hand seems like a good one…

    Also, you might try to calculate the number of balls in the Ross-Littlewood paradox if you have an afternoon to spare.

    I’ll have to check it out…

    But these things remind me why I never took a statistics course when I studied math. My girlfriend at the time did, and I had a hard time understanding the stuff because I cannot switch off my intuition (and statistics is pretty often very counter-intuitive). I have no problems visualizing curves in tangent bundles over bounded manifolds, but statistics is my kryptonite.

    There’s your problem—you should have studied probability (these are all probabilistic fallacies), not statistics. If you can handle tensors on compact manifolds you could probably understand probability* (especially if you were good with PDEs as well—Brownian motion is a consequence of the heat equation), but statistics is something very different (although it uses probability to do all of the heavy lifting…). Types of mathematical intuition, like other sorts of intuition, are developed by training—it’s probably more accurate to say that your statistical intuition wasn’t very good because you never took a statistics course—just my $0.02.

    * pun intended ;-)

  16. avatar
    Slartibartfast September 27, 2012 at 5:58 am #

    You don’t want to cross the MSM—have you ever wondered what happens when the conspiracy theorist gets it right? Bwa-ha-ha-HA-ha!

    Keith: Its a conspiracy I tell you! I’m right and the MSM are all ignorant ignoramuses.

  17. avatar
    Thrifty September 27, 2012 at 7:06 am #

    So I assume that in Birther circles, Mr. Monckton is a Certified Mathematical and Probability Expert?

  18. avatar
    Slartibartfast September 27, 2012 at 7:55 am #

    Right—except that the birthers probably fawn over his made-up title in a stunning display of thoughtless hypocrisy…

    Thrifty:
    So I assume that in Birther circles, Mr. Monckton is a Certified Mathematical and Probability Expert?

  19. avatar
    Tarrant September 27, 2012 at 8:34 am #

    This tirade by Mr. Monckton made me laugh – not because of the way he multiplied all these correlated events together (although that was good), but in the haphazard way he just assigns probabilities.

    “Let’s say the odds of the stamp showing up in a separate clipping layer are 100 to 1.”

    No justification, no nothing. He pulls the numbers for everything quote literally out of his ass and then concludes by arguing that the math is conclusive and straightforward.

    I mean I can say “Let’s say the odds of me having breakfast today are 1000000:1.”

    But I did have breakfast today…OMG it’s a million to one rarity! And EVERY DAY I hit that million to one jackpot! I’m the luckiest person alive!

    Or perhaps those odds are wrong, or its an event for which probability really doesn’t apply. Nah, couldn’t be.

  20. avatar
    The Magic M September 27, 2012 at 8:52 am #

    Thrifty: So I assume that in Birther circles, Mr. Monckton is a Certified Mathematical and Probability Expert?

    Makes perfect sense. In their bizarro world, everything is upside-down. They would likely hire Stephen Hawking to play on their basketball team and give the science department to Mike Tyson. No, wait, I forgot, Tyson’s black…

    Slartibartfast: Psychologically, people are very biased towards going with their original choice

    Psychologically, people are conditioned to know that if the host offers you money to switch, the odds are you picked the winner and he’s trying to lure you away. That’s something that probably outweighs any probability evaluations the candidates might have made.

    Slartibartfast: especially if you were good with PDEs as well

    No, PDE’s also weren’t my strongest suit, but I never had to take any exams there either. I love number theory and got my degree in differential geometry and computer science.

  21. avatar
    Scientist September 27, 2012 at 8:58 am #

    Tarrant: This tirade by Mr. Monckton made me laugh – not because of the way he multiplied all these correlated events together (although that was good), but in the haphazard way he just assigns probabilities.

    But, I think we could come up with some very good numbers for the probability of a US citizen living in Hawaii travelling to Kenya to give birth in 1961. There were 4.28 million births in the US in 1961. According to the State Department report that Doc posted here a while ago, there was 1 birth to a US citizen in all of East Africa in 1961 (and that was almost certainly to a mother who lived there rather than a tourist). So that places the odds of the President being born in Kenya at <1:4.28 million. Unlike Monckton's, that is a real number.

  22. avatar
    misha September 27, 2012 at 9:48 am #

    Lord Monckton is Sasah Baron Cohen: http://www.youtube.com/watch?v=w833cAs9EN0

  23. avatar
    Thrifty September 27, 2012 at 10:22 am #

    It kinda reminds me of Ziggy, the supercomputer from Quantum Leap, who was always calculating arbitrary probabilities of events that really had no quantitative values to calculate a probability on. “Ziggy computes that there’s a 86% chance that if you arrest this criminal, the victim’s wife will live happily ever after” and so on.

    Tarrant: This tirade by Mr. Monckton made me laugh – not because of the way he multiplied all these correlated events together (although that was good), but in the haphazard way he just assigns probabilities.

  24. avatar
    John Potter September 27, 2012 at 10:59 am #

    Thrifty: So I assume that in Birther circles, Mr. Monckton is a Certified Mathematical and Probability Expert?

    Absolutely.

    I mentioned elsewhere that his improbable blunderings had cost him dearly once (see the Eternity Puzzle). His mistake there was pandering to people of greater intelligence than his (and putting his own skin in the game!). He’s wised up and moved on to much safer endeavors … namely, pandering to fools on their dime.

  25. avatar
    The Magic M September 27, 2012 at 11:09 am #

    One of my favourite examples of miscalculating the odds in a legal context involved a murder case (don’t remember the country, I think it was England, but do they have trial by jury?) with DNA as the prime evidence.

    The scientific result was that one in a billion people had the DNA sequence that was found at the crime scene (and also in the defendant).

    Now the proper conclusion is that there are 7 people in the world who could have been the killer, therefore a low, but still pretty good chance that the defendant was innocent.

    The DA however presented this to the jury as “there is a 1:1 billion chance that the defendant wasn’t the killer”.

    (In related news, I always chuckle when people boast how their provider guarantees them a 99% yearly uptime, not realizing this means their online shop can be down for 3.5 days in a row, possibly in the middle of Christmas sales. My current employer – not a run-of-the-mill web hoster – guarantees a 97% service uptime. Clients are happy. Go figure.)

  26. avatar
    John Potter September 27, 2012 at 11:17 am #

    Monckton’s masturbatory “mathematics” are a better approximation of the likelihood of the birther explanation, as the facts he assigns values too are themselves unlikly birther memes.

    The Magic M: not realizing this means their online shop can be down for 3.5 days in a row

    3.6525 days … c’mon now, M, you’re spoting them nearly 4 hours! :P

  27. avatar
    Dr. Conspiracy September 27, 2012 at 11:32 am #

    DNA evidence becomes more and more problematic when there are more and more people in DNA databases. What does a one in a million match mean when there are 10 million DNA results in the database? If you’re thinking of the same case in England that I am, the defendant whose DNA matched with a high probability, was the victim Parkinson’s disease that confined him to a wheel chair, but it was alleged that he committed a crime that required him to climb up a wall and enter a second-story window despite the fact he lived 200 miles away and had an alibi. He was not convicted.

    The Magic M: The scientific result was that one in a billion people had the DNA sequence that was found at the crime scene (and also in the defendant).

  28. avatar
    The Magic M September 27, 2012 at 12:16 pm #

    Dr. Conspiracy: If you’re thinking of the same case in England that I am

    Not sure, just that one statistical fallacy remained in memory.

  29. avatar
    foreigner September 27, 2012 at 2:08 pm #

    if he were a mathematician he would have realized what interesting
    properties Eternity had for algorithmic examination and teaching.
    It turned out to be a really interesting task for programmers and
    (nondeliberately) well in the small window of solvable-but not too easy.
    (not the ~10^25 years needed to solve E2)
    Monckton should have (co)written an article in some scientific
    journal about it. But all he was interested in was how to make it attractive
    for hand-solvers and to get good publicity in the newspapers.

  30. avatar
    foreigner September 28, 2012 at 3:25 am #

    none of the mathbots noticed the calculation error that WND even put
    into the headline ?

  31. avatar
    RuhRoh September 28, 2012 at 7:22 am #

    Monckton is going to speak at Southeastern Louisiana University about another subject he knows nothing about-climate change! http://www.desmogblog.com/2012/09/25/southeastern-louisiana-university-has-honor-hosting-climate-denial-activist-lord-monckton

  32. avatar
    Bran Mak Morn September 28, 2012 at 7:56 am #

    Monckton is the biggest fraud of them all. Which is what is so ironic about birthers loving him.

    Just look at his Eternity Puzzle and what happened with that: http://www.scotsman.com/news/scottish-news/top-stories/aristocrat-admits-tale-of-lost-home-was-stunt-to-boost-puzzle-sales-1-679237

    He does publicity stunts … you know.. lies…

  33. avatar
    Bran Mak Morn September 28, 2012 at 7:57 am #

    Also, with the Eternity Puzzle, his math was shown to be wrong… again.. he thought it wouldn’t be able to be solved in the time limit he gave for the prize! LOL.

  34. avatar
    misha September 28, 2012 at 8:39 am #

    RuhRoh: Monckton is going to speak at Southeastern Louisiana University about another subject he knows nothing about

    Bran Mak Morn:Monckton is the biggest fraud of them all. Which is what is so ironic about birthers loving him…He does publicity stunts … you know.. lies…

    Monckton is Sasha Baron Cohen: http://www.youtube.com/watch?v=w833cAs9EN0

  35. avatar
    John Potter September 28, 2012 at 9:17 am #

    RuhRoh: Monckton is going to speak at Southeastern Louisiana University about another subject he knows nothing about-climate change!

    Another subject on which the willing are eager to hear they are right rather then the truth, even willing to pay for the privilege of their own stupefication.

    I wish I could burden my opponents in Civ 5 with similar plagues of the stupid. Gin up a few demagogues and go to town!

  36. avatar
    The Magic M September 28, 2012 at 9:39 am #

    John Potter: Gin up a few demagogues and make money!

    FIFY

  37. avatar
    G September 28, 2012 at 10:57 am #

    There is a point where the nonsense is so clearly bogus that you don’t even waste your time. All of his numbers are pulled out of his arse and his correlations are ficticious. At that point, you just roll your eyes and dismiss complete garbage as not worthy of paying it any attention. Random stupidity cobbled together isn’t a real calculation in the first place.

    foreigner:
    none of the mathbots noticed the calculation error that WND even put
    into the headline ?

  38. avatar
    gorefan September 28, 2012 at 11:59 am #

    Dr. C

    “If anything they were in alphabetic order by last name, and Obama’s number is correct. The neonatal death is the only one out of alphabetic sequence (much higher). ”

    According to Verna Lee, the BCs were collected monthly and sorted geographically. I agree that they were then sort alphabetically. The neonatal was not born at Kapiolani or even in the city of Honolulu, but at Wahiawa General. which is 20 miles away.

    There were 15578 births in Hawaii in 1961. If the first certificate in January was 00001 and adding the monthly totals, the last BC issued in July, 1961 was 09942. The first child in August would have number 09943.

    The WND girl was 09945 (the third issued in August) and Sunahara was 11080 (the 1128th issued in August).

    According to the NCHS the geographic area of Honolulu County was divided into the city of Honolulu and the rest of the county.

    I think they collected the BCs monthly, separated them by geographic area and then alphabethized them within their respective geographic area.

    If we test this with Edith Coates BC from 1962, we see that she was born June 15th at the same hospital as Sunahara and her cert # is 8498. Between January 1 and May 31st, 1962 there were 7400 births. That would mean that there were 1097 certificate numbers issued before her’s. With a last name that begins with “C”, she should have a lower cert #. But if all of the city of Honolulu births for June were number ahead of her’s, a higher number makes sense.