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Oswald evidence

Aaron Edlin writes:

This story is interesting in its own right . . . I have a question so I thought I would ask a Bayesian statistician.

One fact I learned on reading this article is that Oswald had a job in the building that Kennedy drove by before Kennedy’s route was chosen. So Oswald didn’t get the job to shoot Kennedy. Does this “prove” there was no conspiracy or indeed have any bearing on the likelihood of that inference?

My reply: I actually have a friend whose father worked on the Warren Commission so I’ve long been convinced that Oswald acted alone.

But, sure, this piece of information should shift the probability a bit. The difficulty is that the amount (and even the direction) of the shifting of the probability depends on the model you are assuming for various possibilities, and these possibilities themselves are not so clearly defined. Bayesian statistician Jay Kadane wrote a book a few years ago on the Sacco and Vanzetti case, going into the evidence supplied by each piece of information. The whole piece of work was impressive but it was hard for me to follow, there were so many little details.


  1. jonathan says:

    Your personal probability? Not “the probability”, right? If the question is “what do you think?”, the answer is personal, isn’t it?

    So for example, lots of people think things like:

    1. There’s no way the “magic bullet” could have hit both Kennedy and Connally (a spelling I keep having to look up because I can only remember it isn’t Connolly). But it’s public information the rear seat was higher because it was a specially designed parade car, so if your “prior” is an assumption about the car, then you’re wrong.
    2. There’s no way Oswald could have fired 3x in a little over 6 seconds with a bolt action rifle. Lots of personal priors again: misinformation about how long a shot takes with that rifle, etc. But it’s hard to evaluate the kind of personal prior that doesn’t realize you count from the 1st shot so it’s 2x in 6+ seconds. Public information, intentionally distorted by some, ignorantly distorted by others, stupidly not thought through by others.

    I could go on but all of these only affect personal probabilities and those can be entirely irrational. And if aggregated, that can be entirely irrational, as for example the widespread belief in creationism in the US … which approaches near unanimity in some countries. Or more insidiously, I think of Thomas Mann’s comment after WWII when invited back to Germany to serve as a sort of cultural, moral beacon, that Germany had sold its collective soul to the devil and he would not so easily redeem it. That phrase “collective soul” refers, doesn’t it, to an astounding in retrospect mass aggregate belief in nonsense like a 10,000 Year Reich and the Master Race, a gathering together of personal probability estimates to make something horrifying in its ridiculousness.

    I know this is not in any way what you are thinking, which is about “the” probability, but it bothers me when people bring up something – a fact, an opinion – which is otherwise readily available, which is otherwise part of a larger structure when what they really mean is “this is new to me”.

    And I can give an example of why this matters to me. Where I live there has been controversy over a particular Islamic group and its Iman, who has made anti-Jewish and anti-gay remarks in the past, but has recanted. OK. Great. So here’s my problem: this person became an Iman and achieved prominence before and while he was publicly making these comments. After a trip to a death camp, he changed his mind, so we could say the new information affected his prior beliefs, etc. OK. Great. But he held his prior beliefs with just as much tenacity as he holds his current beliefs, so maybe he’ll change back. A flexible mind is better than an inflexible one, but is it really “good” to be told, as I am, that I should respect this person because his views have changed. It’s not like actual information about Jews and gays hasn’t been available. It’s not like he just came from some country where Jews don’t exist and gays are put to death. Does his “conversion” mean the place he represents has actually been lying – that it holds these lousy beliefs and pretends otherwise – because I question why and how else would he rise to his position in it and give public statements as its representative if he didn’t represent its beliefs?

    • Clive says:

      Just thought you’d love to know that at least one ‘creatinist’ read your comments…and, indeed, reads this blog. So, evolve that one, pal.

      • Clive says:

        Of course, I meant ‘creationist’…darn lack of spelling checker…

      • Eric W says:

        Since he said that the belief is widespread in the US and some other countries, and this blog is read by people from the US (and other countries), one might expect that at least one creationist reads this blog/comment.

        The question is, should jonathan change his assesment of creationism as irrational simply because a creationist might read that assesment?
        (I don’t think so, but given your comment, you might disagree.)

  2. Steve Sailer says:

    Interesting question. I’d never thought of trying to quantitatively analyze the JFK question.

    Personally, I ended up with a gestalt insight: the reason Oswald had so much contact with the KGB, the CIA, various flavors of Cubans, etc. was not because he was part of a conspiracy, but because he _wanted_ to be part of a conspiracy. Potential co-conspirators would sooner or later figure out that Oswald was Bad News and drop him. The thick KGB file on Oswald is particularly comic and poignant: It’s covered with warnings to never throw it out, because, they claim, the papers inside prove that, while the Soviets did host Oswald in Minsk for a couple of years, they eventually got sick of him.

    But, the meta-question is: does the Bayesian approach have uses for thinking about unique historical events like this?

    • Anonymous says:

      If I believe all swans are white, a single instance of a black swan is enough to convince me otherwise. So single event can be informative.

      My pet theory is that Oswald may have thought he acted alone. If I knew, as the Cubans may have known, that he was going to shoot and where, I could have a back up to finish the job. All blame to Oswald. And he would never know.

      Far fetched? Richard Feinman was similarly used during the Challenger investigation. He thought he discovered the fault himself but instead the evidence had been planted for him to “discover”.

      There is no better agent than an unwitting one.

    • Entsophy says:

      In Poyla’s “Mathematics and Plausible Reasoning” he showed how closely heuristic plausible reasoning followed the equations of probability theory. In that sense Historians must use Bayesian reasoning informally all the time.

      But if you mean using formal Bayesian Statistics, I’m not sure whether people do. They certainly could however. One example I’ve often though about is the controversy on the origin of indo-european people. Several origination points have been proposed, with the most likely being north of the Caspian Sea (I believe), but they’re all controversial.

      One linguistic strategy for locating them, which was actually carried out, was to look for words for plants and animals or other natural features which have common cognates in most indo-european languages. The idea is that if Persian, Sanskrit, German and Greek have similar words for “beavers” then they probably came from a common root word in the proto indo-european language. Which probably means indo-europeans originated in a place with beavers.

      Similarly, if these languages have very different words for “beach tree”, which were borrowed from unrelated native languages, then it’s likely the indo-european homeland didn’t have beach trees.

      That’s the idea anyway.

      An enterprising Bayesian could take that work for all those words and use Bayes theorem to create a probability “heat map” showing the most likely locations.

      • Rahul says:

        Interesting idea. Knowing a bit of both Sanskrit & German, my (non-expert) suspicion is that you’ll end up finding so many cognates & so few geographically unique markers that your heat map becomes a very diffuse map of the entire continent. Asides the practical difficulty of ascertaining which areas did indeed have beavers and beech trees back then.

        Do you have a link to anyone who’s tried this?

        • j_bulbulia says:

          Hi Rahul,

          Yes, some folks at the University of Auckland:

          Mapping the Origins and Expansion of the Indo-European Language Family
          Remco Bouckaert et al.
          Science 337, 957 (2012);
          DOI: 10.1126/science.1219669

          Get it here:

          or here:

          This article has something for everyone, the Anatolian v. Stepp conjecture, Bayesian phylogeography, its use to resolve a longstanding historical debate … you name it, except a mention of the Oswald conspiracy.

          Short summary + video here:


          • Entsophy says:

            What a great paper. Thank you very much. I’d love to do Bayesian applications to history.

            Choice quote “we can incorporate into the analysis prior information about the shape of the Eurasian landmass”. All those people walking around saying priors represent peoples opinions and have no objective meaning or can’t be verified should get go down to Walmart and purchase “a clue”. Because they need to get one.

            They even use Bayes Factors to quantify how strongly the evidence favors an “out of Turkey” origin vs a “north of Caspian Sea” origin.

            • Rahul says:

              I’m having some doubts about the accuracy of their coding though. e.g. Look at the geographical location of Urdu. #96 in map below. Why would they infer Urdu is currently spoken in that tiny region in the North of India? Isn’t Urdu a lot more prevalent? What gives?


              • Entsophy says:

                It looks like they got Urdu right, if they’re looking at areas where the language is dominant. I though Urdu was a major language in Pakistan, and it is but this is what Wikipedia had to say:

                Urdu is the national and one of the two official languages of Pakistan, along with English, and is spoken and understood throughout the country, whereas the state-by-state languages (languages spoken throughout various regions) are the provincial languages. Only 8% of Pakistanis have Urdu as their native language, but Urdu is understood all over Pakistan.

          • Rahul says:

            Very interesting! Thanks!

            If I understand what they did correctly, they aren’t using @Entsophy’s second idea of “originated in a place with beavers / beech etc.” Right?

            They only use the language clusters that have many-common-cognates to infer how and when these languages diverged? Their geospatial cues are entirely based on where these languages are / were spoken. Far less sophesticated than @entsophies strategy?

            • Entsophy says:

              yeah, they’re using a diffusion type model and using evidence from changes in cognates to determine the model.

              That wasn’t my idea. I read somewhere an account of the work linguists did using the idea mentioned to determine the indo-european homeland. In the account I read though, they only qualitatively combined evidence from different words and couldn’t get strong conclusions (if memory serves). Which potentially means they underestimated how strongly the evidence builds up for certain locations.

              • j_bulbulia says:

                Hi Rahul,

                ++ Methods

                Here is a clear (and mercifully brief) discussion of the many analyses the team ran:


                It is also worth reading their reply to critics:


                ++ Inference and uncertainty

                I think these guys (who — disclaimer — are friends) would be the first to admit the limitations of their study. However, they are also correct, in my view, to emphasise its virtues. The study offers a nifty illustration for how to quantify uncertainty conditional on your data under different model-theoretic assumptions, a recurring theme of this blog. And unlike conspiracy theorists weaving together a string of already-known facts to support a position, the team sought novel, theory-descriminating evidence. I doubt the article offers the final word on the Indo-European Question — we don’t get the equivalent of mathematical proofs in science — but I think it’s a solid achievement, and a sign of good things to come as the historical disciplines gradually adopt the rigorous tools and intellectual habits of Bayesian data analysis. Exciting times!

                ++ Linguistic Paleontology

                The strategy Joseph Wilson suggests above is called linguistic palaeontology. It’s a very clever idea. However, for the Indo European Question, linguistic palaeontology is problematic. To reconstruct a term to the common ancestor of all Indo-European languages, it must be present in those languages at the base of the tree. Yet the Anatolian languages at that base of this tree overwhelming lacked support for **Steppe**. Also, technology-related words — the sorts of words that linguistic palaeontologists use in support of *Steppe* — are highly prone to being borrowed. Think of the lengths the French have gone in order to keep “computer” from infiltrating. A gadget is novel. Nothing in a mother tongue needs displacing, and efficient pragmatic speakers will simply adopt the existing term, and this will happen even in groups that love the sound of their mother tongue as much as the French do.

                ++ How to budge a conviction?

                This group would have been happy enough to have supported the Steppe hypothesis (who cares?) It’s just that the overwhelming support, under a bunch of different model theoretic assumptions, favours Anatolian origins.

                Yet generally speaking, it’s interesting how entrenched most of us — myself included — become in our beliefs about history, and many other matters of fact. To resolve debates, it’s important to look for discriminating evidence — asking theory-discriminating questions whose answers we don’t already know, as the U of Auckland team did in their study. We need such evidence to update our posterior beliefs in good Bayesian fashion. Yet if you have a conviction about Oswald, think about what sort of evidence it would take for you to favour the *other* side? (Those are the sort of data you need to look for). And what happens when the data don’t go your way? Sure, a bit of movement, maybe, but I find it’s a struggle to move much when the rival position strike me at a visceral level as naive or barking. Lots of challenges ahead, too…


                * Jared Diamond referred to the Indo European Question as “the most well-studied and recalcitrant problem in historical linguistics.”

  3. Entsophy says:

    There was an issue once with a foreign national neighbor of mine which raised suspicion that was I was being targeted by a foreign intelligence agency.

    When the appropriate folks were looking into it, it was amusing to me how interested they were in whether I had moved in next to him, or whether I was there first and he had moved in next to me.

  4. FredR says:

    “Bayesian statistician Jay Kadane wrote a book a few years ago on the Sacco and Vanzetti case, going into the evidence supplied by each piece of information.”

    At first I thought I wouldn’t complain because I could just look up on Amazon what he concluded about their guilt or innocence, but even the amazon page doesn’t say.

  5. Dan says:

    I think the Bill James theory has the most evidence: Oswald acted alone, but it was a Secret Service agent’s accidental discharge that actually killed Kennedy.

    • Andrew says:


      I think Bill James has fallen for his own hype.

      • Dan says:

        Well, the theory does not actually belong to James, it derives from the book “Mortal Error” written by Bonar Menninger. I just heard James recently talk about it and apparently he endorses the theory in his own book, “Popular Crime”.

        What is most convincing to me is that the theory suggests no conspiracy to assassinate, but a conspiracy to cover up a mistake. Given all the evidence that points to something more complicated than a lone shooter, and the fact that the theory still supports Oswald acting alone (in his attempt to kill), it just seems like a strong and plausible explanation for what happened. Especially when you consider that plenty of insiders (government officials/SS agents) would be on board with hiding the sad truth from the American public to avoid embarrassment for a situation that was devastating regardless. The president was killed because someone attempted to assassinate him, mistake or not.

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