Suppose that you are taking the bullet train from Kyoto, Japan to Tokyo, as I did yesterday. The woman seated across from you has somewhat unusual facial features. You are curious to know whether she is Japanese, Caucasian, or some mix of both.

Suppose furthermore that I asked you to estimate, in percentage terms, the likelihood of each of these three possibilities (ignoring others like that she might be Korean, Latina, etc.) Certainly, there are lots of other clues that we might look for to improve our estimate: How is she dressed? How tall is she? What type of mobile phone is she carrying? What is her posture like? (The more forthright among us, of course, might also seek to start a conversation with her, in which case the answer might become clear more quickly.) That notwithstanding, in the absence of further information, most of us would tend to equivocate: perhaps there is a 25 percent chance that she is Japanese, we might say, a 25 percent chance that she is Caucasian, and a 50 percent chance that she is of mixed ethnicity.

But that would be a fairly bad answer. Even in the absence of additional information about the woman, we have another very important clue that can become surprisingly easy to forget if we become too fixated on the details: we are in Japan! There are a lot more Japanese people in Japan than there are Caucasians (indeed, the country remains among the more ethnically homogeneous industrialized societies.) It probably follows also that there are a lot more white-looking Japanese people in Japan than there are Japanese-looking white people. It’s therefore quite a bit more likely that we’ve encountered one of the former than one of the latter on our train ride. A better ‘prediction’ about her ethnicity, then – conditioned on the fact that we are in Japan — might be something like this: there is a 60 percent chance she is Japanese, a 35 percent chance she is mixed, and only a 5 percent chance she is Caucasian. If we were on a train from Boston to New York, instead of from Kyoto to Tokyo, the probabilities would gravitate toward the other end of the spectrum.

Psychologists and behavioral economists have conducted a lot of experiments along these lines, testing our ability to think through problems that involve what statisticians call Bayesian inference: those that require to us to infer the likelihood of various possibilities based on a combination of prior, underlying conditions (we are in Japan: most people we encounter here will be of Japanese ancestry) and new information (but based on this woman’s appearance, it is hard to tell whether she is Caucasian or Japanese!) They’ve found that, in general, we do pretty badly with them: we tend to get lost in the most immediate details and we forget the underlying context.

I was reminded about this recently when reading WikiLeaks founder Julian Assange, who is wanted for questioning by Swedish authorities on charges that that he has committed sexual assault. People have spent a lot of time debating the details of the charges, which invoke a number of difficult questions about what constitutes consent during a sexual encounter. Commenters differ in their interpretations both about the facts intrinsic to the case and in their readings of Swedish law.



I certainly do not intend to resolve those debates, although they are by no means uninteresting or unimportant. What I would suggest, however, is that it would be a mistake, from the standpoint of Bayesian reasoning, to think we can separate out the merits of the charges from their political motivations.



There is virtually no chance that the case against Mr. Assange would have proceeded in quite the same manner if he were instead an itinerant painter named Jens Andersen, or a traveling salesman named John Andrews — instead of an internationally renowned provocateur. Indeed, the charges might not have been brought against Mr. Assange in the first place. Sweden has among the highest rates of reported rape cases in the European Union. But unfortunately, few cases are brought to trial (only between 10 and 20 percent, according to various reports), and fewer still result in convictions.



That alone might not tell us much. There are other ways, however, in which the behavior of the authorities has been quite unusual.



The initial warrant in the case against Mr. Assange had been issued in August. But it was revoked the next day, due to what the lead prosecutor cited as a lack of evidence. It was only last month – just as WikiLeaks was preparing to release a set of confidential diplomatic cables – that Sweden again issued a warrant to detain him.



After turning himself in to the authorities in London, Mr. Assange was initially denied bail (although he has since been awarded it) — which is particularly unusual given that Swedish authorities have still not formally charged him with a crime, but merely want to bring him in for questioning. Most unusually still, Sweden had issued an Interpol red alert for Mr. Assange’s arrest, something they have done for only one other person this year accused of a sex crime: Jan Christer Wallenkurtz, who is suspected of multiple cases of sexual assault against children.



The handling of the case has been highly irregular from the start, in ways that would seem to make clear that the motivation for bringing the charges is political.



Does that mean, however, that the underlying charges themselves are spurious, trumped up, outright false, or otherwise dubious? (Some have speculated, for instance, that Mr. Assange may have been entrapped.) No, not for certain, of course — but it does have an impact on the probabilities.



From our standpoint, there is a lot of uncertainty about what happened between Mr. Assange and the two women in Sweden. This is common in sexual assault cases, which can be very difficult to prove, in part because victims are often too scared or too traumatized to provide as many details about the case as authorities might want. Also, of course, prosecutors will want to make the case seem as strong as possible, while the defense will want to make it seem as weak as possible, so they will be selective about which facts they release to the public.



A case that might intrinsically be very strong (if we were omniscient and knew exactly what happened) might seem relatively weak to us; likewise, a case that were relatively weak could be made to seem strong. It is as though we are again on that bullet train in Japan, trying to discern the identity of the passenger seated next to us, but having only a limited and ambiguous set of clues with which to do so.



What is less ambiguous here, however — as in the case of my bullet train analogy — is the underlying context. The handling of the charges suggests that the motivation for bringing them against Mr. Assange is political. If the motivation is political, then the merits of the charges might matter less. Even if they fail to result in a conviction, the authorities might nevertheless succeed in, in essence, incapacitating Mr. Assange for several months, and preventing him from releasing further documents through WikiLeaks. They might also injure Mr. Assange’s reputation among the public: certainly I have learned more about details Mr. Assange’s personal life in recent days than I would care to know.



Under these circumstances, then, it becomes more likely that the charges are indeed weak (or false) ones made to seem as though they are strong. Conversely, if there were no political motivation, then the merits of the charges would be more closely related to authorities’ zealousness in pursing them, and we could take them more at face value.



I suspect this point will seem obvious to many of you: the fact that the charges are (apparently) politically motivated is indeed a reason to regard them skeptically, and they make it less likely — perhaps much less likely — that Mr. Assange is guilty of them. (Although he may be guilty of being a creep even if he is not guilty of a crime.)



Nevertheless, I have come across a number of analyses that try to evaluate the merits of the charges without regard to this political context, or which otherwise seem caught up in debating their salacious details. That is likely a mistake: in a world of limited information, the political motivation behind the charges might be the most important clue we have in evaluating their merit.