BAYES THEOREM AND A MYSTERIOUS BAG OF BANGKOK BAGELS
There was a recent court case in England involving a murder conviction based on expert witness testimony premised on Bayes’ Theorem. That theory, of course you will recall, comes from an 18th century English mathematician whose name coincidentally was named Bayes. Actually the theory is intended to give a mathematical probability that given one event has happened suggests the relationship with a related event. Often it has been suggested that Bayes’ Theorem supplies the math to demonstrate what our common sense, logical mind tells us is the connection between things related in time.
For example, the cop pulls over someone who has run a red light and the driver has alcohol on his breath. The cop asked, “Sir, have you been drinking?” The driver slurs his words, “Not a drop, officer.” The driver smells of beer and there is an open bottle of beer on the passengers seat that is half empty. You don’t need to be a mathematician to draw a conclusion that the probability is high that the driver is lying and that indeed he has been drinking.
But a recent UK court decision threw out a murder conviction on the basis the footwear expert’s faulty calculations and poor explanations concerning footprints left behind by the murderer. The evidence came down to whether the accused had worn the Nike running shoes that had left tracks at the murder scene. If the judgment had been left that the expert had got it all wrong, then Bayes’ Theorem would remain in an expert’s arsenal and effective weapon at that. But court attacked the theory!
As the Guardian reported, “In the shoeprint murder case, for example, it meant figuring out the chance that the print at the crime scene came from the same pair of Nike trainers as those found at the suspect’s house, given how common those kinds of shoes are, the size of the shoe, how the sole had been worn down and any damage to it. Between 1996 and 2006, for example, Nike distributed 786,000 pairs of trainers. This might suggest a match doesn’t mean very much. But if you take into account that there are 1,200 different sole patterns of Nike trainers and around 42 million pairs of sports shoes sold every year, a matching pair becomes more significant.”
The problem was the expert couldn’t testify as to the precise number of the type of Nike trainers had been sold in England. He relied on what the Guardian called “rough national estimates.” The judge decided that unless the underlying statistics were “firm” the Nike shoeprint evidence wasn’t reliable enough to justify a murder conviction.
The analysis of the court has led others to conclude that there is a misunderstanding between judges, prosecutors and lawyers on the one hand, and mathematicians on the other. Many criminal cases are based on circumstantial evidence. The question is how to assess such evidence, and place it in a context that ranks the odds of the evidence pointing to the guilt of the accused. Bayes’ Theorem can never provide a certain, fixed connection. It can only give the odds of such a connection.
Something like Bayes’ Theorem is a likely companion for law enforcement agencies. Profiling has a Bayes’ Theorem backbone, suggesting that the odds of catching a bomber increases in the presence of certain age, gender, racial and other personal characteristics. This is why at airports you are told the searches are ‘random’ because many people are uncomfortable with the idea of being profiled. Though from a Bayes’ Theorem point of view, calculating the odds by taking into account such factors may increase the odds of catching a bomber before he/she has set off the bomb.
On Tuesday, I was riding the BTS from Chidlom Station to Asoke Station. I had been to meet a friend for lunch, and afterwards, I stopped to buy 18 bagels for a friend who lives in Chiang Mai. The bagels were put in a brown bag and the brown bag slipped into a clear plastic bag, which I carried. On the train, I noticed two police officers had cornered a black man on the Nana Station platform. One of the cops flipping through what looked like a passport. I figured the cops had profiled him: black, T-shirt, jeans, young and in the Nana area of Sukhumvit Road.
When I got off the train at Asoke, I walked toward the MRT (the underground train in Bangkok) only to be immediately joined by a uniformed Thai cop. He saddled up beside me. “What’s in your bag?” he said. “Bagels.” He looked at me. I asked him, “Do you know what a bagel is?” Apparently not wanting to admit he didn’t, he said, “Bagels.” I said, “Bagels.” Then he reached toward my bag and started squeezing the bagels. Not once, but two or three times. The top, the middle and close to the bottom of the bag. It was bagels all the way down.
In Thai cop school there must be a class where the resident Bayesian expert teaches street cops that bagels have a certain squeeze identification factor that increases the odds that indeed they are bagels as opposed to drugs, a bomb, pirated CDs, body parts, or any number of things that cops think that foreigners traveling between the BTS and MRT might be transporting.
Then he asked (in English) where I was from. “Canada,” I said. And I asked where he was from. “The South,” he said. He asked where I was going. I told him my soi number. Then I asked where he was going. He shrugged. The policeman didn’t seem to have any place in mind as to where he was going next.
Having had a good squeeze of bagels, he looked slightly disappointed. He said that he was from the South of Thailand. If there was one place, where a good theory based on Bayes’ Theorem ought be used, it was in the South, where daily bombing and assassination is an odds on certainty. I left him watching as I walked through the scanner frame to the MRT and the security were waiting. I took off my backpack, which has multiple zipper pockets, unzipped one of the smaller ones, the security guard, glanced, turned away and I walked through. He had no interest in my bagels. Didn’t ask to look. Didn’t request a squeeze. Come to think of it, the cop never asked me to open my backpack.
When you come to Bangkok, you need to understand that Bayes’ Theorum is colored by local culture and what might seem odds on a bag of bagels to you, is something quite sinister to a Thai cop who by the way didn’t seem to know where I could buy lox and cream cheese.