Bayes’ Rule: How a Theory You May Not Have Heard of Impacts the World Around Us

Sharon Bertsch McGrayne is the author of highly praised books about scientific discoveries and the scientists who make them. She is interested in exploring the cutting-edge connection between social issues and scientific progress – and in making the science clear and interesting to non-specialists.


In this interview, she discusses her book The Theory That Would Not Die: How Bayes’ Rule Cracked the Enigma Code, Hunted Down Russian Submarines, and Emerged Triumphant from Two Centuries of Controversy.


Though many of us are not familiar with Bayes’ Rule, its use permeates our everyday life from DNA decoding to Homeland Security. Sharon reveals why respected academics rendered it professionally taboo for decades – while decision-makers relied on it to solve crises involving great uncertainty and scanty information, such as how Alan Turing used Bayes to break the German U-boats’ Enigma code during World War II.


She also discusses how Bayes was used to free innocent mothers in the 1990’s who had been convicted of murdering their young babies, when in reality, they had suffered from Sudden Infant Death Syndrome.


Finally, Sharon discusses some of her other books and surprises she encountered when researching female scientists throughout the years.





Laura: Hi and thank you for joining us for the annual video series from the International Symposium on Human Identification. We’re here with our friend Sharon, who was kind enough to join us today. She’s presenting this year at ISHI. Sharon, thank you for joining us remotely.


Sharon: Well, thank you for inviting me. I’m Sharon Bertsch McGrayne. I should probably say that, and I begin every talk conversation with some truth in advertising, and I say that I’m not a statistician, a scientist, or a mathematician. I come out of newspapers and reporting news for newspapers, and now I write non-technical books about scientists and their discoveries. The book I talked about at ISHI is the backstory really for what many of you at ISHI do every day. You’re using science to give back to society. You’re using Bayesian probability for social justice and to find the truth (as much as we can). The book has a long title. It’s called The Theory That Would Not Die: How Bayes’ Rule Cracked the Enigma Code, Hunted Down Russian Submarines, and Emerged Triumphant from Two Centuries of Controversy. How’s that for a title?


Laura: I love it, and I know you wrote a wonderful article for us on Bayes for the ISHI Report, and now it’s amazing to have the presentation and to go into a little bit more depth this year. Can you summarize for us what Bayes’ Rule is and tell us a little bit about that?


Sharon: Sure. It’s a simple one-line theorem. It’s a lot shorter than the title of the book! Simply put, Bayes said you can start by assigning the probability of your initial belief about something and then you have to multiply it over and over again with each new fact that appears; each new piece of evidence to give us a more probable, better, probability and belief. And it was immensely controversial for a long time. It helps people make decisions based on new knowledge, but it wound up as a veritable food fight (I was told) like children in a lunchroom.

First, Thomas Bayes himself, an English mathematician said that “if you don’t know too much about your belief, just start with a guess.” He actually used the word ‘guess’. And if you don’t know even that much, just say 50/50 chance of being right. But it also commits us to this relentless updating of what we know with every piece of new data that comes up. The second problem was that scientists in the 19th century, particularly, came to believe that science had to be objective and the idea of starting with a personal belief was appalling. They called it “ignorance coined into science” and they said it smacked of astrology and alchemy, and they said you had to judge the probably of the future event only on the number of times the event had occurred in the past. Nowadays, you pick and choose the method that’s best for the problem that you have, but they’re saying no, you’ve got to do it by the numbers.


Laura: Wonderful, yes, it absolutely does. I really liked in your article when you talk about that Bayes really does get to the heart of the fundamental issue of how do we analyze information and come to a decision, and I know you told some very interesting stories that included Alan Turing. Maybe you can tell us a little bit about that?


Sharon: Yeah, sure. What I discovered researching the history of Bayes was that it operated for a long time… for more than a hundred years on two levels. The first was that it has to be frequentism based only on the number of times that it’s happened before. But the other one was that real life people who had to make emergency decisions and couldn’t wait for all the knowledge in the world to be accumulated. Those who had to often make life and death decisions often kept right on using Bayes, often in secret, because Bayes helped them make do with what they had, basically. So, you had insurance actuaries setting the next year’s premium rates. Before DNA, you had lawyers who used Bayes in paternity suits, and the army, particularly in Britain, France, Russia, and the United States used Bayes to aim their artillery fire and to test their weapons and ammunition.

So, it was also used in courtrooms more than 100 years ago. It helped free Alfred Dreyfus who was a French Jew. He was one of the top generals in the French army in the 1890’s and he was falsely accused by antisemites of forging a document and getting it to the enemy. And in the scandal that rocked France, split it in two, but also much of the western world. Dreyfus was actually found guilty of treason and there was actually a military ceremony in which he stood up and they ripped off his rank and all of his medals and he was sentenced to life imprisonment and hard labor. Now, Dreyfus’ lawyer asked France’s top mathematician whether he thought Dreyfus had forged that document, and he wrote (he preferred frequency to Bayes statistics) the court that he considered Bayes’ Rule the only sensible way for a court of law to update a hypothesis with new evidence, and the courtroom erupted into cheers. It was a military court. All the judges and the lawyers had studied Bayes in military textbooks and military schools, and they understood what he was talking about. So, in this respect, Dreyfus had an advantage over many of the ISHI members who have to explain their situations to a jury who hasn’t the foggiest notion of what they’re talking about. They understood what the lawyer was saying and a few weeks later, Dreyfus was pardoned.

But you asked about Alan Turing because that involved another courtroom. By the time the second World War started in 1939, Bayes was basically taboo. During the war, England was cut off from the French farms that had kept it supplied, and England could feed only one in three of its residents, and it depended on convoys of unarmed mercenary ships bringing food and supplies from Africa (picking them up in South America and going up through the Caribbean, the United States, and Canada). And they were forming huge convoys delivering 30 million tons of food and supplies every single year through to England. And the German U-boats were so effective that they would sink almost 3,000 allied ships and kill more than 50,000 merchant marine seaman.

Hitler said U-boats would win the war. Churchill said that the only thing that worried him during the war were those U-boats. They were ordered around to get at the convoys by encrypting messages that were radioed to the U-boats in the Atlantic. And these messages were encrypted with word scrambling machines called Enigmas and they could churn out millions upon millions of permutations within hours, and neither the Germans nor the British ever thought the British would be able to read those encrypted messages to U-boats. Fortunately, Alan Turing was not a statistician, he was a mathematician, and when war was declared, he goes up to the secret English coding and decoding headquarters north of London. He was 27, but he looked 16. He was handsome, athletic, shy, nervous, and during college at Cambridge, he had lived openly as a homosexual. When he gets to Bletchley Park, he gets whispers of what the words going to the U-boats might mean. They knew, of course, the most probable letter combinations in the German language, and a prisoner of war told them that Enigma operators spelled out all the numbers, so they knew the word for one “ein” and articles like “a” or “an” would appear in 90% of the messages. This is my favorite; the Germans had stationed weather roads across the top of the Atlantic and they were to report each night what the weather had been and what it should be by the time it arrives here in the continent. Weather doesn’t have a wildly descriptive vocabulary, so they repeated the same words in different coded messages night after night and that was an enormous help.

Turing soon develops a very Bayesian system on pencil and paper that let him guess a stretch of letters in an original German message to U-boats and then he could hedge his bets, measure his belief and validity by assessing their probabilities and add more clues as they arrived. And within a year and a half, Turing could read those U-boat messages within an hour of their arrival and then Bletchley Park could re-route the convoys and avoid the U-boats. Not a one was attacked during that time.

Then the German army came up with a super sophisticated system and Bayes’ system were embedded into the computers that the British were developing to break those codes. So, Turing was this enormous hero, and it could well be that without Turing, people might not have survived the war.

So, the Turing story ends with a real tragedy, because during Cold War (the secrecy after World War II), Turing was not recognized anywhere for his work, and a local court convicted him for homosexuality in his own home with a consenting adult and sentenced him to chemical castration and he ultimately commits suicide. It’s a terrible story.

The Cold War, of course, continued this fight between the Bayesian and their opponents, and the public’s shear ignorance to statistics and Bayes was a big handicap for the Bayesian believers, which, as I said before, ISHI members may have experienced themselves in the courtrooms. And it was another, very sad, case involving a young mother. A young lawyer, in fact, in England named Sally Clark.

During the late 1990’s, quite recently in terms of history, British mothers were being arrested for murder and sentenced to life imprisonment if two or more of their babies died in their cribs. For example, Sally Clark’s little boy who had died at 11 weeks. She’d gotten pregnant with another boy, and he died when he was 8 weeks old. She was convicted of murder in 1999. The court had asked a prominent pediatrician; not a statistician or a mathematician, to state the odds of those children dying naturally. He said it’s simple. It’s one in 73 million, so naturally, she had murdered her children, so she was sentenced to prison.

The pediatrician had assumed incorrectly that each sibling’s death had occurred independently of the other. If they had used Bayes, it would have brought out the fact that some families, like Sally Clark’s, are predisposed to either environmentally or genetically to SIDs or crib death.

There was an uproar among statisticians. They petitioned the courts and parliament. They wrote newspaper articles, and the court said that Bayes did not belong in the courtroom, and it was medical reports that later freed her. But the whole experience was so devastating because she dies three years after being freed from prison. How she dies was acute alcohol intoxication, so it was not good. So, statistics are very important.


Laura: Right, I think we take for granted how important something like that is.


Sharon: Exactly.


Laura: How did you get involved in the work that you’re doing?


Sharon: Well, I was involved with newspapers first. Is that what you mean? How did I come do this?


Laura: Yes, that would be great.


Sharon: Yeah, well I had been in newspapers, so when the industry became troubling, and I switched to what a lot of reporters do, which is to write books. And, I really like putting the puzzles together of scientific problem and then the evidence comes in. It’s a very Bayesian process, and you put it all together and it’s done with interesting people. So, that’s what I like.


Laura: It’s wonderful. The stories are incredible. We talk about all the statistical theorems, but we don’t talk about all the interesting stories that brought them to what they are today. What’s it like when you’re researching and writing? I’d love to hear about the process.


Sharon: Well, I had to read the original papers. A lot of Bayesians didn’t know about these stories. But, I found it to be like when you’re walking through a food market and you see all these juicy plums and you pull them down and every one of them would be one of these fabulous stories. So, that part of it was very nice. The whole game changed very quickly in the late 1990’s. Cheaper desktop computers came on. There were Markoff Chain, Monte Carlo techniques, free off the shelf Bayesian software, and all of a sudden, Bayes could be used to solve complex problems, because it was so powerful and so complex. It really went overnight. No one changed their philosophies on Bayes, but it just worked!


Laura: Right, what a turn around. That’s amazing. It really is such a fascinating story. Were there any surprises while you were writing? It’s certainly filled with many twists and turns.


Sharon: Well, in the beginning, I got involved in the food fight, because I would call statisticians and ask for help. Is it accurate? What else should I write about, blah blah blah. And, often they said, “No, we won’t help you.” And the other thing that would happen is some of them would get very, very angry. One man screamed into the telephone so loud that I had to put the phone receiver out as far as my arm would go and hold it there that, “This is awful! This is stupid! This is dangerous! And you book will be stupid and awful and dangerous.” He just went on and on without taking a pause for a breath, and when he finally took a breath, I said, “thank you very much for your help. Goodbye.”


Laura: I think that was probably the right answer, yeah. Well, I know that’s not the only work that you’ve done. You’ve also written about many Nobel Prize winning women. Do you want to talk about that a little bit?


Sharon: Sure. I wrote a book called Nobel Prize Women in Science before the onslaught of women’s studies and so on, particularly women in science, about 20 years ago. Most of these women, 15 of them that I found, had contributed in a very important way to someone else’s prize or who won the prize themselves. There were 15 of them and I profiled each and so on. And almost all of them were still alive, because I was doing this when I was young. Even Marie Curie, I could talk to the daughter who wrote the famous book about her that turned so many women on to science. Rosalind Franklin had died of cancer, but I could talk to all of the members of her laboratory, and the way that they described Rosalind Franklin was totally different from James Watson’s description in his book and so on.


Laura: That is fascinating. Any surprises when you were talking with Marie Curie’s daughter or the associates of Rosalind Franklin? I just think people would be so interested to know what that was like. What an opportunity.


Sharon: People told me (the assumption was) that every woman in science was blah, grey, uninteresting. They were all alike. What I found was that every single one of them was different. They were all fabulous. They loved what they were doing. And they were varied. There wasn’t any one who was like another. Some were mountain climbers, some were couturiers for their clothing, some were fashionable cooks, and so on. They were all just fabulous, and the people who knew about them weren’t in science for profit or career. They were in it and supported these women because they believed in the science. It was great fun.


Laura: That sounds wonderful. And I understand you’re working on another project that sounds just as fascinating. I believe you mentioned something with Rita Calwell?


Sharon: Yes, yes, that’s a book that’s just recently published and has come out in paperback (much cheaper). She was the first woman to direct the National Science Foundation. The only microbiologist. It’s called (a long title again): A Lab of One’s Own: One Woman’s Personal Journey Through Sexism and Science and I co-authored that with Rita Calwell. I started writing a book about the revolution in biology to the use of Bayes’ Rule (very mathematical and statistical) in biology. It wound up to be a story of discrimination that women faced and still faced, and what they can do about it.


Laura: I love the topic! What draws you to women in science? How did that begin?


Sharon: What drew me to it? Well, I knew from my own children’s high school that the only girls who took calculus, which you need for science, were in the calculus classrooms because their fathers were physicists and they demanded that their daughters take it. And I thought that was so strange, because during a period when the media and government were going crazy saying we don’t have as many women engineers or scientists as the Japanese do, and we’ll never catch up. I thought, well, this is a simple solution. You get the sisters of all the brothers who go into science to go into science, so I’ll write about other women and that’ll be a simple solution. That was 20 years ago and we’re still working on the problem.


Laura: Well, I hate that we’re working on the problem, but I love that you’re working on it and bringing it to life and I love to see the progress in that area too. I know that it’s something we celebrate here and having you speak is a part of that. What’s next for you?


Sharon: I don’t know! I’m looking for a topic, and if some of the members of ISHI have some ideas for me, it would be very kind of them to send me a message and would wish all of them very, very good luck in their lives in the future and their careers.


Laura: Thank you Sharon. That was lovely, and I bet you will get some great suggestions from our audience. Thank you for your willingness to do this with us today and remotely too.


Sharon: That was very nice, thank you.