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A LITTLE PERSPECTIVE

Bayesian statistics and a new car!

A once obscure field known as Bayesian statistics - mathematical rules that use new data to continuously update beliefs or existing knowledge - is rippling through everything from physics to cancer research, ecology to psychology. Scientists often marvel that it propels them through a different kind of scientific reasoning than they'd experienced using classical methods. "Statistics sounds like this dry, technical subject, but it draws on deep philosophical debates about the nature of reality," said the Princeton University astrophysicist Edwin Turner. Invented in the 18th century by an English Presbyterian minister named Thomas Bayes, Bayesian statistics are helping scientists crosscheck work done with the classical approach, known as frequentist statistics. The two methods approach the same problems from different angles.

The frequentist technique applies probability to data. If you suspect your friend has a weighted coin, for example, and you observe that it came up heads nine times out of 10, a frequentist would calculate the probability of getting such a result with an unweighted coin. The answer (about 1 percent) is not a direct measure of the probability that the coin is weighted; it's a measure of how improbable the nine-in-10 result is - a piece of information that can be useful in investigating your suspicion.

By contrast, Bayesian calculations go straight for the probability of the hypothesis, factoring in not just the data from the coin-toss experiment but any other relevant information - including whether you've previously seen your friend use a weighted coin.

A famously counterintuitive puzzle that lends itself to a Bayesian approach is the Monty Hall problem, in which Hall, longtime host of the game show Let's Make a Deal, hides a car behind one of three doors and a goat behind each of the other two. The contestant picks Door No. 1, but before opening it, Hall opens Door No. 2 to reveal a goat. Should the contestant stick with No. 1 or switch to No. 3, or does it matter?

A Bayesian calculation would start with one-third odds that any given door hides the car, then update that knowledge with the new data: Door No. 2 had a goat. The odds that the contestant guessed right - that the car is behind No. 1 - remain one in three. Thus, the odds that she guessed wrong are two in three - bad odds. And if she guessed wrong, the car must be behind Door No. 3. So she should indeed switch. (And computer simulations, despite the apparent contradiction with common sense, prove that choice right.)

F.D. Flam, New York Times

No. 1 baby name in Israel: Muhammad

Muhammad was by far the most popular name for babies born in Israel last year: 1,986 boys shared the name of the Muslim prophet, nearly twice the number of the top girls' name, Tamar, at 1,092. That fact alone was worthy of note, a reminder that the Arab minority in Israel is 21 percent. But even more striking was that Israel's population authority left Muhammad off the annual Top 10 list of baby names it issued last month before Rosh Hashana, the Jewish New Year. A spokeswoman for the agency that published the list described the missing Muhammads as something between a mistake and a misunderstanding. The list, she said, was simply a response to requests "for Hebrew names" in conjunction with the start of "the Hebrew New Year." It would have been better, she acknowledged, to put an asterisk noting that what she called "obviously Arabic names" were left off. The list the population authority published had Yosef in the top spot with 1,173, edging out Daniel, at 1,088, and Uri, which means "my light," at 1,071.

Jodi Rudoren, New York Times

Economics of those who don't give birth

When the economy tanks, women have fewer babies. But what happens in the following years, when conditions improve? A massive new study suggests that for some U.S. women, living through a recession can mean they will never have children.

On a societal level these effects are small. The projected number of childless women is a tiny fraction of the 9 million women in that age group, 20-24. The drop-off in births isn't much for a nation that produces around 4 million babies a year.

But the results still show "a pretty profound effect on some women's lives," said study author Janet Currie, a health economist at Princeton University. Currie and colleague Hannes Schwandt presented their analysis in a paper released by the Proceedings of the National Academy of Science.

They looked for evidence that women who defer having children during tough times make up for it later on, ending up with the same number they would have had otherwise. When the research showed a shortfall for women who experience those tough times at ages 20 to 24, "we were surprised." Currie said many women at that age are at a crossroads in deciding whether to get married and have children. Poor economic times may discourage many women from doing so, and once the economy improves and the women have gotten older, they may be less likely to go ahead, she speculated.

Malcolm Ritter, Associated Press

Can't pull yourself up by bootstraps

When the Pew Economic Mobility Project conducted a survey in 2009 - hardly a high point in the history of American capitalism - 39 percent of respondents said they believed it was "common" for people born into poverty to become rich, and 71 percent said that personal attributes like hard work and drive, not the circumstances of a person's birth, are the key determinants of success. Yet Pew's own research has demonstrated that it is exceedingly rare for Americans to go from rags to riches, and that more modest movement from the bottom of the economic ladder isn't common either. In fact, economic mobility is greater in Canada, Denmark and France than it is in the United States.

The yawning gap between the dearly held ideal of the self-made man and the difficulty of actually improving your station in America, particularly if you're poor, made me wonder about the utility of the rags-to-riches story. Is it a healthy myth that inspires us to aim high? Or is it more like a mass delusion keeping us from confronting the fact that poor Americans tend to remain poor Americans, regardless of how hard they work?

The very language we use to describe the self-made ideal has these fault line embedded within it: To "pull yourself up by your bootstraps" is to succeed by dint of your own efforts. But that's a modern corruption of the phrase's original meaning. It used to describe a quixotic attempt to achieve an impossibility, not a feat of self-reliance. You can't pull yourself up by your bootstraps, any more than you can by your shoelaces. (Try it.) The phrase's first known usage comes from a sarcastic 1834 account of a crackpot inventor's attempt to build a perpetual motion machine.

John Swansburg, Slate

So, if baboons can be kinder and gentler...

Some would explain, if not excuse, the misogynistic culture of Internet trolls who traffic in stolen celebrity photos as an unfortunate example of base human nature. But baboons may teach us otherwise. Baboons are notorious for the aggressive behavior that males display toward females. Yet within every population, whether we are looking at baboons or humans, there is a range of variation in traits, affected by the environment in which the population lives.

In the early 1980s in Kenya, a group of olive baboons known as "Forest Troop" underwent a unique natural experiment. The territory of their neighbors, "Garbage Dump Troop," overlapped with that of a tourist lodge. The Garbage Dump Troop had access to the leftover meat that had been discarded. The most aggressive males from Forest Troop invaded to access the meat for themselves. Soon afterward, tuberculosis ravaged the baboons from both troops who had been feeding at the garbage dump. Because it was only the most aggressive males of Forest Troop that died out, the results were twofold: Less aggressive males were more common in the population, and the female-to-male ratio had now doubled.

The social consequences were startling. According to Stanford University primatologist Robert Sapolsky, who documented the event and followed the troop for the next 20 years, the brutal hierarchy that was common among male baboons disappeared, and the amount of affiliative behaviors - such as males and females grooming one another - increased markedly. What was most surprising was what followed over the intervening years. Males always migrate to other troops at puberty, and new immigrant males to the Forest Troop adopted the local culture that they encountered. Even though none of the original population is alive today, this highly cooperative baboon society remains intact.

Eric Michael Johnson, Slate

Going to Mars on the budget plan

An Indian orbiter reached Mars last month, making India the first Asian country to send a spacecraft to the planet - and the whole project reportedly cost $74 million, less than production of the movie Gravity. The New York Times noted that the morning the probe reached Martian orbit, "children across India were asked to come to school by 6:45 a.m., well before the usual starting time, to watch the historic event on state television. The Mars Orbiter Mission, or MOM, was intended mostly to prove that India could succeed in such a highly technical endeavor - and to beat China."

Ben Mathis-Lilley, Slate

How campfire tales made us human

Don't underestimate the value of sitting around a campfire, listening to stories, singing songs and letting yourself stare mesmerized into the flickering flames. These activities may have played an essential role in early societies. A new study suggests socializing and storytelling around a communal fire may have offered our hunting and gathering ancestors a unique time to expand their minds and imaginations in ways that were not possible during the hard work and harsh light of the daytime hours.

When humans first learned to control fire about 400,000 years ago, the quality of their lives changed dramatically. Brain size and gut size increased, predators no longer posed such a dire threat and our ancestors' circadian rhythms shifted as firelight extended the day by several hours, according to the study.

The light of the fire interfered with melatonin production, allowing people to stay awake during a time when productive work was difficult to accomplish. Anthropologist Polly Wiessner wondered whether this newfound leisure time may have created a space for different types of social interactions as well. In a paper published in PNAS, she argues that conversations that take place at night around a fire have a different quality, and different content, than those that take place during the day.

Forty years ago, she recorded conversations of the Ju/'hoansi Bushmen in southwestern Africa and then returned in recent years to do so again. "During the day, the conversation was kind of nasty a lot of the time," Wiessner said. "But at night they would mellow out ... They traveled, in the stories, to other realms."

Deborah Netburn, Los Angeles Times

Don't let statistics get your goat

Say you're a Bayesian statistician on Let's Make A Deal. There are three doors, behind them one car and two goats. You know the odds are one in three that any given door hides the car you hope to win. You pick Door No. 1. Monty Hall opens one of the other doors to reveal a goat. Now you have new information. Your chosen door still has only a one in three chance of being right. But the unchosen door is now the better option, with odds of winning at two in three. Here are how the possibilities break down - and why you as a good Bayesian should switch to the door that Monty Hall is offering you.

Behind Door 1 Behind Door 2 Behind Door 3 Result if staying at Door 1 Result if switching to door offered car goat goat car goat goat car goat goat car goat goat car goat car

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