May 22, 2016

XL-Files: Lectures (Marriages?) That Last

Contributing Editor Xiao-Li Meng writes:

Other than zero, I have a hard time coming up with an estimate for the number of readers of my XL-Files of July 2013 who still recall the Harvard Horizons program, which trains students to present a five-minute TED-style talk on their research. But the number is clearly not zero in terms of students who wanted me to experience what I had put them through, because there were enough of them who nominated me for the annual “Lectures That Last” (at Harvard’s Memorial Church on February 6, 2016), where each faculty was given 5–7 minutes on the theme of Crossroads. After much agonizing, I settled on “Marriages That Last.” I hope none of you need my unsolicited advice, but just in case you do, feel free to read a synopsis below or watch online (with enhanced laughter track) https://www.youtube.com/watch?v=UpFBA3yvppg, while holding a glass, or someone’s hand, or both.

Many of you must be wondering what a statistician can say about marriages, other than that the success rate of remarriages is statistically significantly lower than that of the first marriages. Indeed, I never thought about the connections between statistics and marriages until about five years ago, when I was approached by a young scholar during a statistical conference. He got my attention with a line that few academics can resist: “I really enjoyed your writing.” But his next line was truly unexpected: “Your article saved my marriage.” Wow! I didn’t know my writing could be this powerful! Naturally, I asked which article. “Remember the parking problem you wrote about?” he reminded me. Now I was even more curious…

To keep the suspense just a little bit longer, let me take a detour—continuing the theme of crossroads—on something else I did as a statistician that ultimately led to a happy wedding in this very church. About a decade ago, I started to offer a course later known as my ‘happy course’: Real-Life Statistics: Your Chance for Happiness (or Misery). It is a course intended to showcase how statistical insights work in real life, and hence I used many real-life stories, including my own.

There are actually very few fundamental statistical insights, and one of them is the bias-variance tradeoff, also known as the robustness-efficiency tradeoff. Basically it says that if you want a method to work really well for a particular case—that is, to be efficient—then it would not be very applicable in general. Conversely, if you want a method to be applicable in general—robust—then it is unlikely to do very well for a particular case. There is no free lunch, you must make a choice.

When I started to use the seven-storey Broadway garage just down the road, which has seven floors, I naturally parked in the first parking spot available when I arrived in the morning. This was an efficient strategy in terms of minimizing the walking distance on the stairs, but its efficiency depends on a crucial assumption: that I would remember on which floor I parked when I returned in the evening. After walking up and down the stairs many times late at night, I laughed at myself for forgetting the robustness-efficiency trade-off! There is a much more robust strategy: always park on the seventh floor, which is never full in the morning.

Apparently, the young fellow who approached me, and his wife, were frustrated by a similar parking problem for their shared car. They had some childcare issues that required them to return to it often several times a day, depending on who happened to have some squeezable moments. But then they often couldn’t locate quickly where the car was parked by the other, and it became almost a daily ritual for them to blame each other for the wasted time. As the frustration escalated from parking lot to bedroom, my young fan was delighted to discover the simple solution offered in my article. And they have lived happily ever after—or so, at least, I hope!

Of course as a statistician, I would not make any scientific claim without having at least two cases. Recall that my happy course ultimately led to a happy wedding [in Harvard’s Memorial Church—described in XL-Files in the December 2013 issue]. Yes, that took place on October 5, 2013, and if you check the Memorial Church’s log book, you might be surprised to find out who officiated the wedding. Yes, the truly statistically yours.

The happy couple were two members of my happy team, a group of graduate students in statistics who helped me to design and teach the happy course. I took both of them to Shanghai as my TFs for a summer school version of the happy course, and they fell in love with each other during that trip. Probably wanting to thank me for being an accidental matchmaker, three years later they asked me to officiate their wedding. I of course wouldn’t waste any opportunity to preach about statistical insights, and this time it is the universal law of regression towards the mean, which in simple terms is that when something is high, it has the tendency to go down, and vice versa. [Editor’s note: to hear more on this, you’ll have to watch Xiao-Li in the Youtube clip cite a part of his preaching from that ceremony, especially if you might be in need of it now!]

And I hope you all would accept what I am trying to convey: that inspirations and solutions in life often come from unexpected sources. I also hope I have given you a helpful line for your marriage or relationship: “Honey, it’s not me—it’s the regression towards the mean.” Joking aside, as a statistician, I’d be delighted if your memories of the two fundamental statistical insights I mentioned would be as lasting as your longest marriage or relationship.

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