Bayesian bar hopping, Einsteinian insanity, and the seduction of soft science

A few months ago I was having dinner with a friend, a professor of physics. We'll call him professor base-rate-neglect. He's one of those hard science jerks who always reminds me that the social sciences are soft sciences. I'm used to claims like these from idiots like him. But, still, I love the guy. So professor BRN was complaining about his love life, or lack thereof. "I don't get it. I'm smart. I'm fairly attractive. I have a good job. But I can't seem to meet women."

Experimentaholic replies, "Well, how are you trying to meet them? Or rather, how have you met the women you've dated most recently?"

Dr. BRN says, "I met Kelly at a bar. That ended horribly. I met Jen at the park. Ended terribly. I met Susan at the bookstore. Ended because she moved to Oregon."

Experimentaholic: "Well, have you ever heard of a guy names Thomas Bayes?"

BRN: Sure. He did Bayes Theorem. I forget about what it says, though. I hated statistics. It's soft math.

Experimentaholic: I hate it when you people say that. Especially since I will use soft math to solve your problems. Bayes dealt with a statistical problem having to do with where billiard balls would end up resting on a table. I think this directly relates to your problem.

BRN: This is why I don't trust you soft scientists. Soft thinking. Billiard balls. What do billiard balls have to do with my love life?

Experimentaholic: More than you'd think. I won't go into the gory details of marginal and conditional probability, because you probably slept through stats. But let me ask you another question. How many times per week do you do any of these activities?

BRN: Well, I might seem a bit like an alcoholic, but I probably go out to bars three times per week. I go running on the weekend, and probably go to the bookstore once a month or so.

Experimentaholic: Okay. Think for a minute. So you go to bars 12 times a month, and you got one hit and 11 misses. You go running four times a month, and you get one hit and three misses. You go to the bookstore once a month, and you get one hit, no misses. Do you get where I am going with this?

BRN: Not really.

Experimentaholic: Dude, for every time you go to the bar each year, say, there is a less than one percent chance you are going to meet someone. Why? Because you head to the bar 144 times per year, and only have one relationship to show for it. You go running 36 times per year, and you have one relationship to show for it. That means the probability of you meeting someone while running is around 2 percent. Now, you go to the bookstore 12 times a year, and you have one relationship to show for it. That's an 8 percent chance that every time you go to the bookstore, you'll meet someone.

It seems as if you're doing everything backwards. What would Thomas Bayes do, if he either were alive today or not a Presbyterian minister, or not a [explicative deleded] lush like you? He would be going to the bookstore 3 times a week, going running twice a week, and avoiding bars altogether. Man, you got your strategies mixed up. All because you are ignoring the base rates - or the hits and misses - of your strategies of meeting people.

BRN: I never thought of it that way.

Experimentaholic: I know you think that my kind of science is soft, and that psychology is bullshit. I think a lot of psychology is bullshit too. But I am forcing you to do a little experiment. I don't care if you keep going to bars three times a week, you're a lush after all, and the tenure track thing is stressful. Drown yourself in beer. But I am forcing you to go to the bookstore three times a week. An hour at the bookstore, perusing the shelves, and let's see how your love life changes.

BRN: We'll see. I'll have to think about it.

Experimentaholic: Think all you want. It's the fact that you're not thinking about base rates that makes you miserably unhappy and sitting here complaining to me, and going home alone to your miserable apartment and crying your lonely self to sleep.

BRN: Whatever, you [explicative deleted] soft scientist.

Now, I haven't seen BRN for a little while, and I just received the following email from him.

Experimentaholic:

Yo, man. Sorry I've been out of touch, but the most amazing thing happened. So at first, I basically ignored your little "experiment" and kept doing what I always do. I thought, "You're dumb, and what do you know?" Then, a few weeks later, after a pretty bad hangover, I decided to try your little experiment. For two weeks, I went to the bookstore three times a week. During the third week, I'm sitting there, reading a copy of Dawkins's The God Delusion, when this totally gorgeous woman walks up and says that she loved that book. We started chatting, and she is a biology grad student at [redacted] university. We totally hit it off, and she gives me her number. I call a few days later, we go out on a date, and you know where this is heading. Long story short, I'm seeing this girl. It's been five weeks now, and I am totally falling for her. Man, I can not believe that a psychologist of all people could [increase the frequency of his sexual encounters]. I thought you soft scientists were idiots. Next time we get together, dinner's on me.

My response?

I guess it takes a psychology professor to remind a physics professor that Einstein defined insanity as "doing the same thing over and over again and expecting different results." Perhaps there is something to soft science after all? Either way, I will relish the dinner. And I look forward to meeting the new lady.

Experimentaholic saves the day.

Prediction and postdiction

I share in the horror over the massacre at Virginia Tech. Part of the shock for all of us in academia is that we tend to think of school as the diving board of life: a place where lives begin, not end. I see my own students and colleagues in the images of both the victims as well as the perpetrator. And that both saddens and terrifies me.

However, I find it upsetting that people are criticizing Virginia Tech for ignoring warning signs. I find that response represents a severe and all-too-common error in thinking about direct versus inverse probability.

The basic premise rests in the fact that the following statements are not identical:

1. Given person A wears a trenchcoat, is quiet, and writes plays involving murder, there is a high probability that he will go on a shooting spree.
2. Given person A went on a shooting spree, there is a high probability that he wore a trenchcoat, was quiet, and wrote plays involving murder.

The first statement is one that is a matter of direct probability. You multiply the proportion of people who wear trenchcoats, who are quiet, and who write plays about murder, and you get a number which represents the proportion of the population that are going to go on shooting sprees. However, there is a little problem: a lot of people wear trenchcoats, are quiet, and write plays about murder. Round them up, and you might find a group that includes a significant proportion of the undergraduate population. However, a significant proportion of the undergraduate population will not end up going on a shooting spree. That concerns the error inherent in mistaking direct and inverse probability.

A 17th century minister named Thomas Bayes noted that probability of event A conditional on B is generally different than the probability of B conditional on A. Bayes came up with a solution that links them mathematically by a simple equation called Bayes Theorem. In short, the theorem explains that the relationship between direct and inverse probability is a function of the base rate, or frequency, of the two events. Psychologists have long known that people ignore base rates, resulting in serious errors in reasoning that can be fatal.

For example, there are many cases of heterosexual, non-IV drug users who killed themselves because they received news of a positive HIV test. Their doctors probably informed them that the HIV test has an accuracy of 99.99 percent. However, that does not mean that they can be 99.99% sure that they have HIV. Why? Because of the base rate: tens of thousands of people take the HIV test, and HIV prevalence is extremely low (about 1 in 10,0000) among that particular population (heterosexual non-IV drug users). Every once in a while, given the fact that tens of thousands of tests are run, a negative sample will test positive (the 0.01 percent inaccuracy part). So the actual probability of being HIV positive given a positive HIV test (again, if you are a heterosexual non-IV drug user) is actually about 50% (I calculated this using Bayes Theorem). But most doctors I've interviewed never even heard of Thomas Bayes or his theorem, and make the same mistake their patients do in assuming that direct and inverse probability are the same.

In a similar way, it is easy to say, after the fact, the postdiction that someone should have known, that someone should have done something, that the university was irresponsible for not having seen the warning signs. But the problem with these statements is that they ignore the base rate of the frequency of these warning signs. A lot of college students show warning signs, and many students show warning signs that are considerably worse than those exhibited by Mr. Cho. And unless one were to come up with a better diagnostic tool than trenchcoats or murderous plays - like a crystal ball - I don't believe it is possible to predict who is just an awkward student (of which there are many) and who is going to be a serial killer. I hope we someday can tell them apart, but knowing a bit about human nature - and the way we make errors in our reasoning about probability - makes me doubt it.