I was intrigued by the title of a post at The American Thinker blog by Jason Kissner, titled: “Bayes’ Theorem and Mr. Obama’s Literary Agency.” Dr. Kissner is reported to hold a Ph. D. in criminology. Bayes’ Theorem is a result from probability theory. The Wikipedia article gives one interpretation1 of it: “it expresses how a subjective degree of belief should rationally change to account for evidence.” “Obama’s Literary Agent” refers to a 1991 publicist’s author portfolio brochure that says Barack Obama was born in Kenya.
I’m a mathematician by training and in graduate school I taught math and graded papers. I thought I’d see if there were something I could grade in this paper at The American Thinker. In order to grade a paper, one must first get inside what the writer is saying and understand the argument. I’ll save everyone a lot of time and say that Dr. Kissner concludes that the answer to how likely it is Obama was born in Kenya is about 50%, which is remarkable, to say the least.
I’ll try to guide you through that process and I guess I need to explain a little about conditional probability first.
Statisticians like to represent outcomes or events by capitol letters taken from the first part of the alphabet and they use the letter “P” to mean “probability of.” When we talk about probability, the old standby is the idealized coin toss. So if the outcome is “the coin comes up heads” is labeled “A,” then the probability of that outcome is written “P(A)”. Probabilities are expressed by a number between 0 (can’t happen) and 1 (must happen). For our coin toss, the probability is 0.5, and we would write P(A) = 0.5.
“Conditional probability” is the probability of an event considering or conditioned on other information. We write “P (A|B)” and read “probability of A given B.” An event not happening is denoted with a “not” symbol as in “¬A.” So let’s say that event A is that a voter votes for Obama and that event B is that a voter is Republican. The P(A) might be around 0.5, but P(A|B) is much smaller, and Bayes’ Theorem gives a way to calculate it. Below is the “extended” version of Bayes’ Theorem that is used by Dr. Kissner:
One can estimate the probabilities in the preceding example by sampling (polling) and arrive at a reasonable answer. The voodoo comes in when dealing with questions where we don’t have hard estimates, where things are subjective. In these cases, there is room for monkey business, hence the quotation popularized by Mark Train: “There are three kinds of lies: lies, damned lies, and statistics.”
The American Thinker article asks: what is the probability of Barack Obama being born in Kenya, given that his 1991 publisher wrote in a brochure that he was? Or as they put it, how much does the “new evidence” of the publishers brochure change a former estimate of the probability.
Kissner’s reader is asked to quantify their current opinion of the probability that Obama was born in Kenya. To arrive at my estimate, I will use just two pieces of evidence: 1) The Hawaii Department of Health says he was born in Hawaii and 2) the Immigration and Naturalization Service reports that no US citizen (e.g. Obama’s mother) traveled from Kenya to the United States by air in the entire year around Obama’s birth. Given that there is only one known published instance of vital records fraud in Hawaii, I am going to be generous and say that there was another one in 1961, so the possibility of Obama having a fraudulent birth registration is about 1 in 14,000 births. The INS report is completely independent of Hawaiian birth records, and I would estimate the probability that the report is wrong about the number of air travelers from Kenya at 1 in 1,000. Because the events are independent, the individual probabilities may be multiplied and the resulting probability that Obama was born in Kenya based on those two pieces of evidence alone is 0.00000007.
I’m going to finish my own calculation at this point. We need P(B|A), the probability that the literary agent wrote Obama was born in Kenya given that he was. 0.999 is a reasonable number: If Obama were born in Kenya, then you would expect the agent to get it right. Next we need P(B|¬A), the probability that the literary agent wrote that Obama was born in Kenya given that he wasn’t. Considering that Barack Obama Sr. was born in Kenya, I would put the probability of a mistake by the agent saying that Barack Obama Jr. was born there at maybe 1 in 100, or .01. So with that we can do the calculation. The answer is that the probability that President Obama was born in Kenya is 0.000007, which is a far cry from 0.5. Why the difference?
The American Thinker article points the way by saying,
The … the calculation can certainly be framed in different ways which are open to debate
My estimate of the starting probability that Obama was born in Kenya is much lower than Kissner’s. He says 0.01, but while my estimate is reasoned, his is based on, believe it or not, the probability that the Colts will win Super Bowl XLVII.
If readers think, on the basis of evidence other than the Breitbart disclosure, that Obama is far less likely to have been born in Kenya than the Colts are to win Super Bowl XLVII, they can revise their prior downward accordingly.
Pulling a number out of the air like that is not going to make me disposed towards awarding partial credit.
Kissner assigns P(B|A) a value of 0.9999. That’s not unreasonable, nor that far from my own estimate. He assigns P(B|¬A) a value of 0.01, which I can hardly argue with since it’s my number too. And from those he correctly comes up with about 0.5; even replacing .9999 with my value of .999, the answer still rounds to 0.5.
The evidence of the publicist brochure makes it more likely that Obama was born in Kenya (50 – 100 times more likely using Kissner’s and my figures respectively), but the overwhelming difference in results is based on the estimate of how likely that Obama was born in Kenya before we ever heard of the promotional brochure. In the end, the application of Bayes’ Theorem does little to illuminate the question, and in fact obscures bias in initial assumptions in a avalanche of words and calculations and the fact that the most important number in the calculation, the initial probability, was pulled out of thin air.
1Bayes’ Theorem is a theoretical mathematical result. There are differing interpretations as to what it might mean in the real world. One faction are the Bayesians, and the statement I quoted is of their view.
I used this spreadsheet for the calculations: