## Archive for September, 2008

### Design Flaws in R #3 — Zero Subscripts

Unlike the two design flaws I posted about before (here, here, and also here), where one could at least see a reason for the design decision, even if it was unwise, this design flaw is just incomprehensible. For no reason at all that I can see, R allows one to use zero as a subscript without triggering an error. (Remember that in R, indexes for vectors and matrices start at one, not zero.)

This is of course a terrible decision, because it makes debugging harder, and makes it more likely that bugs will exist that have never been noticed. (more…)

### Applied Statistics PhD Comprehensive Question #2

PhD students in the Dept. of Statistics at the University of Toronto normally write three comprehensive exams at the end of their first year, in Probability, Theoretical Statistics, and Applied Statistics. Below is a question I set for the 2007 exam in Applied Statistics. It may be an interesting exercise for others too. It should in theory be doable by someone with just a good introductory undergraduate course in statistics, including multiple regression. However, many PhD students had difficulty with it, so I wouldn’t say it’s easy.

The question is here. I’ll post my answer in a week or so.

My previous post with a question from the 2008 exam is here.

**Update:** Here is the post with the answers.

### Down Syndrome and Decision Theory

I have a wonderful 11-month-old daughter, who thankfully is entirely healthy. During the pregnancy, my wife and I were of course worried about the possibility of a congenital defect, of which the most prominent is Down Syndrome. Today, couples must make a series of complex decisions — whether to have a screening test for Down Syndrome, whether (based on its result) to have a more risky diagnostic test, and of course, what to do if the final result is that the fetus has Down Syndrome. These decisions depend on moral judgements, on various facts regarding the nature of the fetus at various ages, regarding the nature of Down Syndrome, and regarding the reliability and dangers of the tests, and finally, on the proper way to use this information to make a decision.

This last aspect is in the domain of decision theory, and will be the main focus of this post. Decision theory purports to show how a decision-maker should use the probabilities of the various possible outcomes along with their personal “utilities” for these outcomes to make a rational decision, which maximizes their expected utility. The validity of decision theory as a guide to rational action has often been challenged. The Allais Paradox describes one situation where decision theory does not accord with the judgements of many people, and some argue that the fault is not with these people, but rather with decision theory. Interestingly, Down Syndrome testing involves an analogue of the Allais Paradox. (more…)