Summer 2007 course

In sequential analysis, data are sampled sequentially in time, and the researcher decides when to stop sampling and to report results. This additional control over the data collection allows to optimize the balance between accuracy and costs, attain desired probabilities of both Type I and Type II errors, and solve problems that admit only sequential decisions.

For example:

• (Quality inspection) There is a sample of 1000 details, and we test if the proportion of defectives exceeds 5%. Suppose that 100 of the first 200 details are defective. Should we inspect the remaining 800 details, or should we rather stop collecting data because the result is already obvious?

• (Clinical trials) Midway through a clinical trial, the data indicate that one treatment is superior to another. For ethical reasons, we have to use this information and minimize the number of patients receiving the inferior treatment.

• (Parking problem) You arrive at the UTD parking lot and look for the optimal parking space. Certainly, you want to park as close as possible to your office or classroom, but you hate to find out that you missed all vacant parking spaces, and you have to go for the second round. If you see an available parking space, should you take it or look for a closer one? What is the optimal rule?

• (Interviews) You interview candidates for a position in your company. N candidates appear in a random order. After each interview, you have to tell the candidate whether she/he is accepted or denied. Certainly, you want to select the best candidate, but prior to the interviews their qualifications are unknown. What is the best strategy?

The final grade will be based on weekly quizzes and two one-hour exams.

Prerequisites: Probability and Mathematical Statistics (STAT 5351-5352 or equivalent) is a minimum. Statistical Inference (STAT 6331) is preferred.