Second week started with a bang, and by that I mean Suki and I were given donuts halfway between our daily stats lesson. Today, Dr. Laber continued his presentation on modeling the ideas behind precision medicine. He spoke of the Horvitz-Thompson estimator that introduced an unbiased estimator under probability sampling designs:
The argmax operator defines input value for maximum output, capital as the optimal regime (most favorable outcome), p as the probability value, w as the event, a as the patient treatment, and x as the correct treatment to provide to the patient. The equation just lays out the fact that the probability for an optimal “a” as defined first by x as a component of event w of components y, x, and a. It’s… rather confusing… There’s a lot of statistical jargon that’s been pretty difficult to understand at first, but it’s become (slightly?) clearer through these mini-lectures.
Dr. Laber also gave us a problem before giving us 7 minutes to solve it consisting of rolling a dice three possible times and wanting to attain the maximum score. We were able to find the correct “cut-off” numbers of {5, 4} for turns 1 and 2 before Dr. Laber stepped in and showed us through the program R that those two numbers did indeed yield the highest possible score. We then met with three very accomplished people, beginning with former department head Dr. Sastry Pantula, who’d been at several high-ranking positions (including the NSF!) and now serves as a dean at Oregon State. We only had about 10 minutes before he had to leave, but we spoke with him about his life, his work, and his daughter (who’s also a rising senior). Next was Dr. Brian Reich, whose work with dust samples later became the plotline for a CSI episode! The fungi from the dust enabled him to pinpoint the origin of the dust within 200 km through the use of many (complicated) statistical equations. The last person we spoke with was Ryan Martin, one of the most published people in the world for his age. His theoretical approach to probabilities defied all previous work with the Bayesian and Classical forms of statistics, earning him a fair share of supports and critics. All the people we spoke with were incredibly accomplished and interesting to speak with- I feel really grateful that they made the time to talk to Suki and me.
