Causal Inference

How are things going Señor Vishnu Vardhan?  Sorry, I don’t know anything about Lagrangian points in orbits being related to frames in linear algebra. 

It is interesting that for some people, a problem makes sense and lights up their mind if presented as a physical problem, but for other people, if presented as just a math problem — the gravities between celestial bodies being one example.  Even if different physical or non-physical problems take the same mathematical form, the former class of people will still think through the common physical problem.  One example close to your heart is of treating all information-related problems as ones of communication.  There are many other examples like thinking of various problems as ones of electrical circuit analysis.  One that has been in my mind, but not in the strict way as would be for the former class of people, is thinking of figuring out the productivity of newly hired salespeople as being the physical problem of deblurring the cameraman image. 

At the end of your lifting session, you brought up randomized trials and the issue of sample selection bias, on which Jun will be presenting some work of ours at the IEEE International Conference on Service Operations and Logistics, and Informatics in Suzhou pretty soon.  When trials are not randomized and the experiments are observational studies in natural environments rather than the type of experiments conceived by Ben Franklin, the type of statistical methods that are applied are known as causal inference.  The common physical problem for causal inference is medical treatment doses and patient responses.  Inference problems in various fields can be thought of as the estimation of dose-response functions.

I want to learn about causal inference and dose-response estimation, especially as thought about by Donald Rubin et al., and hope to put up a few more posts as I learn about it.  As a starting point, here is a paraphrasis of a Wikipedia article:

Rubin’s model is based on potential outcomes and assignment mechanisms.  Every patient has different potential outcomes depending on their assignment. A person may have one income at age 40 if he attended a private college and a different income at age 40 if he attended a public college.  To measure the causal effect of going to a public college as opposed to a private one, we should look at the outcome for the same individual in both alternative futures, which obviously can’t be done.  What can be done is a a randomized experiment, in which any difference between populations can be attributed to the assignment because that is the only difference between the groups.

In a randomized experiment, the assignment mechanism is completely random. In observational data, there is a non-random assignment mechanism: in the case of college attendance, people may choose to attend a private versus a public college based on their financial situation, parents’ education, relative ranks of the schools they were admitted to, etc. If all of these factors can be balanced between the two groups of public and private college students, then in Rubin’s model, the effect of college attendance can be attributed to the college choice.