# Bayesian Tensor Regression

#### My Elevator Pitch

Since I have begun working on my research project for my PhD in earnest, I find that I'm constantly working on my “elevator pitch”. If you're unfamiliar with the term, an elevator pitch is the cursory explanation of your body of work that you should be able to deliver to someone in the span time no longer than that of a short ride in an elevator. I have had varied success trying to explain it to my classmates, and I have yet to try in earnest with my parents. If I had to boil it down, I would say that my elevator pitch is as follows:

There is a large amount of medical research geared toward the classification and prediction of different anomalies and maladies. One popular tool used is the functional magnetic resonance image (fMRI). The basic way that an fMRI works is that different levels of electrical activity are detected in different regions of the brain while a task is being performed (hence the word “functional”). This requires that we are able to detect which parts of the brain have a significant effect on the likelihood of having some characteristic (such as a disease). Imagine you have a sculpture of a brain made entirely out of sugar cubes. This three-dimensional structure is represented as a tensor, which is another word for a three-dimensional array. Each of those sugar cubes is what is referred to as a “voxel”. Traditional methods of analysis simply take all of the voxels and stack them on top of each other, and then test to see which voxels have a significant effect on the chance of having the response characteristic. What I am doing is using a method that keeps the voxels in the shape of a brain, which makes the estimation more accurate by recognizing that close-together parts of the brain are more likely to have similar effects than two distant parts of the brain. I'm doing this using (Bayesian) methods that more fully quantify uncertainty in the model.

You may note that I do not use too many terms that a random person would not know. I allude to Bayesian methods, but I omit them from this pitch in order to keep it brief. The average undergraduate would probably not be aware of the division in statistical thinking, a debate that goes on and on and on.