4 min read

Nonlinear Models Self Study

Spring 2019 is my last semester in the M.S. Statistics program at SDSU. But the courses offered this semester either focus on material I’m already familiar with or conflict with my schedule. So I decided to take a self study course. Thankfully Dr. Barbara Bailey agreed to be my supervisor.

Why am I doing this?

This is actually something I’ve wanted to do for a long time and this is my last chance so I had to do it or I wouldn’t be happy with myself. There are a lot of reasons for me wanting to do self study. One of them is that the statistics program at SDSU is mostly traditional in their content. To be fair, there are several courses that aren’t but unfortunately (or fortunately?) I’m already familiar with most of the material in these courses. Actually, there is a special course on neural networks this semester which I would have loved to take but can’t because of schedule conflicts.

In any case, I was sort of stuck going into the semester so I had to find alternatives. A self study course seemed like the way to go. I get to study the topics that I want to learn about without having to review old topics, do homework on them, and take tests about them. Frankly, I’m tired of taking tests. I just want to learn about statistics without worrying about what’s going to be on a test and regurgitating random examples from lecture. So I asked Dr. Bailey, she said yes, and now here I am.

What will I learn about?

So what will I be studying? Mostly nonlinear models but that’s sort of just the backdrop for the course. My main goal is to learn about nonlinear time series models. Going in, I knew I wanted to learn more about time series but I wasn’t sure what that would look like. Dr. Bailey suggested nonlinear time series models since that is one of her specialties. She noted that if I wanted to learn about nonlinear time series models, I should first learn more about nonlinear models (non time series) and then see how to extend them to time series.

For the first part of the semester I’m going to focus on splines of various varieties, generalized additive models, and possibly neural networks. While I do have some exposure to all of these I’ve never really covered them in any depth. I sort of know the basic ideas behind them but haven’t looked at the theory or applied them to data. Theory you say? Yes, theory. I probably won’t go into too much depth but I would like to understand the theory behind the models. What I mean by that is I don’t plan on doing a bunch of proofs but I will look at some equations and possibly derive some results. This may not be for everyone but I find it hard to fit models without having at least some exposure to the underlying theory. It helps me understand what’s going on. After that, who knows. I want to see how to extend these models to time series. Then maybe I’ll look into some other models and apply them to time series. How much material I cover mostly depends on how much time I have.

I plan on writing posts here for everything that I study. Some will probably focus on theory, some will demonstrate how to fit a particular model in R, some might just be my thoughts on a given class of models. Hopefully this will help other people interested in nonlinear models. But mostly writing everything up is to help me learn and for reference for my future self. If you’re interested in what I am doing feel free to reach out with questions/comments/corrections at andrewbates73@gmail.com. I also have a GitHub repository for all the code and such I will use.