I’ve been doing some pro bono data and statistics work for a nonprofit focused on keeping constituents informed of how well their elected representatives are representing them between elections. The goal is to allow users to vote along with their representatives and to receive information on how aligned their views are with the votes of their representatives.
We are trying to maintain and analyze data from a number of different sources: about the users (e.g. congressional district, join date); about the bills being voted on; about user engagement; and about numerous other topics.
Switching to Emacs Org mode and ox-hugo I was previously using blogdown to generate this static website from .Rmd documents. I was working almost exclusively with R at the time, and I didn’t see that changing. Blogdown was a wonderful package to use to get this site up and running and it worked well for my first posts. However, my interests changed; I found it a little difficult to use outside of the context of RStudio; and it became a little harder to translate my current activities into .
Introduction In this and some of the following posts, I’ll be trying something a little bit different (and a little more aligned with the original intent of this site). I’m going to be writing about perceptrons and the perceptron learning algorithm. The perceptron learning algorithm was developed by Frank Rosenblatt in the late 1950s, making it one of the oldest machine learning algorithms.
I’m tentatively planning four posts on this topic: the first will provide some background and context, explaining what the “perceptron” is and what motivated its development.
Introduction This is a followup to a prior post on the same topic, where I used R’s base plotting system to visualize a linear programming provelm. I’m again looking at section 1.4 of Introduction to Linear Optimization. This time, we’ll consider Example 1.8 on page 23 (Bertsimas and Tsitsiklis 1997, 23). The optimization problem in this example is:
\[\begin{align*} -x_1+x_2 &\leq 1 \\ x_1 &\geq 0 \\ x_2 &\geq 0 \end{align*}\]
Some preliminary notes This time, instead of using the base R package, we’re going to plot the problem using the ggplot2 package (Wickham 2009).
Introduction In this post, I outline the basics of setting up and using OpenBUGS on linux. BUGS stands for Bayesian inference Using Gibbs Sampling. OpenBUGS allows for the analysis of highly-complex statistical models using Markov-chain Monte Carlo methods. It is specifically focused on Bayesian methods.
This guide may not be generalizable to all Linux systems, but it worked for me. It wasn’t too difficult, but I did have to pull together a number of different sources to get everything working as intended.
Motivation I’m revisiting my old statistical inference textbook with the aim of slowly working through many of the problems. When I started out, Casella and Berger’s Statistical Inference was my first ever exposure to statistics, and I didn’t have the mathematical preparation for it. Since then, I’ve developed greater mathematical maturity and better general knowledge and intuition about statistics.
I also want to learn how to implement some of the procedures and verify some of the properties in the book using R.
Introduction Today, I’m looking at section 1.4 of Introduction to Linear Optimization. The goal of this section is to find “useful geometric insights into the nature of linear optimization programming problems”. I will recreate the examples from the book in R.
In the following examples, we want to visually examine linear programming problems in order to:
See what the objective function being optimized looks like Visualize the feasible set based on the given constraints If possible, visually identify solution.
One of the first books I’ll be working (partially) through is Introduction to Linear Optimization (Bertsimas and Tsitsiklis 1997). I recently took a statistical computing class that covered a selection of optimization topics. Though the course was far from comprehensive, it highlighted the value of having a range of optimization techniques, and a thorough grounding of how they work, in your toolbox. I will be working through the first four or five chapters of this book before moving onto nonlinear programming.
Welcome to my site! I will be using this site for a few different purposes:
Writing a blog Aggregating my other publications Posting notes and exercises from my statistics and math self-study Writing short reviews of the books I read blog I used to write a lot more when I was a History of Science student at the University of Chicago. Studying statistics doesn’t give me as many opportunities to write, but I think it’s very important for people to write–and read–about statistics.