Last week, I got a call to come pick up my son from his preschool because he was identified as a close contact of someone that tested positive for COVID-19. Obviously, we were worried and trying to figure out how to keep the rest of the family safe. We also were staring down two weeks during which my son would be at home. Then, the next day, we were notified that the student had originally tested positive via an antigen rapid test, but had tested negative using RT-PCR nasal swab test.

A few weeks ago, my post-doc adviser, Mandy, asked me to examine a scenario. It was a basic random effects model of the form
\[ W_{ijk} = X_{ik} + E_{ijk}, \quad i = 1,\ldots,n, \quad j = 1,\ldots,J, \quad k = 1,\ldots,K, \]
in which the response for subject \(i\) for replicate \(j\) and component \(k\) (\(W_{ijk}\)) is generated through a latent effect (\(X_{ik}\)) and some observational noise (\(E_{ijk}\)). The model can be applied to neuroimaging in which different unobserved structures or networks have some effect on blood oxygen levels.

Consider a scenario in which noisy data are observed, with variance driven by two primary sources: signal and noise. We can write the data generation as
\[ W_{ij} = X_i + E_{ij}, \quad i = 1,\ldots, n, \quad j = 1,2 \]
Here, consider \(X_i\) as the signal and \(E_{ij}\) as the noise, with values generated from zero-mean normal distributions.
\[ X_i \sim \text{Normal}(0,\sigma_x^2), \quad E_{ij} \sim \text{Normal}(0,\sigma_e^2) \]

The next few posts on this website will be based on emails that I have been sending to the Applied Mathematics and Statistics department every Monday as part of a reminder of the weekly doughnut social event that I help facilitate. In many of those emails, I include a data vizualization with very little explanation. I’ll include more here, like the motivation and the thought process, as well as the code and data source used to make the visualization.

Last summer, I was fortunate to be able to take a two-day short course with Abel Rodriguez here at UCSC. He based the course on the quarter-long Art of Data Visualization course that he had taught that winter quarter. It was super interesting, and it motivated me to try a few things on my own, including a word cloud. I use Google Voice, which saves all of my text messages in spreadsheet format.