May 13, 2023
Introduction to DAGs, and modeling of causal effects using Julia —
In this blog post, I’ll introduce the concept of Directed Acyclic Graphs (DAGs) and I’ll show how you can use simulation studies to demonstrate that unbiased effects can be estimated by blocking the backdoor paths identified in DAGs.
A DAG is a diagram which demonstrates which things cause other things in a situation of interest. Here, we have a DAG showing the relationship between social factors, smoking, and heart disease. We believe that social factors might cause smoking (for example, people of lower incomes might be more likely to smoke than people of higher incomes).…
May 13, 2023
Using Burnside's Lemma for Chord Counting: An Illustrated Guide —
One day, my friend texted me a problem out of the blue:
How many different bracelets can be made with 8 beads, where there are 2 red beads, 2 yellow beads, 2 green beads, and 2 blue beads?
(You must use all beads. Bracelets that can be transformed into one another by rotation or reflection do not count as different bracelets. That is, the bracelets have no beginning or end, no front or back.…
May 13, 2023
Using Julia to Simulate a Gift Exchange —
Simulation study Simulation studies are used in statistics to estimate the probability of a certain event happening using pseudorandom numbers generated by a computer. Because it can be expensive and time-consuming to collect lots of real-world data on a phenomenon, statisticians sometimes use computers to create many simulated worlds and determine the frequency of an event happening in those simulated worlds. Simulation studies are used when it is difficult or impossible to analytically compute the probability of an event happening.…