okay but now Latin-ize it to make it sound fancier

This is one of my more out there papers. So, it is just sitting on arXiv (not submitted yet) because I am hoping to get additional feedback first

So, please consider giving it a read and letting me know your thoughts

arxiv.org/abs/2511.01960

I do want to try to submit something there based on the journal name alone

I should read more of Manski's papers

This is one of my more out there papers. So, it is just sitting on arXiv (not submitted yet) because I am hoping to get additional feedback first

So, please consider giving it a read and letting me know your thoughts

arxiv.org/abs/2511.01960

To contextualize those ideas, I then build and evaluate a simple pharmacodynamic model for a medication on systolic blood pressure using the developed concepts. This section hopefully brings together all the ideas

The conclusion then discusses next steps of where this work can go

With the vacuous model, I then discuss point and partial identification for the mathematical model. Using a vacuous model ensures there is a solution

Some implications for math models of this setup are reviewed

I then walkthrough a simple mathematical model, turning a mechanism into a series of functions. There are a few properties I have these functions satisfy

These properties mean that a mathematical model will cover the entire parameter space. Math models that satisfy this I call /vacuous/

I connect everything using potential outcomes (big surprise) and bounds

The paper starts by reviewing some foundational results from causal inference in the statistical modeling tradition. This is hopefully a nice review for those who haven't seen as much of this area

I'm far from the first to think about this overlap (see the first 20+ references), but I do think how I go about connecting these frameworks is distinct

So now a brief summary of the paper

So that is where this pre-print lies in the context of my research monologue

Here, I try to put together two methods traditions in epidemiology into a shared potential outcomes language. As part of this, I try to better get at what I mean with Eq 7 and identification with mathematical models

But there was still a gap in that work. Namely, how I am *really* doing identification with a mathematical model

My follow-up paper to the previous develops this idea a little (Eq 7), but I think there was more to be said

pubmed.ncbi.nlm.nih.gov/39810877/

... the methodological traditions

Reflecting on this is what inspired my work on combining these methods to address non-positivity

pubmed.ncbi.nlm.nih.gov/37757864/

But I've always had an interest in linking the traditions. In my broader reading of science and philosophy of science, the mathematical modeling tradition has (and still does) play an important role

Nearing the end of my PhD and start of my postdoc, I was interested in the interactions between...

During my masters degree in epi at Ohio State, I did a bit on the mathematical modeling of infectious disease side

During my PhD, I learned the g-formula and quickly became a member of the causal inference cult. It fundamentally changed how I think about a lot of quant stuff