Let’s Model It Out

Building mathematical and computational models from first principles

Author

Dan Sprague

What happens when we take an interesting idea, state its assumptions, derive the model, and build it ourselves?

Let’s Model It Out is an implementation-driven notebook-free blog about building mathematical and computational models from first principles.

The first series, Bayes Through Physics, begins with a desire to watch Bayes’ theorem happen as a physical process. Probability distributions become energy landscapes, Bayesian updating adds physical potentials, KL divergence becomes excess free energy, and probability moves through diffusion, least-action transport, information geometry, and eventually discrete Generative Flow Networks.

Every chapter includes a Julia implementation that can be run without a notebook interface.

The Case for Julia in Computational Biology

Julia

Why Julia? Python excels as a general purpose programming language and as a wrapper for neural network implementations, whereas R excels at data analysis, plotting…

Thinking Machines

Statistical Modeling

To think before one speaks is to consider a set of possible responses and choose the one that best conveys one’s intent. This is a task that most humans do intuitively and…

Neighborhood Conservation Districts Suppress Housing in Cambridge, MA

Statistical Modeling

Cambridge is a small city immediately adjacent to Boston, Massachusetts with one of the worst housing crises in the country. Despite this, the city has done remarkably…

Bayesian Uncertainty Estimation for Small Sample LogNormal Data

Statistical Modeling

Julia

Simplex Projection (Sparsemax) for Differentiable Discrete Cluster Assignments

Statistical Modeling

Julia

Code for this analysis can be found here.

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What happens when we take an interesting idea, state its assumptions, derive the model, and build it ourselves?

**Let's Model It Out** is an implementation-driven notebook-free blog about building mathematical and computational models from first principles.

The first series, **Bayes Through Physics**, begins with a desire to watch Bayes' theorem happen as a physical process. Probability distributions become energy landscapes, Bayesian updating adds physical potentials, KL divergence becomes excess free energy, and probability moves through diffusion, least-action transport, information geometry, and eventually discrete Generative Flow Networks.

Every chapter includes a Julia implementation that can be run without a notebook interface.