[2024/09/12] From Random Walks to the Diffusion Equation

Deriving the diffusion equation starting from the random walk.

[2024/08/30] mechagrad

An implementation of reverse-mode automatic differentiation in Rust. Crunch the numbers.

[2024/08/30] Forward-Mode Automatic Differentiation with Dual Numbers

A simple scalar (forward-mode) automatic differentiation implementation using dual numbers.

[2024/08/15] The Gray-Scott Model of Autocatalytic Reactions

An exposition of the Gray-Scott model, ending with pretty pictures. Check it out!

[2024/08/10] Heat

An introduction to the Laplacian and heat diffusion. Finite difference approximations. Some numpy tricks. Let's get heated.

[2024/06/10] The Gamma Distribution

A short note on the Gamma distribution.

[2024/06/05] The Fisher Information Matrix

Connecting the Fisher Information Matrix to the Hessian of the log-likelihood.

[2024/06/02] Maximum Likelihood Estimation: A Brief Outline

A very brief note outlining the idea of maximum likelihood.

[2024/05/18] Normalizing the Gaussian Integral: The Multivariate Case

A note showing how to normalize an n-dimensional Gaussian integral.

[2024/05/08] Laplace's Method of Integration

An informal derivation of Laplace's method. Let's approximate!

[2024/05/03] Normalizing the Gaussian Integral: The Single-Variable Case

A brief note showing how to compute a 1D Gaussian integral.

[2024/04/28] The Prosecutor's Fallacy

A short exposition of the prosecutor's fallacy. Objection!.

[2024/04/09] Deriving the Matrix form of Linear Regression

A note showing how to solve a multivariate least squares regression. Let's regress.

[2024/02/03] A Limit Problem

A fun little limit problem. continue reading . . .

[2023/08/14] Simple Exponential Smoothing with JAX

This notebook demonstrates simple exponential smooth models using JAX. continue reading . . .

[2023/08/12] Fitting an AR(1) model with JAX

This short notebook shows a simple method for fitting a first-order autoregressive process with JAX.

[2023/08/07] Logistic Regression the JAX Way

This Kaggle notebook demonstrates a simple logistic regression model for the Titanic dataset using the JAX library.