Random Walks on Polls
A while ago, the Economist published an explanation of their model of the 2016 US presidential election. This post implements a simplified form of that model.
Posts by Year
2025
Converting Dataframes to Pytrees
Numpyro models expect data in the form of a pytrees: nested lists or dictionaries of multidimensional arrays. But datasets usually don’t start that way: we u...
GP Matching in Observational Studies
Accounting for confounders using Gaussian Processes
2024
Advent Of Code
I’ve been playing Advent of Code this year. I started writing solutions in R, but soon realized I was better served by a more general purpose language. Julia...
Basu’s Bayesian Bears
Bayesian calibrated survey sampling
Hop Lists
Hop Lists are a novel retroactive set data-structure that allow for a branching timeline.
Graph SLAM
Tracking a robot’s motion with maximum likelihood estimation.
Difference In Differences
Causal effect estimation with quantified uncertainty
Handlers for Arviz
Better integration between Arviz and Numpyro
Simple Numpyro GLMs
Building a DSL for R-style generalized linear modeling in Numpyro.
Finite Particle Approximations
Say you have a discrete distribution $\pi$ that you want to approximate with a small number of weighted particles. Intuitively, it seems like the the best ch...
Testing With Julia
The standard way of writing tests Julia is to write a test/runtests.jl file. Running Pkg.test() will when start a new Julia process that loads your package a...
Finite Basis Gaussian Processes
If your GP kernel corresponds to an inner product in a low enough dimensional space, you can speed up inference by taking a weight space view.
Nearest Neighbor Gaussian Processes
In a k-Nearest Neighbor Gaussian Process, we assume that the input points $x$ are ordered in such a way that $f(x_i)$ is independent of $f(x_j)$ whenever…
Krylov Methods
The $i$th Krylov subspace $\mathcal{K}_i$ for a symmetric matrix $A$ is the subspace spanned by repeatedly multiplying $A$ by an initial vector $b$. This mos...
2023
Adversarial Extensions To Information Directed Sampling
The Bayesian perspective offers a simple and elegant framework for tracking uncertainty in online optimization problems. In structured bandit settings, it na...
Fast CRDT Reconsiliation with Patricia Chains
A mean field analysis of the gossip protocol shows that distributed consensus with CRDTs can happen in constant expected time.
Fast Slam
Instead of representing the joint distribution of an object and landmarks’ locations with a multivariate Gaussian, we can use a particle filter.
EKF Slam
A hands-on introduction to an old technique for simultaneous localization and mapping.
Conjugate Computation
This post is about a technique that allows us to use variational message passing on models where the likelihood doesn’t have a conjugate prior. There will be...
Generative ODE Models are VAEs
Generative image models based on ordinary differential equations can be seen as forms of variational auto-encoders.
2022
A Taste Of Qmc
Error with standard Monte Carlo methods decreases as $O(n^{-1/2})$. Quasi Monte carlo methods have error that decreases as $O(n^{-1})$, as we demonstrate wit...
2021
Sparse Variational Gaussian Processes
This notebook introduces Fully Independent Training Conditional (FITC) sparse variational Gaussian process model. You shouldn’t need any prior knowledge abou...
Differential Equations
In my freshman year of college, I took an introductory differential equations class. That was nine years ago. I’ve forgotten pretty much everything, so I tho...
Likelihood Ratios
Say you’re trying to maximize a likelihood $p_{\theta}(x)$, but you only have an unnormalized version $\hat{p_{\theta}}$ for which…
2020
Jupyter For Everything
Forget vim or emacs of VSCode. Jupyter is hands down the best editor out there. The literate programming support, complete with images and beautiful latex sn...
Blogging With Jekyll
This blog is written using Jekyll and Github Pages. Jekyll is a static website generator, which converts directories of markdown files into pretty, hyperlin...