# Posts

Occasionally I will post here about things I find interesting.

### MondrianForests.jl

My new Julia package for Mondrian random forest regression is available on GitHub.

### Inference with Mondrian random forests

I’m excited to share my new preprint, titled “Inference with Mondrian random forests” and coauthored with Matias Cattaneo and Jason Klusowski.

### Bernstein's Inequality

Bernstein’s inequality is an important concentration inequality. In this post we motivate, state and prove a “maximal inequality” version which I think is clearer than the usual formulation.

### Advent of Code 2022

In 2022 I tackled Advent of Code for the first time, using the Julia language. Here are some of my thoughts; my code is on GitHub.

### Princeton University SEAS Award for Excellence

I’m honoured to receive the School of Engineering and Applied Science Award for Excellence from Princeton University! Many thanks to my advisor Matias Cattaneo and to my other collaborators.

### Yurinskii's Coupling for Martingales

I’m pleased to share my new preprint, titled “Yurinskii’s Coupling for Martingales” and coauthored with Matias Cattaneo and Ricardo Masini.

### Local Polynomial Regression 4: Application to Global Warming

In this final post on local polynomial regression we apply the local polynomial estimator to global warming data from NASA.

### Local Polynomial Regression 3: Correcting Bias

This post is the third in a series on local polynomial regression, motivating the local polynomial estimator through bias reduction.

### Local Polynomial Regression 2: Bandwidth Selection

This post, the second in a series on local polynomial regression, investigates bandwidth selection procedures for the Nadaraya–Watson estimator introduced previously.

### Dyadic Kernel Density Estimation

An update on my research and software relating to dyadic kernel density estimation.

### Local Polynomial Regression 1: Introduction

Local polynomial regression is an important statistical tool for non-parametric regression. This post, the first in a short series, covers the general problem setup and introduces the Nadaraya–Watson estimator.

### The Waiting Time Paradox

Why is my train always late? Do light bulbs last longer than they should? These questions can be answered with the waiting time paradox and the inspection paradox.

### Julia Sets and the Mandelbrot Set

Julia sets and the Mandelbrot set arise naturally in complex dynamics. We explore some of their properties and methods for plotting them.

### motifcluster

A software package for motif-based spectral clustering of weighted directed networks.

### Goodstein Sequence Calculator

To complement my earlier post on Goodstein sequences, I wrote a Python script to calculate them.

### The Dirichlet Problem and Continuous Local Martingales

The Dirichlet problem is an important boundary value problem, with applications in physics. Although hard to solve analytically, we can construct probabilistic approximations using continuous local martingales.

### Goodstein Sequences

Goodstein sequences grow fast and appear to diverge to infinity. But a neat application of ordinal arithmetic gives a surprising result.

### Modes of Convergence

The notion of

*modes of convergence*is central to probability theory. This short article focuses on the relative strengths of these convergences and includes a helpful diagram.### My New Website

Here is my new website, built using Jekyll and hosted with GitHub Pages.