Math, Music Occasionally, and Stats
Math, Music Occasionally, and Stats
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Hamiltonian Monte Carlo
Hamilton’s Equations Suppose \(\mathbf{q} = \mathbf{q}(t) \in \mathbb{R}^d\) is a position vector of a particle at time \(t \geq 0\). We recall that \[\begin{align} \mathbf{v} &= \dfrac{\mathrm{d}\mathbf{q}}{\mathrm{d}t} \\ \mathbf{a} &= \dfrac{\mathrm{d}^2\mathbf{q}}{\mathrm{d}t^2} \end{align}\]
Last updated on Apr 7, 2026
7 min read
Why I am now a Bayesian at heart
TL;DR my viewpoint I am in practice a Frequentist, but at heart a Bayesian. Regression To understand why I might take this perspective, let’s go through some theory. First, let’s assume a standard data-generating process for a regression:
Last updated on Apr 8, 2026
6 min read
My third semester of OMSCS
Views and opinions expressed are solely my own. The inevitable question: I got an A in Computer Networks (CS 6250) and a B in Database System Implementation (CS 6422).
Last updated on Dec 16, 2025
4 min read
Proof of the invariance of Jeffreys' prior
Views and opinions expressed are solely my own. As I have been learning Bayesian statistics, one result that I have been somewhat aware of but have found it very difficult to find a proof of is the following statement: Jeffreys’ prior is invariant.
Last updated on Jan 29, 2026
3 min read
Data Tech 2024: a preview
Views and opinions expressed are solely my own. Introduction In my talk in Data Tech 2024 on June 7, 2024, I will be taking the audience from a background in undergraduate probability through a journey through what I have learned about reinforcement learning over the last school year, through an intro to deep reinforcement learning (DRL).
Last updated on May 21, 2024
3 min read
Review of my second semester of OMSCS: Deep Learning
Views and opinions expressed are solely my own. The inevitable question: I got an A in Deep Learning (CS 7643). Introduction This post marks the day when my grade for Deep Learning (DL) has been released for my second semester in OMSCS (Spring 2024).
Last updated on Feb 1, 2026
2 min read
Using deep reinforcement learning to solve the Zelda Thrill Digger in PyTorch: static environment (part 1)
Views and opinions expressed are solely my own. Background In a previous post - about two years ago - I speculated that one could solve Thrill Digger using reinforcement learning (RL).
Last updated on Mar 13, 2024
11 min read
Using conventional alpha values for hypothesis tests obscures the meaning of "statistical significance"
Views and opinions expressed are solely my own. I once had a conversation with someone who wanted help designing an A/B test for a website. The design was more or less what one would have for a conventional two-sample proportions \(Z\)-test: users would be assigned randomly, by IP address, to one of two versions of a website.
Last updated on Mar 9, 2024
5 min read
Review of my first semester of OMSCS: Computer Vision and Reinforcement Learning
Views and opinions expressed are solely my own. The inevitable question: I got an A in Computer Vision (CS 6476) and a B in Reinforcement Learning (CS 7642).
Last updated on Dec 18, 2023
8 min read
A minimal audio and video production setup for lecturing
Views and opinions expressed are solely my own. Introduction When I taught at Normandale Community College from Fall 2019 through Spring 2021, I transitioned the course I taught from an in-person to online mode of instruction in Spring 2020.
Last updated on Jul 16, 2023
3 min read
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