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Writing is how I find out what I think.

Long-form pieces on econometrics, operations research, machine learning and the principles that outlast any single project, each worked through until I could explain it.

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11 pieces since 2018

Every piece

2026

  1. Machine learning · 13 min read

    A Neural Network from Scratch I build a neural network and its automatic-differentiation engine from bare Python arithmetic, and find nothing underneath but the chain rule and maximum likelihood.

2025

  1. Econometrics · 23 min read

    Comparative Analysis of Market Risk in AI-Driven Tech Stocks vs. Large Value Stocks Using Value at Risk We find one-day Value at Risk for AI stocks more than double that of value stocks; only Historical Simulation and Student-t GARCH pass every back-test.

  2. Operations research · 10 min read

    A Multi-Objective Network Optimization Problem A modified minimum spanning tree builds a freight network that balances profit, emissions and regional reach; anchoring it on high-revenue cities scores best.

  3. Econometrics · 6 min read

    Forecasting Commodity Prices: A Comparative Analysis of Common and Mixed Frequency Approaches I forecast commodity price inflation with an AR model and two MiDAS models fed daily stock returns; both beat the AR model, and neither consistently beats the other.

2024

  1. Operations research · 8 min read

    Queuing Theory and Markov Chains in Airplane Boarding: An Econometric Approach An hour-long boarding led me to model the aisle as a queue and a Markov chain: back-to-front compounds delays, and random or window-to-aisle boarding eases them.

  2. Econometrics · 6 min read

    Bootstrapping in R: A Mathematical and Computational Approach We derive the bootstrap, implement a bootstrap test of the mean in R, and show why it can be trusted when the underlying distribution is unknown.

  3. Econometrics · 7 min read

    Portugal: A Macroeconomic Risk Analysis We model Portugal’s growth, unemployment and inflation from 1970 to 2005 with VAR and ARIMA, and find an accelerated Phillips curve fits better than the classical one.

2023

  1. Operations research · 8 min read

    Game Theoretic Approaches to Competitive Location Choice: A Mathematical Perspective My answer to a university assignment on where competing firms locate: eliminating dominated strategies picks Utrecht, while local search settles on Eindhoven.

  2. Essay · 4 min read

    Writing myself into understanding Writing is a thinking tool, not only a way to communicate: explaining an idea on the page shows me the gaps in my understanding, so I write in order to understand.

2019

  1. Essay · 10 min read

    Even a Key Can Expire: A Comprehensive Analysis of Internet Security Principles Internet security rests on cryptography built into network protocols, traced from Caesar ciphers and public keys to post-quantum schemes and a custom Ethereum token.

2018

  1. Essay · 4 min read

    Stoicism Without the Universe Modern Stoicism kept the ethics and dropped the physics and logic they were built on. Does it still hold up?