My work arises from the conviction that mathematical rigor is necessary but not sufficient. One must also care about the nature of the objects one is manipulating on paper. A formally valid system with ill-defined or mismatched inputs produces sophisticated garbage. In other words, I sail under the banner of Gauss, Riemann, and Poincaré, rather than Hilbert, Russell, and Bourbaki. The look and feel of this site is an homage to the time when it wasn't common for scientists to mistake mathematical theories for reality.
Probability theory is the perfect example. The frequentist- sigma-algebra methodology still dominates, despite the severe issues with its definition and its widespread reliance on intuitive ad-hoc procedures. Many scientists will be surprised to learn that the random-variable, and t-test methodology that they learned at university doesn't treat probability as a quantification of knowledge. In fact, in this theory, inference (a change in the plausibility of a hypothesis) is an intuitive meta-judgement, which the formalism cannot accommodate.
In challenging contexts such as quantitative finance, the superior rigor and principles of the bayesian inference shine. If well applied it is better at detecting faint signals in data, because it uses all information available. Its rules automatically avoid overfitting, and can render very high-dimensional problems tractable. Prior probabilities are assigned through the maximum entropy principle, eliminating arbitrariness.
An investigation into the capacity of liquid time-constant neural networks to beat classical GARCH benchmarks by using information on the down-time between trading days. Awarded full marks.
A discourse on Knuth and Skilling's derivation of probability, showing that the rules of probability follow from a few symmetries of the lattices of logical statement and need not be taken as axioms.
The Mathematics of Asking the Right Question
A follow-up to a well-received discourse on Knuth and Skilling's lattice-theoretic derivation of probability, exploring the epistemology of probabilistic inquiry itself.
In addition to English, I also speak German, Swiss German, and Italian. They are my mother tongues.
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