[Quant Lecture] Information Entropy

Probability for algorithmic traders

Why your signals are too confident—and how entropy reveals hidden uncertainty in your edge

Every strategy makes assumptions. But most never question their certainty. Information entropy forces you to confront how much your models actually know—and how much they don't.

This chapter shows how to quantify information, uncertainty, and belief to sharpen your decision-making.

What’s inside:

🔹 Entropy demystified: Shannon, Rényi, and Tsallis entropy explained for quants—what they measure, how they differ, and when to use them.

🔹 From uncertainty to information gain: Learn how to quantify surprise, encode belief updates, and use information-theoretic priors in trading models.

🔹 Entropy in market regimes: Capture hidden structure in volatility, flows, and returns with entropy-based segmentation and drift detection.

🔹 Kullback–Leibler and friends: Use KL divergence, mutual information, and cross-entropy to compare models, distributions, and signals.

🔹 Python-driven analytics: Compute entropy over signals, rolling KL for regime shifts, and optimize decisions with information gain.

🔹 Shrinkage, uncertainty, and calibration: Why entropy beats naive confidence—and how to inject caution into overfit systems.

This isn’t a math curiosity. This is strategic uncertainty management—using entropy to refine what you know, expose what you don’t, and protect your edge in a noisy world.