Discussing the article: "Uncertainty as a Model (Part 3): Mathematical Statistics — How to Extract Knowledge from Data"

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Check out the new article: Uncertainty as a Model (Part 3): Mathematical Statistics — How to Extract Knowledge from Data.

This part of the series examines the mechanisms of the Law of Large Numbers (LLN) and the Central Limit Theorem (CLT) as the theoretical foundation for understanding market patterns. This section describes the tools of descriptive statistics and methods for finding point and interval estimates of distribution parameters. Particular attention is paid to the methodology for testing statistical hypotheses, which makes it possible to objectively distinguish genuine market anomalies from random noise. Each theoretical concept is accompanied by a practical example in the appendix, which helps reinforce the material using specific data.

We write trading scripts and regularly encounter the same practical problem: we have a history of price quotes, but it’s unclear what in it represents a stable market characteristic and what represents a random fluctuation in a specific sample. Because of this, it's easy to mistake noise for a signal — “the mean is positive,” “there is a correlation,” “the distribution is close to normal” — and end up failing in real-world trading.

The purpose of this article is to provide a practical statistical framework for analyzing historical data: how to properly conceptualize a sample (both as a model and as specific numbers), which limit theorems (the LLN and the CLT) support conclusions for finite N, and which practical procedures can be quickly implemented in code to test distributions, estimate parameters, and distinguish statistically significant effects from illusions. In this context, the i.i.d. model is introduced not as a dogma, but as a testable hypothesis — a key focus of EDA and CDA. The article presents practical steps and examples of MQL5 scripts that can be immediately integrated into our testing pipeline.


Author: Aleksey Nikolayev

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