---
name: advanced-math-trading/foundations-core
description: Probability, moments/tails, Bayes, and statistical learning foundations for systematic trading.
---

# What this covers
- Probability spaces, random variables, moments, tail risk, Bayes updates.
- Core statistical learning basics and regularization.

# Navigation (load on demand)
- docs/knowledge-base/domains/foundations/advanced-mathematics/Algorithmic Foundations for Systematic Trading.md — probability, moments, tail risk, Bayes code.
- docs/knowledge-base/domains/foundations/advanced-mathematics/statistical-foundations.md — stats core.
- docs/knowledge-base/domains/foundations/advanced-mathematics/probability-and-stochastic-processes.md — probability + processes overview.
- docs/knowledge-base/domains/foundations/advanced-mathematics/probability-spaces-and-random-variables.md — formal definitions.
- docs/knowledge-base/domains/foundations/advanced-mathematics/statistical-learning.md — learning basics.
- docs/knowledge-base/domains/foundations/advanced-mathematics/regularization-methods.md — regularization patterns.

# Quick workflows
- Tail metrics: lift VaR/ES/Hill estimators from Algorithmic Foundations.
- Bayesian updates: use conditional-probability code for regime/parameter updates.
- When in doubt, start with Algorithmic Foundations then pull topic-specific MDs above.

# Notes
- Load only the files needed; avoid bulk-loading the whole directory.