Probability & Statistical Inference · Probability Theory

Advanced probability theory: Conditional probability and independence

Public introduction · full guide in Eikos

Introduction

What this guide covers

Mathematical and formal analysis of the principles of conditional probability, complex probabilistic systems, total probability and Bayes theorems, counterintuitive paradoxes and high-precision clinical applications.

Overview

Topics covered

  • Introduction
  • Advanced Probability: Conditionality, Independence and Bayesian Inference
  • Probability Spaces and Axiomatics
  • The Fine Structure of -algebra
  • Kolmogorov's Axioms
  • Essential Derivative Theorems

Related concepts

Main connections

  • Conditional probability & independence
  • Bayes' theorem & priors
  • Diagnostic test evaluation & ROC
  • Maximum likelihood estimation
  • Epidemiological measures & risk ratios
  • Survival analysis & Kaplan-Meier

Compatible notation

Mathematical sample in LaTeX

The expression is rendered accessibly, with its LaTeX source preserved below.

⋂i=1∞Ai=(⋃i=1∞Aic)c∈ℱ
View LaTeX source\bigcap_{i=1}^{\infty} A_i = \left( \bigcup_{i=1}^{\infty} A_i^c \right)^c \in \mathcal{F}