Probability & Statistical Inference · Probability Theory

Probability: Introduction and general principles

Public introduction · full guide in Eikos

Introduction

What this guide covers

From sample space to Bayes' theorem: a rigorous axiomatic construction of probability as a measure, with combinatorial, conditional and random variable tools that support statistical inference and evidence-based clinical practice.

Overview

Topics covered

  • Introduction
  • The formal language of uncertainty
  • Random phenomena and sample space
  • 1.1. The concept of random phenomenon
  • 1.2. Sample space
  • 1.3. Events: general definition

Related concepts

Main connections

  • Diagnostic test evaluation & ROC
  • Bayes' theorem & priors
  • Conditional probability & independence
  • Epidemiological measures & risk ratios
  • Permutation & exact tests
  • Variance & standard deviation

Compatible notation

Mathematical sample in LaTeX

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

(A∪B)c=Ac∩Bc(A∩B)c=Ac∪Bc
View LaTeX source(A \cup B)^{c} = A^{c} \cap B^{c} \qquad \qquad (A \cap B)^{c} = A^{c} \cup B^{c}