Advanced & Applied Topics · Simulation & Monte Carlo Methods

Simulation: Introduction and statistical foundations

Public introduction · full guide in Eikos

Introduction

What this guide covers

Introduction // Computational Methods · Rigorous Approach

Overview

Topics covered

  • Introduction
  • Statistical Simulation: Theory, Algorithms and Applications
  • Introduction and History of Simulation
  • Formal Probability and Random Variables
  • The Central Limit Theorem and the Law of Large Numbers
  • The Law of Large Numbers (LGN)

Related concepts

Main connections

  • Variance & standard deviation
  • Monte Carlo simulation
  • Calculus & differentiation
  • Markov chain Monte Carlo (MCMC)
  • Bayes' theorem & priors
  • Linear algebra & matrices

Compatible notation

Mathematical sample in LaTeX

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

X−1(B)={ω∈Ω∣X(ω)∈B}∈ℱ
View LaTeX sourceX^{-1}(B) = \{\omega \in \Omega \mid X(\omega) \in B\} \in \mathcal{F}