• Simulation notes
  • Printable course contents
    • Slides
    • Printer-friendly pdf files
    • Problems
  • 1 Monte Carlo
    • 1.1 Probability and inference refresher
    • 1.2 Statistical validation techniques (GoF tests)
    • 1.3 Random numbers
    • 1.4 Approximation of probabilities and volumes
    • 1.5 Monte Carlo integration
  • 2 Simulating random variables and vectors
    • 2.1 Inverse transform
    • 2.2 Aceptance-rejection
    • 2.3 Composition approach
    • 2.4 Multivariate distributions
      • 2.4.1 Multinomial distribution
    • 2.5 Multivariate normal distribution
  • 3 Discrete event simulation
    • 3.1 Poisson processes
      • 3.1.1 Homogeneous Poisson process
      • 3.1.2 Nonhomogeneous Poisson process
      • 3.1.3 More about Poisson and counting processes
    • 3.2 Gaussian processes
      • 3.2.1 Brownian motion
      • 3.2.2 Geometric Brownian motion
    • 3.3 Discrete event simulation
      • 3.3.1 Single-server queuing system
      • 3.3.2 Inventory model
      • 3.3.3 Collective risk model
  • 4 Variance reduction techniques
    • 4.1 Antithetic variables
    • 4.2 Control variates
    • 4.3 Stratified sampling
    • 4.4 Importance sampling
  • 5 MCMC techniques
    • 5.1 Markov chains
    • 5.2 Metropolis-Hastings
    • 5.3 Gibbs sampling
  • References
  • Published with bookdown

Notes for Introduction to Simulation

Notes for Introduction to Simulation

Master in Statistics for Data Science at UC3M

Ignacio Cascos

2019-09-10, v1.0

Printable course contents

Slides

  • Monte Carlo
  • Simulating random variables and vectors
  • Discrete event simulation
  • Variance reduction techniques
  • MCMC techniques

Printer-friendly pdf files

  • Monte Carlo
  • Simulating random variables and vectors
  • Discrete event simulation
  • Variance reduction techniques
  • MCMC techniques

Problems

  • Monte Carlo
  • Simulating random variables and vectors
  • Discrete event simulation
  • Variance reduction techniques