@book{mcbook,

author = {Art B. Owen},

year = 2013,

title = {Monte Carlo theory, methods and examples}

}

Copyright Art Owen, 2009-2013.

- Introduction
- Simple Monte Carlo
- Uniform random numbers
- Non-uniform random numbers
- Random vectors and objects
- Processes
- Other integration methods
- Variance reduction
- Importance sampling
- Advanced variance reduction
- Markov chain Monte Carlo
- Gibbs sampler
- Adaptive and accelerated MCMC
- Sequential Monte Carlo
- Quasi-Monte Carlo
- Lattice rules
- Randomized quasi-Monte Carlo

Chapters 1 and 2

1 Introduction

- Example: traffic modeling
- Example: interpoint distances
- Notation
- Outline of the book
- End notes
- Exercises

2 Simple Monte Carlo

- Accuracy of simple Monte Carlo
- Error estimation
- Safely computing the standard error
- Estimating probabilities
- Estimating quantiles
- Random sample size
- When Monte Carlo fails
- Chebychev and Hoeffding intervals
- End notes
- Exercises

3 Uniform Random Numbers

- Random and pseudo-random numbers
- States, periods, seeds, and streams
- U(0,1) random variables
- Inside a random number generator
- Uniformity measures
- Statistical tests of random numbers
- Pairwise independent random numbers
- End notes
- Exercises

4 Non-uniform Random Numbers

- Inverting the CDF
- Examples of inversion
- Inversion for the normal distribution
- Inversion for discrete random variables
- Numerical inversion
- Other transformations
- Acceptance-rejection
- Gamma random variables
- Mixtures and automatic generators
- End notes
- Exercises

5 Random vectors and objects

- Generalizations of one-dimensional methods
- Multivariate normal and t
- Multinomial
- Dirichlet
- Multivariate Poisson and other distributions
- Copula-marginal sampling
- Random points on the sphere
- Random matrices
- Example: classification error rates
- Random permutations
- Sampling without replacement
- Random graphs
- End notes
- Exercises

6 Processes

- Stochastic process definitions
- Discrete time random walks
- Gaussian processes
- Detailed simulation of Brownian motion
- Stochastic differential equations
- Non-Poisson point processes
- Dirichlet processes
- Discrete state, continuous time processes
- End notes
- Exercises

7 Other quadrature methods

- The midpoint rule
- Simpson's rule
- Higher order rules
- Fubini and the curse of dimensionality
- Hybrids with Monte Carlo
- Additional methods
- End notes
- Exercises

8 Variance reduction

- Overview of variance reduction
- Antithetics
- Example: expected log return
- Stratification
- Example: stratified compound Poisson
- Common random numbers
- Conditioning
- Example: maximum Dirichlet
- Control variates
- Moment matching and reweighting
- End notes
- Exercises

9 Importance sampling

- Basic importance sampling
- Self-normalized importance sampling
- Importance sampling diagnostics
- Example: PERT
- Importance sampling versus acceptance-rejection
- Exponential tilting
- Modes and Hessians
- General variables and stochastic processes
- Control variates in importance sampling
- Mixture importance sampling
- Multiple importance sampling
- Positivisation
- What-if simulations
- End notes
- Exercises

10 Advanced variance reduction

- Grid-based stratification
- Stratification and antithetics
- Latin hypercube sampling
- Orthogonal array sampling
- Adaptive importance sampling
- Nonparametric AIS
- Generalized antithetic samplinlg
- Control variantes wtih antithetics and stratification
- Bridge, umbrella and path sampling
- End notes
- Exercises