Statistical Computing  Monte Carlo Methods
CPSC 535D
Course schedule
Two lectures per week (Tuesday and Thursday from 3.30 to 5.00)
in ICCS 238.
If you want to arrange a meeting, just send me an email at the
following address: arnaud at cs dot ubc dot ca
Announcements
 NO LECTURE ON
THURSDAY 5th APRIL
 Project Presentation on Thursday 12th April: 15 minutes per
student.
 Third assignement posted.
Projects
Handouts
 Lecture 1 (Tuesday 16th
January): Introduction ps
Additional
reading: Chapter 1 of the Bayesian Choice by C.P. Robert or the nice
handouts h1
h2
by B. Vidakovic
 Lecture 2 (Thursday 18th
January): Review of Basic Principles of Statistics ps
 Lecture 3 (Tuesday 23rd January): Basics of
Bayesian Statistics ps
Additional reading: Chapter 1 of the Bayesian Choice by C.P. Robert or h3
by B. Vidakovic
 Lecture 4 (Thursday 25th January): More
Bayesian Statistics (Example, Testing hypothesis, Bayes factors) ps
Additional reading:
 h6
by B. Vidakovic
 R. Kass and A. Raftery, Bayes
Factors, JASA, 1995 paper
 R. Kass, Bayes Factors in
Practice, The Statistician, 1992 here
 M. Lavine and M.J. Schervish,
Bayes Factors: What they are and what they are not, The American
Statistician, 1999 here
 Lecture 5 (Tuesday 30th January): Bayesian model selection ps
 Chapter 7 of the Bayesian Choice by
C.P. Robert
 J. Hoeting, D. Madigan, A. Raftery and
C. Volinsky, Bayesian model averaging: A tutorial, Statistical Science,
1999 here
 A. Raftery, D. Madigan and J. Hoeting,
Bayesian model averaging for linear regression models, JASA, 1997 here
 Lecture 6 (Thursday 1st February):
Introduction to Monte Carlo ps
Additional reading:
 Section 3.1 and 3.2 of Monte
Carlo Statistical Methods.
 Lecture 7 (Tuesday 6th
February): Classical Methods (inverse
transform, accept/reject) pdf
Additional reading:
 Chapter 2 of Monte
Carlo Statistical Methods.
 Scale mixture of
Gaussians, JRSS B, 1974 here:
very useful representation of nonGaussian distributions as
infinite mixture of Gaussians
 W. Gilks and P. Wild, Adaptive
rejection sampling for Gibbs sampling, Applied Statistics, 1992 here
 B.D. Flury,
Rejection sampling made easy, SIAM Review, 1990 here
More advanced
 A. Peterson
and R. Kronmal, On mixture methods for the computer generation of
random variables, The American Statistician, 1982 here
 J. Halton,
Reject the rejection technique, J. Scientific Computing, 1992. (by the
way please don't reject it)
 A. Beskos and G.
Roberts, Exact simulation of diffusions, Annals of Applied Proba, 2005.
here
Check
Proposition 1 and its proof for a very clever and useful remark about
rejection sampling.

Lecture 8 (Thursday 8th February): Importance
Sampling pdf
Additional
reading:
 Chapter 3 of
Monte Carlo Statistical Methods.

Y. Chen, Another
look at rejection sampling through importance sampling, Stat. Proba.
Lett., 2005 here
 J. Geweke,
Bayesian inference in econometric models using Monte Carlo integration,
Econometrica, 1989 here
 H. Van Dijk, J.
Hop, A. Louter, An Algorithm for the Computation of Posterior Moments
and Densities Using Simple Importance Sampling, The Statistician, 1987 here
Optional reading
 A. Owen and
Y. Zhou, Safe and effective importance sampling, JASA, 2000 here
 Lecture 9 (Tuesday 13th
February): More Importance Sampling, Sampling Importance Resampling,
Sequential Importance Sampling pdf
 Chapter 11 of Robert
& Casella
 A.F.M. Smith, A.E.
Gelfand, Bayesian Statistics without Tears: A Sampling Importance
Resampling Perspective, The American Statistician, 1992 Pdf
file here
 A. Doucet, N. De Freitas
and N.J. Gordon, An introduction to Sequential Monte Carlo, SMC in
Practice, 2001 Ps file here
 A. Kong, J.S. Liu
and
W.H. Wong, Sequential Imputations and Bayesian Missing Data Problems,
JASA, 1994
Pdf
file here
 J.S. Liu and R.
Chen, Sequential Monte Carlo methods for dynamic systems, JASA, 1998 Pdf
file here
 Lecture 10 (Thursday
15th February) More Sequential Importance Sampling, Sequential
Monte Carlo extended version of slides9 pdf
 Lecture 11 (Tuesday 27th
February): We will fnish SMC methods and will start Gibbs sampling pdf
Matlab code to generate fractal
image code
Additional reading:
 D.
Mackay, Introduction to Monte Carlo methods, here
 R. Neal,
Probabilistic Inference Using Markov Chain Monte Carlo Methods,
Technical report, 1993 here
 C.
Andrieu, A. Doucet, N. De Freitas and M. Jordan, Markov chain Monte
Carlo for Machine Learning, Machine Learning, 2003 here
 S. Brooks,
Markov chain Monte Carlo Methods and Its Application, The Statistician,
1998 here
 G. Casella and
E.I. George, Explaining the Gibbs sampler. The American Statistician,
1992 here
 S. Chib and
E. Greenberg, Understanding the MetropolisHastings algorithm, The
American Statistician, 1995 here
 Lecture 12 (Thursday
1st March): More Gibbs sampling
extended version of previous slides here
 Lecture 13 (Tuesday 6th
March): More Gibbs sampling for Hidden
Markov models here
 Lecture 14 (Tuesday 13th
March): MetropolisHastings algorithm here
 Lecture 15 (Thursday
15th March): More MetropolisHastings here
 Lecture 16 (Tuesday 20th
March): We will finish MetropolisHastings and start Transdimensional
algorithms here

Chapter 11
of Robert & Casella
 P.J. Green,
Transdimensional Markov chain Monte Carlo, Highly Structured Stochastic
Systems, OUP, 2003 Pdf
file here
 S. Sisson, Transdimensional Markov chains: A decade of progress and
future perspectives., JASA, 2005 Pdf
file here
 Lecture 17 (Thursday
22nd
March): More transdimensional
algorithms here
 Lecture 18 (Tuesday
27th
March): Computing normalizing constants here
 Gelman and Meng, Simulating normalizing
constants: from importance
sampling to bridge sampling to path sampling, Statistical
Science, 1998. here
 Neal, Annealed importance sampling, Stat.
Computing, 2001. here
 Lecture 19 (Thursday
29th March): Advanced methods here
 Chapter 8
of Robert & Casella
 C. Andrieu,
L. Breyer & A. Doucet, Convergence of Simulated Annealing using
FosterLyapunov
Criteria, Journal Applied Probability, 2001. Pdf
file here
 Paul
Damien, Jon Wakefield, Stephen Walker, Gibbs Sampling for Bayesian
NonConjugate and Hierarchical Models by Using Auxiliary Variables,
JRSS B, 1999 Pdf
file here
 R. Neal,
Sampling from Multimodal Distributions using Tempered Transitions,
Statistics and Computing, 1996 Pdf file
here
 C. Geyer & E. Thompson, Annealing Markov Chain Monte Carlo with
Applications to Ancestral Inference, JASA, 1995 Pdf
file here
 Lecture 20 (Tuesday 3rd
April): Dirichlet processes here
 M.I. Jordan
Tutorial on Nonparametric Bayes, NIPS 2005 Ps file
here
 R. Neal MCMC
for
Dirichlet Process Mixture Models, JCGS, 2000. Pdf
file here
 Lecture 21 (Tuesday 10th
April): Introduction to Markov chains theory here
Assignements
Volatility data
Probabilistic Nearest Neighbour
paper here
Course contents
 Introduction to Bayesian
Statistics.
 Probability as measure of uncertainty.
 Posterior distribution as compromise between data and prior
information.
 Prior distributions: conjugacy and noninformative priors.
 Bayes factors.
 Large sample inference.
 Introduction to Monte Carlo Methods
 Limitations of deterministic numerical methods.
 Monte Carlo integration and NonUniform random variable
generation (inverse method, accept/reject)
 Importance sampling.
 Variance reduction techniques (RaoBlackwellisation, antithetic
variables).
 Markov Chain Monte Carlo
Methods  Basics
 Introduction to general statespace Markov chain theory.
 MetropolisHastings algorithm.
 Gibbs sampler.
 Hybrid algorithms.
 Case studies: CaptureRecapture experiments, Regression and
Variable selection, Generalised linear models, Models for Robust
inference
 Case studies: Mixture models and Hidden Markov models,
Nonparametric Bayes, Markov random fields.
 Markov Chain Monte Carlo
Methods  Advanced Topics
 Variable dimension algorithms (Reversible jump MCMC).
 Simulated tempering.
 Monte Carlo optimization (MCEM, simulated annealing).
 Perfect simulation.
 Case studies: Nonlinear Regression and Variable selection,
Mixture models, Hidden Markov models, Bayes CART.
 Sequential Monte Carlo Methods
& Particle Filtering Methods
 Dynamic generalized linear models, hidden Markov models,
nonlinear nonGaussian statespace models.
 Sequential importance sampling and resampling.
 Filtering/smoothing and parameter estimation.
 Sequential Monte Carlo for static problems and extensions.
 Case studies: Switching StateSpace models, Stochastic
Volatility models, Contingency tables, Linkage analysis.
Textbook
 Christian P. Robert and George Casella, Monte Carlo Statistical
Methods, Springer, 2nd edition (you don't need to buy it but it
is a good reference).
We will also use
 JeanMichel Marin and Christian P. Robert, Bayesian Core: A
Practical Approach to Computational Bayesian Statistics, Springer, to
appear.
 Denis G.T. Denison, Chris C. Holmes, Bani K. Mallick and Adrian
F.M. Smith, Bayesian Methods for Nonlinear Classification and
Regression, Wiley.
 Arnaud Doucet, Nando De Freitas and Neil J. Gordon (eds),
Sequential Monte Carlo in Practice, Springer.
 Andrew Gelman, John B. Carlin, Hal Stern and Donald B. Rubin,
Bayesian Data Analysis, Chapman&Hall/CRC, 2nd edition.
 Christian P. Robert, The Bayesian Choice, Springer, 2nd edition.
Grading
This will be based on several assignments and a
final project (exact weighting yet to be decided). The computational
part of the
assignments will be done
using the R
statistical language or Matlab.
If you don't know what these are, I urge you to familiarize yourself
with them.
Note that R is open source and can be downloaded
for free.
Some interesting links  other Bayesian
computational courses