ST3456: Modern Statistical Methods II

Module Code: ST3456 (descriptor)

Module Title: Modern Statistical Methods II (Simulation methods)

Cohorts: Maths 

Week range: 03-08, 10-14

Semester: S1 (Michaelmas) 

Total hours: 33 (28 classes + 5 labs)


Timetable: 

- Monday, h. 12-14, room LB01

- Tuesday, h. 10-11, room LB 1.07 (or ICT lab when labs are scheduled)


Textbook: 

  • Lecture notes will be uploaded to this webpage

Other references:

  • Ross, "Simulation"
  • Rubinstein & Kroese, "Simulation and Monte Carlo Method"
  • Robert & Casella, "Monte Carlo statistical methods"
  • Robert & Casella, "Introducing Monte Carlo methods with R"
  • Devroye, "Non-uniform random variate generation"


Links:

Lecture notes (password protected)

  • 10/09/18: Section 1: motivating examples (pdf)
  • 11/09/18: Section 2.1: inverse transform method (pdf)
  • 17/09/18: Section 2.2: transformation methods (pdf)
  • 18/09/18: Section 2.3: acceptance-rejection method (pdf)


Slides (password protected)
  • 10/09/18: Class 1 (pdf)


Syllabus (lecture by lecture):

  • 10/09/18 (2 h): motivating examples: Monte Carlo integration, Bayesian Inference, analysis of leukaemia data
  • 11/09/18 (1 h): inverse transform method (with proof), ITM for exponential random variables (example 2.5), max and min of IID random variables (first method) 
  • 17/09/18 (2 h): max and min of IID random variables (ITM method), ITM for discrete random variable, Transformation methods, Box-Muller method.
Assignment: see Example 2.7 (ITM for Gamma(n, lambda)).
  • 18/09/18 (1 h): acceptance-rejection method


Videos:
  • 18/09/18: acceptance-rejection for bounded density on compact support:

AR_movie.mov


  • 18/09/18: acceptance-rejection for truncated Normal(0,1) with Exponential(1) envelope:

AR_movie_HALF.mov