ST3456: Modern Statistical Methods II

## Module Code: ST3456 (descriptor)Module Title: Modern Statistical Methods II (Simulation methods)Cohorts: Maths Week range: 03-08, 10-14Semester: 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 webpageOther 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:www.random.org for true random number generation (link to Box-Muller method for normal random generation)

• 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)

• 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: