2014/2015, Semester 2
Yale-NUS College (Yale-NUS College)
Modular Credits: 5
This module is a key bridging module for those specialising in statistics in the Mathematics and Computer Science (including statistics) Major, which will give the requisite knowledge to be able to take any of the subsequent modules, as well as elective modules in Statistics or Biostatistics taught in NUS proper. Topics will include the likelihood function, Bayesian inference, the central limit theorem, likelihood ratio tests, model comparison and frequentist desiderata. The course will be organized in the lecture plus tutorial/computer lab format.
You need to have done QR already! You should ideally have at least super basic calculus (as in, you have done some differentiation at some point in your life, and maybe an integral or two).
At the time of writing, it's looking like this will be a
small class, and unless there is a sudden deluge of students enrolling, we might just make the whole semester discussion-based... If, however, the class size prohibits this, then the course will be run with a lecture on Monday, followed by a tutorial and/or computer lab later in the week to reinforce the material.
A list of what is covered each week can be found in the lesson plan. The course is split into four parts:
Chapter 1 is on probability, or data generating processes. This occupies the first four weeks of the course, and covers, among other topics, the axioms of probability, random variables, moments and functions of random variables, distribution families and limiting distributions.
Chapter 2 introduces classical or frequentist inference, covering likelihood functions, maximum likelihood estimation, frequentist properties of estimators, and classical measures of uncertainty. It occupies weeks 5 to 7.
Chapter 3 introduces Bayesian inference, including priors, posteriors, methods for computing posteriors and Bayesian decision theory. It occupies weeks 8 to 10.
Chapter 4, during weeks 11 to 13, covers hypothesis testing, from the basic principles to different kinds of tests, including Wald, likelihood ratio and permutation tests.
At the end of the first three chapters of the course there will be a test. At the end of the entire course there will be a final. We'll also do a project towards the end of the course. The weights breakdown is:
Mid-term test 1 (0.15)
Mid-term test 2 (0.15)
Mid-term test 3 (0.15)
Final exam (0.35)
Of course, these weights don't really mean much unless the variances in each component are standardised. However, the likely class size means that standardisation by e.g. z-scoring probably wouldn't make any sense.
Workload Components : A-B-C-D-E
A: no. of lecture hours per week
B: no. of tutorial hours per week
C: no. of lab hours per week
D: no. of hours for projects, assignments, fieldwork etc per week
E: no. of hours for preparatory work by a student per week