Requirements/prerequisites: 251
Duration: Michealmas, Hilary and Trinity
Number of lectures per week:
Assessment:
End-of-year Examination:
Description:
Statistical inference is the process of learning via observations that are subject to uncertainty. This course is a fairly rigorous investigation of the theory and methods of statistical inference.
CONTENT:
Part 1.
Bayesian Statistical Inference
Calculus of probability, meaning of probability (the three views)
Coherence and the Bayesian paradigm
Parameters, the likelihood and the prior
Bayes' theorem
Conjugate priors, loss functions and Bayes' estimators
Elicitation of prior beliefs
Numerical methods for computing posterior distributions:
Monte-Carlo simulation, importance sampling, Markov chain methods
Examples
Part 2.
Classical Statistical Inference
Introduction
The Likelihood Principle, Frequentist Approach, and Bayesian Approach
Parameter estimation. Interval Estimation. Hypothesis Testing. Prediction
Comparison of Various Approaches Of Statistical Inference
Examples
Textbooks:
Bayesian Inference, Vol 2B. Arnold.
Oct 11, 2001