Statistical Inference (MXB341)

2 weeks of lecturing for this 3rd year probability course in 2020. The other lectures were given by Dr Gentry White.

Course description: This is an advanced unit in mathematical statistics covering the theory of point estimation and inference using both classical and Bayesian methods. Statistical inference is the practice of both estimating probability distribution parameters and using statistical testing to validate these results, and plays a crucial role in research, and many real-world applications. You will use the methods of least squares, moments, and maximum likelihood to construct estimators of probability distribution parameters and evaluate them according to criteria including completeness, sufficiency, and efficiency. Results will be computed both analytically and numerically using software such as R. You will learn and apply the Neyman-Pearson Lemma for the construction of statistical tests, including to real-world applications, and learn Bayesian statistics for finding posterior distributions of parameters and evaluating their performance. Results will be communicated both orally and in written form.