# Statistical Inference (L.7) (867G1)

15 credits, Level 7 (Masters)

Spring teaching

The aim of this module is to provide the mathematical basis and context for many of the widely used statistical techniques. The course is divided into a Frequentist and a Bayesian part and is accompanied by R computer practicals, where synthetic or collected data sets are used to test some of the theory. A substantial part of the frequentist statistical methods used here is built on the methods developed in the companion module Linear Statistical Models.

In the frequentist part, the module covers point estimates using maximum likelihood, hypothesis testing and the construction of confidence intervals. The Bayesian part includes the Bayesian paradigm priors, prior and posterior relation and Bayesian model selection. The module illustrates clearly how many of the well-known and well-used concepts in statistics are derived from rigorous mathematical arguments.

Part of the module is to develop skills sought-after by employers. In particular, the module enhances your ability to identify appropriate tests and write codes to test theoretical results but also guides you to understand how the theory can be correctly applied to several applications.

Some of the questions we will be focusing on are:

• How can we decide if several independent statistical samples have the same statistics, like e.g. mean, variance etc, and why is this important in applications (e.g. for pollsters)?
• Given a data set, what are the most likely parameters that identify the distribution and how can we find them?
• Given that we have prior information about a random sample, which may or may not be reflected in the data set, how can we use it to refine our statistical model in order to use it for more accurate predictions?

### Teaching 85%: Lecture 15%: Practical

### Assessment 20%: Coursework (Portfolio, Problem set, Software exercise) 80%: Examination (Unseen examination)