Advanced statistics: statistical inference (half course)

Описание мероприятия

Описание программы

To infer means to make general statements on the basis of specific observations. From an early age, human beings are experts at inference. It is such a fundamental part of our intelligence that we do it without even thinking about it. We learn to classify objects on the basis of a very limited set of examples. In statistical inference, we go from specific to general via a mathematical model. Our specific observations come from a data set; that is, a collection of numbers, or at least, information that can be represented numerically. The mathematical models that we use draw on distributions of probability that are described in the companion half course ST3133 Advanced statistics: distribution theory. Methods for using probabilistic models to make general statements on the basis of an observed set of data is the central topic of this half course.

Aims and objectives

The aim of this half course is to provide a thorough theoretical grounding in statistical inference. The course teaches fundamental material that is required for specialised courses in statistics, actuarial science and econometrics.

Assessment

This half course is assessed by a two-hour unseen written examination.

Учебный план:

• Data reduction; Sufficiency, minimal sufficiency. Likelihood.
• Point estimation; Bias, consistency, mean square error. Central limit theorem. RaoBlackwell theorem. Minimum variance unbiased estimates, Cramer-Rao bound. Properties of maximum likelihood estimates.
• Interval estimation; Pivotal quantities. Size and coverage probability.
• Hypothesis testing; Likelihood ratio test. Most powerful tests. Neyman-Pearson lemma.

Результат обучения:

At the end of this half course and having completed the essential reading and activities students should be able to:

• explain the principles of data reduction
• judge the quality of estimators
• choose appropriate methods of inference to tackle real problems.

Требования к поступающим:

If taken as part of a BSc degree, courses which must be passed before this half course may be attempted:

• ST104a Statistics 1 and
• ST104b Statistics 2.

Co-requisite

Students can only take ST3134 Advanced statistics: statistical inference at the same time as or after ST3133 Advanced statistics: distribution theory, not before.