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The module covers methods of disclosure control for tabular data and microdata, and how the utility of the resulting data is traded off against the risk of disclosure.

Functions of one and several random variables are considered such as sums, differences, products and ratios. The central limit theorem is proved and the probability density functions are derived of those sampling distributions linked to the normal distribution. Bivariate and multivariate distributions are considered, and distributions of maximum and minimum observations are derived.

This module is a pre-requisite for all subsequent statistics modules, and desirable for Actuarial Mathematics I and II and Simulation and Queues

Functions of one and several random variables are considered such as sums, differences, products and ratios. The central limit theorem is proved and the probability density functions are derived of those sampling distributions linked to the normal distribution. Bivariate and multivariate distributions are considered, and distributions of maximum and minimum observations are derived.

This module is a pre-requisite for all subsequent statistics modules, and desirable for Actuarial Mathematics I and II and Simulation and Queues

Functions of one and several random variables are considered such as sums, differences, products and ratios. The central limit theorem is proved and the probability density functions are derived of those sampling distributions linked to the normal distribution. Bivariate and multivariate distributions are considered, and distributions of maximum and minimum observations are derived.

This module is a pre-requisite for all subsequent statistics modules, and desirable for Actuarial Mathematics I and II and Simulation and Queues

Statistical genetics has played a pivotal role in the discovery of genes that cause disease in humans. This module introduces the basic concepts and terms in genetics and demonstrates the use of statistical models to identify disease genes in humans.

Statistical genetics has played a pivotal role in the discovery of genes that cause disease in humans. This module introduces the basic concepts and terms in genetics and demonstrates the use of statistical models to identify disease genes in humans.

Statistical genetics has played a pivotal role in the discovery of genes that cause disease in humans. This module introduces the basic concepts and terms in genetics and demonstrates the use of statistical models to identify disease genes in humans.

This module develops some mathematical foundations of statistical inference: the theory of learning from data under uncertainty. We begin by studying a selection of useful tools and techniques from probability theory, including moment generating functions and transformations of random variables. Then we proceed to explore fundamental methods for point estimation, interval estimation and hypothesis testing, with a particular emphasis on maximum likelihood theory. We also introduce the framework of Bayesian inference and discuss the frequentist and subjective interpretations of probability.

This module develops some mathematical foundations of statistical inference: the theory of learning from data under uncertainty. We begin by studying a selection of useful tools and techniques from probability theory, including moment generating functions and transformations of random variables. Then we proceed to explore fundamental methods for point estimation, interval estimation and hypothesis testing, with a particular emphasis on maximum likelihood theory. We also introduce the framework of Bayesian inference and discuss the frequentist and subjective interpretations of probability.

Statistical inference involves using data from a sample to draw conclusions about a wider population. Given a partly specified statistical model, in which at least one parameter is unknown, and some observations for which the model is valid, it is possible to draw inferences about the unknown parameters and hence about the population from which the sample is drawn. As such, inference
underpins all aspects of statistics. However, inference can take different forms. It may be adequate to provide a point estimate of a parameter, i.e. a single number. More usually, an interval is required, giving a measure of precision. It may also be necessary to test a pre-specified hypothesis about the parameter(s). These forms of inference can all be considered as special cases of the use of a decision function.

There are a number of different philosophies about how these inferences should be drawn, ranging from that which says the sample contains all the information available about a parameter (likelihood), through that which says account should be taken of what would happen in repeated sampling (frequentist), to that which allows the sample to modify prior beliefs about a parameter’s value (Bayesian).

This Module aims to explore these approaches to parametric statistical inference, particularly through application of the methods to numerous examples.