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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.

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.

Statistical learning and data science provide us with new forms of data and powerful new analysis tools. Advances in AI have allowed huge improvements in our ability to predict, but at the same time, these methods and data sources generate important ethical issues that we must consider. This module will provide students with the tools to appreciate the power of AI but also its limitations, and to be able to understand which AI tools might be suitable for particular tasks.

Statistical learning and data science provide us with new forms of data and powerful new analysis tools. Advances in AI have allowed huge improvements in our ability to predict, but at the same time, these methods and data sources generate important ethical issues that we must consider. This module will provide students with the tools to appreciate the power of AI but also its limitations, and to be able to understand which AI tools might be suitable for particular tasks.

Statistical mechanics links the microscopic properties of physical systems to their macroscopic properties. Thermodynamics, which describes macroscopic properties, can then be derived from statistical mechanics with a few well motivated postulates. It leads to a microscopic interpretation of thermodynamic concepts, such as thermal equilibrium, temperature and entropy. In the course the basic principles of statistical mechanics will be introduced with applications to the physics of matter.

Statistical mechanics links the microscopic properties of physical systems to their macroscopic properties. Thermodynamics, which describes macroscopic properties, can then be derived from statistical mechanics with a few well motivated postulates. It leads to a microscopic interpretation of thermodynamic concepts, such as thermal equilibrium, temperature and entropy. In the course the basic principles of statistical mechanics will be introduced with applications to the physics of matter.