MAS294 Statistical Reasoning (NJTech)

Note: Information for future academic years is provisional. Timetable information and teaching staff are especially likely to change, but other details may also be altered, some courses may not run at all, and other courses may be added.

 Semester 1, 2017/18 10 Credits Lecturer: Dr Miguel Juarez Reading List Aims Outcomes Assessment Full Syllabus

Statistics is about learning from data - often uncertain and variable - about underlying regularities of the real world. At first sight the methods for statistical analysis can appear particular to each application. This unit however shows that they can be founded on simple universal principles of statistical reasoning. There are two principal forms of statistical reasoning, known as frequentist and Bayesian inference These principles simplify understanding and give powerful tools for analysing new problems. They form the basis for more specialist modules in Level 3/Level 4. The course will show how practical analyses follow from the principles, and will illustrate their power through a set of case studies of real-world problems from areas such as medicine, economics, technology and the environment.

There are no prerequisites for this module.
No other modules have this module as a prerequisite.

Aims

• To formulate the process of inference in terms of parametric models.
• To introduce both frequentist and Bayesian inferential frameworks.
• To illustrate the scope of the principles with practical applications.

Learning outcomes

• Understand the aims of statistical inference and the importance of likelihood as a tool that underlies the principal theories of inference.
• Find maximum likelihood estimates and likelihood intervals and regions for simple models.
• Understand the principles of frequentist inference.
• Apply those principles to construct point estimates, confidence intervals and significance tests.
• Combine prior information and observed data into a posterior distribution for a parameter.
• Use the posterior distribution to make summary statements and formal inference about parameters.
• Appreciate the differences between the likelihood, Bayesian and frequentist theories of inference.

32 lectures, 32 tutorials

Assessment

One formal 2 hour written examination. All questions compulsory.

Full syllabus

• Inference and reasoning: the nature of statistical reasoning, inference and the likelihood function.
• Case studies drawn from areas such as medicine, business, science, technology and the environment: will be introduced early in the module and used throughout to illustrate the applicability and power of the methods.
• Likelihood: definition, examples, numerical calculation; maximum likelihood estimates and likelihood intervals.
• Frequentist methods: inference rules, point estimation, interval estimation and hypothesis testing; unbiasedness, mean square error and minimum variance unbiased estimators; confidence intervals; null and alternative hypotheses, power and significance tests.
• Bayesian methods: parameters as values of random variables, combination of prior information and observed data to yield a posterior distribution for a parameter, nature of prior information, use of posterior distribution to make summary statements an formal inferences about parameters.