## MATH2715 Statistical Methods

### 10 creditsClass Size: 240

Module manager: Sofya Titarenko / Dr Luisa Cutillo
Email: "L.Cutillo@leeds.ac.uk / S.Titarenko@leeds.ac.uk

Taught: Semester 1 (Sep to Jan) View Timetable

Year running 2022/23

### Pre-requisite qualifications

(MATH1712 or MATH2700) and (MATH1005 or MATH1010 or MATH1050), or equivalent.

### This module is mutually exclusive with

 SOEE3650 Methods in Statistics

This module is approved as a discovery module

### Module summary

Statistical models are important in many applications. They contain two main elements: a set of parameters with information of scientific interest (eg the mean of a normal distribution, or the slope in a regression model) and an "error distribution" representing random variation. This module lays the foundations for the analysis of such models.The first part deals with suitable choices for the "error" term, in particular looking carefully at methods for analyzing continuous distributions. The second part focuses on the construction of appropriate statistical models and the development of methods to gain information about the unknown parameters. The main emphasis is on the use of likelihood methods. We shall use practical examples from a variety of statistical applications to illustrate the ideas.

### Objectives

The aims of this module are to introduce mathematical techniqes for analyzing probability distributions and to develop the tools for statistical model building.

On completion of this module, students should be able to:
a) manipulate univariate and bivariate probability distributions, including moments and transformations;
b) use univariate moment generating functions to derive the classic limit theorems of probabilty;
c) understand the principles of statistical modelling, from data collection to model assessment and refinement;
d) deal with robustness problems in statistical estimation;
e) carry out elementary Bayesian statistical modelling.

### Syllabus

1. Moments and transformations for univariate probability densities.
2. Conditional and marginal distributions for bivariate distributions; bivariate normal distribution.
3. Moment generating functions; law of large numbers; central limit theorem.
4. Issues in statistical modelling: data collection; model formulation; model assessment; model diagnostics; model refinement.
5. Estimation; method of moments; maximum likelihood.
6. Hypothesis testing. Type 1 and Type 2 errors; power; likelihood ratio test.
7. Robustness; median and trimmed mean; transformations to normality.
8. Bayesian modelling; prior and posterior distributions.

### Teaching methods

 Delivery type Number Length hours Student hours Workshop 10 1.00 10.00 Lecture 22 1.00 22.00 Private study hours 68.00 Total Contact hours 32.00 Total hours (100hr per 10 credits) 100.00

### Private study

Studying and revising of course material.
Completing of assignments and assessments.

### Opportunities for Formative Feedback

Marked examples sheets

### Methods of assessment

Coursework
 Assessment type Notes % of formal assessment In-course Assessment . 20.00 Total percentage (Assessment Coursework) 20.00

There is no resit available for the coursework component of this module. If the module is failed, the coursework mark will be carried forward and added to the resit exam mark with the same weighting as listed above.

Exams
 Exam type Exam duration % of formal assessment Standard exam (closed essays, MCQs etc) 2 hr 00 mins 80.00 Total percentage (Assessment Exams) 80.00

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated