## Mathematical and Statistical Modelling

### Module aims

• To give a solid grounding in the concepts of probability and statistical modelling.
• Emphasis is placed on asking the right questions, and testing and questioning assumptions, and on using robust statistical tools that can cope with departures from the assumptions. Graphical analyses are used whenever possible, and "exploratory" data analysis is encouraged. Exercises are introduced regularly throughout the lectures to immediately reinforce the material being discussed; these are usually of a practical nature.

### Learning outcomes

On successful completing this course unit, students will be able to:

• Understand the concepts outlined in lectures.

### Module syllabus

• This course gives students an introduction to basic probability and statistics, with applications relevant to Environmental Engineering and Hydrology.
• It begins with descriptive statistics and graphical display of information. Probability theory and random variables are introduced with examples of practical applications.
• The second half of the course covers topics in statistical inference, including estimation, hypothesis testing and linear regression.
• The final topic is modelling extreme events, for instance peak river flows, using the Gumbel distribution.
 No. Topic Staff 01 Introductory examples. Data display and interpretation – Univariate measures of location, scale, asymmetry and shape; robust measures. Graphical summaries such as scatter plots, histograms, stem-and-leaf displays and box plots. tbc 02 Probability – Main rules of probability. Conditional probability. tbc 03 Probability – Bayes' theorem. Random variables. Means and variances. Distribution and density functions for common discrete distributions. Optional marked question 1. Introduction of extreme value distribution as an example. tbc 04 Random variables – Distribution and density functions for common continuous distributions. tbc 05 Estimation methods – Based around river flow data. The method of moments and maximum likelihood. tbc 06 Confidence intervals. Hypothesis testing 1. tbc 07 Hypothesis testing 2. Optional marked question 2. tbc 08 In-class hands-on session – hand written exercises and interpretation. tbc 09 Linear regression – Least-squares using mean sea level data. tbc

### Teaching methods

The course is delivered in the autumn term as nine two-hour sessions, which will include lecture, class exercises and problem-solving

### Assessments

Information will be provided separately.