Department:Mathematics and Statistics
Level:Part II (yr 2)
Course Convenor:Dr MP Sperrin
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Prior to MATH235, the student must have successfully completed:
The student must take the following modules:
The following modules may not be taken:
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Curriculum Design: Outline Syllabusback to top
Hypothesis testing and Estimation
- Estimates and Estimators
- Paired and unpaired t-tests
- Confidence Intervals
- Least squares estimaton
- Parameter testing and confidence intervals
- Model comparison
- Model checking
- Model interpretation
- Maximum Lidelihood estimation
- Distributions of maximum likelihood estimators; Fisher information
- Confidence intervals of parameters
- Information suppression and sufficiency
Curriculum Design: Pre-requisites/Co-requisites/Exclusionsback to top
Prerequisites: MATH105 Statistics; MATH230 Probability
Educational Aims: Subject Specific: Knowledge, Understanding and Skillsback to top
At the end of the module students should be able to:
This course aims for students:
- to appreciate the importance of statistical methodology in making conclusions and decisions.
- to recognize the role, and limitations, of the linear model for understanding, exploring and making inferences concerning the relationships between variables and making predictions.
- to appreciate the central role of the likelihood function in statistical inference.
- to appreciate the role of statistics in making sense of uncertainty.
Educational Aims: General: Knowledge, Understanding and Skillsback to top
This course aims for students:
- to gain skills in problem solving and critical thinking.
- to appreciate the importance of communicating technical ideas at an appropriate level.
- to appreciate the importance of making evidence-based decisions.
Learning Outcomes: Subject Specific: Knowledge, Understanding and Skillsback to top
At the end of the course the students should be able to demonstrate subject specific knowledge, understanding and skills and have the ability to:
- Apply appropriate statistical procedures to answer simple research questions, using appropriate data.
- Explain the concept of sampling distribution
- Write down likelihood functions for simple models and calculate maximum likelihood estimators for parameters
- Fit linear regressions using the least squares method to appropriate data
- Construct confidence intervals for estimators, perform hypothesis tests, and appreciate the similarities and differences between the two approaches.
- Understand some of the asymptotic theory and properties of statistical inference methods
- Critically evaluate whether modelling assumptions are appropriate.
- Compare and contrast different models, and be able to make an informed choice about which is the most appropriate to answer a given question
- Interpret the results and conclusions implied by fitted models in real world situations.
- Use the statistical package ?R' to fit and evaluate models.
Learning Outcomes: General: Knowledge, Understanding and Skillsback to top
At the end of this course students should be able to:
- Communicate technical ideas at an appropriate level. Critically evaluate approaches taken to solve problems.
- Make conclusions and decisions based on evidence, and relate these to real world problems.
Assessment: Details of Assessmentback to top
Assessment will be through
(i) weekly coursework, aimed at testing and consolidating understanding of the basic elements of the course;
(ii) an examination in the Summer which assesses more fully the students' understanding and summative knowledge of the topics.
Curriculum Design: Select Bibliographyback to top
The following are perhaps best viewed as background reading.
Rice, John, A. (2007) Mathematical Statistics and Data Analysis, Duxbury
Diggle,Peter, J. and Chetwynd, Amanda, A. (2011) Statistics and Scientific Method: An Introduction for Students and Researchers, OUP.1
Draper, N.R. and Smith, H. (1998) Applied Regression Analysis, Wiley
Ryan, T. P. (2009) Modern Regression Methods, Wiley
Roussas, G (2003) An Introduction to Probability and Statistical Inference, Elsevier
Casella, G and Berger, R.L. (2002) Statistical Inference, 2nd Ed., Duxbury
Pawitan, Y (2001) In All Likelihood: Statistical Modelling and Inference using Likelihood