MMath Mathematics and Statistics

This course unit aims to introduce some important statistical concepts and methodology, and to provide students with experience in the use of the statistical system R in applying them to data. Skills in report writing are also to be developed. 

 

MATH20811 Pre-Requisites: MATH11711 and MATH11712

This course unit aims to introduce some important statistical concepts and methodology and to provide the students with experience in the use of the statistical system R in applying them to data.  Skills in report writing are to be developed.

On completion of this unit students will be able to:

• use the statistical software R to explore and interpret data using graphical presentations, data summaries, confidence intervals and test statistics 
• estimate the sample correlation coefficient from a sample of bivariate data and make inferences about the true population value 
• make inferences about the characteristics of an underlying bivariate distribution when the data is categorical 
• apply appropriate goodness-of-fit tests to assess distributional assumptions about sample data 
• use R to conduct simple Monte Carlo experiments to estimate parameter values and the sampling distribution of their estimators 
• Communicate informatively and discursively the results of computations arising from data analysis.

Exploratory data analysis (2 weeks) Data collection and presentation, organisation of data analysis in R. 

Correlation (2 weeks) Pearson’s sample correlation coefficient: numerical properties and interpretation, estimation of population correlation and hypothesis tests for correlation; Spearman’s rank correlation: estimation, interpretation, hypothesis testing. 

Discrete data analysis (2 weeks) Discrete data: univariate probability models, Chi-squared goodness-of-fit test for univariate data; Bivariate discrete data and probability models; testing independence; testing the homogeneity hypothesis. 

Assessing Goodness-of-Fit (3 weeks) The cumulative distribution function (cdf); distribution quantiles; sample order statistics and their properties; the probability integral transformation; the empirical cdf; empirical quantile function; quantile-quantile plots; Kolmogorov-Smirnov goodness-of-fit test. 

Monte Carlo Sampling (2 week) Basic Monte Carlo integration, importance sampling, rejection sampling. 

A blended teaching approach will be used, with pre-recorded videos released ahead of the review class for students to watch. R demonstration will feature heavily throughout the course, in both review sessions and computer classes. 

100% coursework based on three take-home projects worth 30%, 30% and then 40%.

 

Feedback tutorials will provide an opportunity for students' work to be discussed and provide feedback on their understanding.  Coursework or in-class tests (where applicable) also provide an opportunity for students to receive feedback.  Students can also get feedback on their understanding directly from the lecturers, for example during the lecturers’ office hours.