Introduction to Statistical Modelling

Describing and understanding relationships in data is important in both scientific exploration and understanding.  Building on methodology from prior studies in probability and stochastic modelling, this unit focuses on the statistical modelling of data with an emphasis on relationships and effects for purposes of statistical inference, prediction and validation.  Attention is also given to the challenges that analysing real-world datasets pose with alternative statistical techniques which yield the valid inference.  This unit provides an introduction to some of the advanced material covered in the latter parts of the Statistical Science major.

Learning Outcomes
On successful completion of this unit you should be able to:

1. Apply elementary statistical modelling techniques in an appropriate way.
2. Apply Monte Carlo based techniques for appropriate statistical inference.
3. Draw inferences using the likelihood function, resampling, simulation and Bayesian statistics.
4. Use statistical software packages such as R commander to model and analyse data.

Content
The mathematical/statistical content of this unit includes:

1. Data Structures and Measurement Types
2. Data Gathering Issues: Design, Representativeness and Bias, Accuracy and Confounding
3. Data Summarisation: Graphical and Numerical Methods, Location/Spread/Shape/Correlation
4. Introduction to Distribution Theory: Normal, Gamma, Binomial, Poisson, Negative Binomial distributions, the Central Limit Theorem and Moment Generating Functions
5. Introduction to Likelihood models
6. The Confidence Interval: Univariate intervals for means and proportions, Tolerance Intervals
7. The Hypothesis Test: Normal and t-tests for univariate means and proportions and chi-squared tests for univariate discrete distributions
8. Contingency Tables: Tests of Independence, Odds Ratios, Difference in Proportions, Chi-Squared Residual Analysis
9. ANOVA: Differences in Means, F-tests, Confidence Intervals for Contrasts, Diagnostics and Heteroskedasticity
10. Simple Linear Regression: Coefficient of Determination, Transformations, Prediction Intervals, Diagnostics and Residual Analysis, the Geometry of Regression and Projection Matrices
11. Analysis of Covariance: Sum of Squares breakdowns, Testing for Interaction
12. Simple Logistic Regression: Via weighted least-squares for grouped data, Via Likelihood and GLM approach.