This module is not currently running in 2024 to 2025.
Each year three topics will be offered and will reflect recent advances in statistical modelling and statistical methodology. Example topics are:
a) Statistical Ecology: Understanding demographic parameters and how they are used to model population dynamics. Estimating abundance and the effect of heterogeneity. Models for estimating survival probabilities. Multi-site and multi-state models. Classical model-selection. Complex models. Case studies.
b) Survival analysis: Survival data, types of censoring. Failure times and hazard functions; Accelerated failure time model. Parametric models, exponential, piecewise exponential, Weibull. Nonparametric estimates: the Kaplan-Meier estimator, and asymptotic confidence regions. Parametric inference. Survival data with covariates. Proportional hazards. Cox's model and inference. Computer software: R and WinBUGS.
c) Regression models with many variables: Examples of high-dimensional problems; Penalized maximum likelihood; Ridge regression; non-negative garrote; Lasso and adaptive Lasso estimation; LARS algorithm; Oracle property; Elastic Net; Group lasso.
d) Modern nonparametric statistics: Bias-variance trade-off, Kernel density estimation, Kernel smoothing, Locally linear and locally quadratic estimation, basis function methods.
In addition, level 7 students will study advanced applications of these techniques (often using R) in all topics.
36 hours
80% examination, 20% coursework
The reading list will depend on the topics offered; for the example topics the list is:
a) Statistical Ecology
McCrea, R. S. and Morgan, B. J. T. (2014): Analysis of capture-recapture data (Chapman & Hall / CRC)
b) Survival Analysis
Collet, D. (2003): Modelling survival data in medical research, Second Edition (Chapman & Hall / CRC)
c) Regression models with many variables
Hastie, T., Tibshirani, R. and Wainwright, M. J. (2015): Statistical Learning with Sparsity (Chapman & Hall / CRC).
d) Modern nonparametric statistics
Larry Wasserman (2006): All of Nonparametric Statistics, Springer: New York.
See the library reading list for this module (Canterbury)
The intended subject specific learning outcomes:
On successfully completing the level 7 module students will be able to:
1 demonstrate systematic understanding of some selected topics within modern statistics;
2 demonstrate the capability to solve complex problems using a very good level of skill in calculation and manipulation of the material the following areas: modern statistical modelling and statistical methods;
3 apply a range of concepts and principles in some selected topics within modern statistics in loosely defined contexts, showing good judgment in the selection and application of tools and techniques;
4 make effective and well-considered use of R
The intended generic learning outcomes:
On successfully completing the level 7 module students will be able to:
1 work competently and independently, be aware of their own strengths and understand when help is needed;
2 demonstrate a high level of capability in developing and evaluating logical arguments;
3 communicate arguments confidently with the effective and accurate conveyance of conclusions;
4 manage their time and use their organisational skills to plan and implement efficient and effective modes of working;
5 solve problems relating to qualitative and quantitative information;
6 make effective use of information technology skills such as online resources (moodle), internet communication;
7 communicate technical and non-technical material effectively;
8 demonstrate an increased level of skill in numeracy and computation;
9 demonstrate the acquisition of the study skills needed for continuing professional development.
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