These research topics are not suitable for students who have restricted their studies to applied courses in statistics. For students with an undergraduate degree from the University of Auckland, these topics require successful completion of STATS 310 (or 732) or 730 with at least an A- or better. A good grade in STATS 331 or 731 is also a requirement for those topics with a Bayesian flavour. (A PhD student could take STATS 730 and 731 in their first year of enrolment if necessary.)
- To log, or not to log?: When the response variable takes non-negative integer values then the data can be analysed by fitting a linear model to the logged response, or a log-linear model to raw data. This project will perform simulations to determine the conditions under which each approach is preferred. [Suitable for BSc Hons project through to MSc thesis.]
- Quasi-Poisson vs Type II negative binomial?: When the response variable is a count variable with variance proportional to its mean then it is common to use quasi-Poisson modeling. A more rigourous approach is to use a Type II negative binomial, but this is a bit more computationally complex. This project will perform simulations to determine the conditions under which each approach is preferred. [Suitable for BSc Hons project through to MSc thesis.]
- Bayesian model comparison: It is essential to have sound methodology for comparison of Bayesian models. The deviance information criterion (DIC, 2002) is widely used but known to suffer several weakness. The most promising new development appears to be the widely applicable information criterion (WAIC, 2010). This research area provides opportunities for project students (in the form of simulation studies) through to PhD (involving methodological assessment/modification of existing approaches).
- Comparison of modeling software: There are several choices for the fitting of complex models to data. These include ADMB, STAN, Template Model Builder and others. This work will seek to determine the strengths and weaknesses of each, primarily through extensive simulation comparisons.