I’m not very good at this whole self promotion thing, but I thought I might make use of this publicity tag to write a little about a few recent Stan models / papers I’ve worked on.

### Australian Rules Football

The first is a model for both match prediction and the rating of offensive and defensive abilities of Australian Rules Football teams. Dynamic (time varying) team ability models are are reasonably popular for Association Football, but the higher scoring (and fundamentally different) nature of Australian Rules means the models require some adaptation.

Manderson, A.A., Murray, K. and Turlach, B.A. (2018). Dynamic Bayesian forecasting of AFL match results using the Skellam distribution, Australian & New Zealand Journal of Statistics. Doi: 10.1111/anzs.12225

### Monotonic polynomials

We implemented a parameterisation for monotonic polynomials that my supervisor had previously considered. The Stan implementation was preferable, as it was able to fit higher degree polynomials (things get pretty correlated for sufficiently high degree polynomials, especially when the usual QR decomposition is not immediately applicable). The paper just deals with a single set of (x, y) data, but I also extended the parameterisation, in a hierarchical manner, to fit many similar sets of (x, y) here (which is in my recently submitted Masters thesis, and might make its way onto a blog post someday).

Manderson, A.A., Cripps, E., Murray, K. and Turlach, B.A. (2017). Monotone polynomials using BUGS and Stan, Australian & New Zealand Journal of Statistics 59(4): 353–370. Doi: 10.1111/anzs.12207

### Exercise-induced pulmonary haemorrhage

We also developed / implemented two models for Exercise-induced pulmonary haemorrhage (EIPH), one to address the covariates that influenced the transition of the disease from low-states to high states (Latent time inhomogeneous Markov chains for a categorical response), and a typical semi-parametric regression to address disease progression. As in all applied statistics projects, there are a few accomodations that must be made (i.e. the need for “p-values” for parameters in a Bayesian analysis) , but the major one was that the combination of semi parametric model and ordinal response was unable to be fit to real data, and generating data from the model and attempting to fit the model back to the data left me questioning if it would ever be able to be fit. The “workaround” is to pretend the response is numeric instead, but this is very unsatisfying and it would be interesting to see how much information can actually be recovered from an ordinal response.

- First model:time-inhomogenous-latent-markov.stan (1.9 KB)
- Second model: semi-par-model.stan (869 Bytes)

Crispe, E.J., Secombe, C.J., Perera, D.I., Manderson, A.A., Turlach, B.A. and Lester, G.D. (2018). Exercise-induced pulmonary haemorrhage in Thoroughbred racehorses: A longitudinal study, Equine Veterinary Journal. Doi: 10.1111/evj.12957

I’m currently building another set of Stan models for various oceanography phenomenon, some of which should hopefully appear in the future. Feel free to ask questions about any of the above models, I’d love to talk about them.