arXiv subjects

J. E. Griffin

Publications and source records attributed to J. E. Griffin.

3 recordsLinked to original sources

arXiv2026

Modelling between- and within-season trajectories in elite athletic performance data

Athletic performance follows a typical pattern of improvement and decline during a career. This pattern is also often observed within-seasons, as an athlete aims for their performance to peak at key events such as the Olympic Games or World Championships. A Bayesian hierarchical model is developed to analyse the evolution of athletic sporting performance throughout an athlete's career and separate these effects whilst allowing for confounding factors such as environmental conditions. Our model works in continuous time and estimates both $g(t)$, the average performance level of the population at age $t$, and $f_i(t)$, the difference of the $i$-th athlete from this average. We further decompose $f_i(t)$ into a season-to-season trajectory and a within-season trajectory, which is modelled by a restricted Bernstein polynomial. The model is fitted using an adaptive Metropolis-within-Gibbs algorithm with a carefully chosen blocking scheme. The model allows us to understand seasonal patterns in athlete performance, how these differ between athletes, and provides individual fitted and trend performance trajectories. The properties of the model are illustrated using a simulation study and an application to 100 metres and 200 metres freestyle swimming for both female and male athletes.

stat.AP↗

arXiv2024

Expressing and visualizing model uncertainty in Bayesian variable selection using Cartesian credible sets

Modern regression applications can involve hundreds or thousands of variables which motivates the use of variable selection methods. Bayesian variable selection defines a posterior distribution on the possible subsets of the variables (which are usually termed models) to express uncertainty about which variables are strongly linked to the response. This can be used to provide Bayesian model averaged predictions or inference, and to understand the relative importance of different variables. However, there has been little work on meaningful representations of this uncertainty beyond first order summaries. We introduce Cartesian credible sets to address this gap. The elements of these sets are formed by concatenating sub-models defined on each block of a partition of the variables. Investigating these sub-models allow us to understand whether the models in the Cartesian credible set always/never/sometimes include a particular variable or group of variables and provide a useful summary of model uncertainty. We introduce a method to find these sets that emphasizes ease of understanding and can be easily computed from Markov chain Monte Carlo output. The potential of the method is illustrated on regression problems with both small and large numbers of variables.

stat.ME↗

arXiv2024

Fast Bayesian inference in a class of sparse linear mixed effects models

Linear mixed effects models are widely used in statistical modelling. We consider a mixed effects model with Bayesian variable selection in the random effects using spike-and-slab priors and developed a variational Bayes inference scheme that can be applied to large data sets. An EM algorithm is proposed for the model with normal errors where the posterior distribution of the variable inclusion parameters is approximated using an Occam's window approach. Placing this approach within a variational Bayes scheme also the algorithm to be extended to the model with skew-t errors. The performance of the algorithm is evaluated in a simulation study and applied to a longitudinal model for elite athlete performance in the 100 metre sprint and weightlifting.

stat.ME↗