Many data collected in sport science come from time dependent phenomenon. This article focuses on Functional Data Analysis (FDA), which study longitudinal data by modelling them as continuous functions. After a brief review of several FDA methods, some useful practical tools such as Functional Principal Component Analysis (FPCA) or functional clustering algorithms are presented and compared on simulated data. Finally, the problem of the detection of promising young swimmers is addressed through a curve clustering procedure on a real data set of performance progression curves. This study reveals that the fastest improvement of young swimmers generally appears before 16 years old. Moreover, several patterns of improvement are identified and the functional clustering procedure provides a useful detection tool.

A novel multi-task Gaussian process (GP) framework is proposed, by using a common mean process for sharing information across tasks. In particular, we investigate the problem of time series forecasting, with the objective to improve multiple-step-ahead predictions. The common mean process is defined as a GP for which the hyper-posterior distribution is tractable. Therefore an EM algorithm is derived for handling both hyper-parameters optimisation and hyper-posterior computation. Unlike previous approaches in the literature, the model fully accounts for uncertainty and can handle irregular grids of observations while maintaining explicit formulations, by modelling the mean process in a unified GP framework. Predictive analytical equations are provided, integrating information shared across tasks through a relevant prior mean. This approach greatly improves the predictive performances, even far from observations, and may reduce significantly the computational complexity compared to traditional multi-task GP models. Our overall algorithm is called Magma (standing for Multi tAsk GPs with common MeAn). The quality of the mean process estimation, predictive performances, and comparisons to alternatives are assessed in various simulated scenarios and on real datasets.

Objective The purpose of this study was to define a new index the Robust Exponential Decreasing Index (REDI), which is capable of an improved analysis of the cumulative workload. This allows for precise control of the decreasing influence of load over time. Additionally, REDI is robust to missing data that are frequently present in sport. Methods 200 cumulative workloads were simulated in two ways (Gaussian and uniform distributions) to test the robustness and flexibility of the REDI, as compared with classical methods (acute:chronic workload ratio and exponentially weighted moving average). Theoretical properties have been highlighted especially around the decreasing parameter. Results The REDI allows practitioners to consistently monitor load with missing data as it remains consistent even when a significant portion of the dataset is absent. Adjusting the decreasing parameter allows practitioners to choose the weight given to each daily workload. Discussion Computation of cumulative workload is not easy due to many factors (weekends, international training sessions, national selections and injuries). Several practical and theoretical drawbacks of the existing indices are discussed in the paper, especially in the context of missing data; the REDI aims to settle some of them. The decreasing parameter may be modified according to the studied sport. Further research should focus on methodology around setting this parameter. Conclusion The robust and adaptable nature of the REDI is a credible alternative for computing a cumulative workload with decreasing weight over time.

Objectives The purpose of this study was to quantify the impact of morphological characteristics on freestyle swimming performance by event and gender. Design Height, mass, body mass index (BMI) and speed data were collected for the top 100 international male and female swimmers from 50 to 1500 m freestyle events for the 2000–2014 seasons. Methods Several Bayesian hierarchical regressions were performed on race speed with height, mass and BMI as predictors. Posterior probability distributions were computed using Markov chain Monte Carlo algorithms. Results Regression results exhibited relationships between morphology and performance for both genders and all race distances. Height was always positively correlated with speed with a 95% probability. Conversely, mass plays a different role according to the context. Heavier profiles seem favourable on sprint distances, whereas mass becomes a handicap as distance increases. Male and female swimmers present several differences on the influence of morphology on speed, particularly about the mass. Best morphological profiles are associated with a gain of speed of 0.7%–3.0% for men and 1%–6% for women, depending on race distance. BMI has been investigated as a predictor of race speed but appears as weakly informative in this context. Conclusion Morphological indicators such as height and mass strongly contribute to swimming performance from sprint to distance events, and this contribution is quantified for each race distance. These profiles may help swimming federations to detect athletes and drive them to compete in specific distances according to their morphology.

Epigenetic changes in early life play an important role in the development of health conditions in children. Longitudinally measuring and forecasting changes in DNA methylation can reveal patterns of ageing and disease progression, but biosamples may not always be available. We introduce a probabilistic machine learning framework based on multi-mean Gaussian processes, accounting for individual and gene correlations across time to forecast the methylation status of an individual into the future. Predicted methylation values were used to compute future epigenetic age and compared to chronological age. We show that this method can simultaneously predict methylation status at multiple genomic sites in children (age 5-7) using methylation data from earlier ages (0-4). Less than 10% difference between observed and predicted methylation values is found in approximately 95% of methylation sites. We show that predicted methylation profiles can be used to estimate other molecular phenotypes, such as epigenetic age, at any timepoint and enable association tests with health outcomes measured at the same timepoint. Limited longitudinal profiling of DNA methylation coupled with machine learning enables forecasting of epigenetic ageing and future health outcomes. Wellcome Trust, Singapore National Research Foundation (NRF), Singapore National Medical Research Council (NMRC), Agency for Science, Technology and Research (A∗STAR), UK Academy of Medical Sciences and the UK Engineering and Physical Sciences Research Council (EPSRC).