Featured Application: This paper studies what models are most suitable for forecasting future values of player performance metrics in association football (soccer). The resulting forecast statistics find applications in team management and player scouting at football clubs. As transfer decisions concern whether a player should play for a club in the future, the predictions of future performance metrics offer a forward-looking improvement over the traditional backward-looking assessments. Transfers in professional football (soccer) are risky investments because of the large transfer fees and high risks involved. Although data-driven models can be used to improve transfer decisions, existing models focus on describing players’ historical progress, leaving their future performance unknown. Moreover, recent developments have called for the use of explainable models combined with methods for uncertainty quantification of predictions to improve applicability for practitioners. This paper assesses explainable machine learning models in a practitioner-oriented way for the prediction of the future development in quality and transfer value of professional football players. To this end, the methods for uncertainty quantification are studied through the literature. The predictive accuracy is studied by training the models to predict the quality and value of players one year ahead, equivalent to one season. This is carried out by training them on two data sets containing data-driven indicators describing the player quality and player value in historical settings. In this paper, the random forest model is found to be the most suitable model because it provides accurate predictions as well as an uncertainty quantification method that naturally arises from the bagging procedure of the random forest model. Additionally, this research shows that the development of player performance contains nonlinear patterns and interactions between variables, and that time series information can provide useful information for the modeling of player performance metrics. The resulting models can help football clubs make more informed, data-driven transfer decisions by forecasting player quality and transfer value.

Often the question arises whether (Formula presented.) can be predicted based on (Formula presented.) using a certain model. Especially for highly flexible models such as neural networks one may ask whether a seemingly good prediction is actually better than fitting pure noise or whether it has to be attributed to the flexibility of the model. This paper proposes a rigorous permutation test to assess whether the prediction is better than the prediction of pure noise. The test avoids any sample splitting and is based instead on generating new pairings of (Formula presented.). It introduces a new formulation of the null hypothesis and rigorous justification for the test, which distinguishes it from the previous literature. The theoretical findings are applied both to simulated data and to sensor data of tennis serves in an experimental context. The simulation study underscores how the available information affects the test. It shows that the less informative the predictors, the lower the probability of rejecting the null hypothesis of fitting pure noise and emphasizes that detecting weaker dependence between variables requires a sufficient sample size.

The past decade has seen an increased interest in human activity recognition based on sensor data. Most often, the sensor data come unannotated, creating the need for fast labelling methods. For assessing the quality of the labelling, an appropriate performance measure has to be chosen. Our main contribution is a novel post-processing method for activity recognition. It improves the accuracy of the classification methods by correcting for unrealistic short activities in the estimate. We also propose a new performance measure, the Locally Time-Shifted Measure (LTS measure), which addresses uncertainty in the times of state changes. The effectiveness of the post-processing method is evaluated, using the novel LTS measure, on the basis of a simulated dataset and a real application on sensor data from football. The simulation study is also used to discuss the choice of the parameters of the post-processing method and the LTS measure.

We study nonparametric Bayesian statistical inference for the parameters governing a pure jump process of the form (Formula Presented) where N(t) is a standard Poisson process of intensity λ, and Z _k are drawn i.i.d. from jump measure μ. A high-dimensional wavelet series prior for the Lévy measure ν = λμ is devised and the posterior distribution arises from observing discrete samples Y _Δ, Y _2Δ, …, Y _nΔ at fixed observation distance Δ, giving rise to a nonlinear inverse inference problem. We derive contraction rates in uniform norm for the posterior distribution around the true Lévy density that are optimal up to logarithmic factors over Hölder classes, as sample size n increases. We prove a functional Bernstein–von Mises theorem for the distribution functions of both μ and ν, as well as for the intensity λ, establishing the fact that the posterior distribution is approximated by an infinite-dimensional Gaussian measure whose covariance structure is shown to attain the information lower bound for this inverse problem. As a consequence posterior based inferences, such as nonparametric credible sets, are asymptotically valid and optimal from a frequentist point of view.

A method is proposed for calculating the shear viscosity of a liquid from finite-size effects of self-diffusion coefficients in Molecular Dynamics simulations. This method uses the difference in the self-diffusivities, computed from at least two system sizes, and an analytic equation to calculate the shear viscosity. To enable the efficient use of this method, a set of guidelines is developed. The most efficient number of system sizes is two and the large system is at least four times the small system. The number of independent simulations for each system size should be assigned in such a way that 50%-70% of the total available computational resources are allocated to the large system. We verified the method for 250 binary and 26 ternary Lennard-Jones systems, pure water, and an ionic liquid ([Bmim][Tf2N]). The computed shear viscosities are in good agreement with viscosities obtained from equilibrium Molecular Dynamics simulations for all liquid systems far from the critical point. Our results indicate that the proposed method is suitable for multicomponent mixtures and highly viscous liquids. This may enable the systematic screening of the viscosities of ionic liquids and deep eutectic solvents.

As a starting point we prove a functional central limit theorem for estimators of the invariant measure of a geometrically ergodic Harris-recurrent Markov chain in a multi-scale space. This allows to construct confidence bands for the invariant density with optimal (up to undersmoothing) L^∞-diameter by using wavelet projection estimators. In addition our setting applies to the drift estimation of diffusions observed discretely with fixed observation distance. We prove a functional central limit theorem for estimators of the drift function and finally construct adaptive confidence bands for the drift by using a completely data-driven estimator.

We consider the Grenander estimator that is the maximum likelihood estimator for non-increasing densities. We prove uniform central limit theorems for certain subclasses of bounded variation functions and for Hölder balls of smoothness s >1/2. We do not assume that the density is differentiable or continuous. The proof can be seen as an adaptation of the method for the parametric maximum likelihood estimator to the nonparametric setting. Since nonparametric maximum likelihood estimators lie on the boundary, the derivative of the likelihood cannot be expected to equal zero as in the parametric case. Nevertheless, our proofs rely on the fact that the derivative of the likelihood can be shown to be small at the maximum likelihood estimator.

We estimate linear functionals in the classical deconvolution problem by kernel estimators. We obtain a uniform central limit theorem with √n-rate on the assumption that the smoothness of the functionals is larger than the ill-posedness of the problem, which is given by the polynomial decay rate of the characteristic function of the error. The limit distribution is a generalized Brownian bridge with a covariance structure that depends on the characteristic function of the error and on the functionals. The proposed estimators are optimal in the sense of semiparametric efficiency. The class of linear functionals is wide enough to incorporate the estimation of distribution functions. The proofs are based on smoothed empirical processes and mapping properties of the deconvolution operator.