The baseball pitch is a repetitive, full-body throwing motion that exposes the elbow to significant loads, leading to a high incidence of elbow injuries. Elbow injuries in pitching are often attributed to high external valgus torques as these are generally considered to be a good proxy for the load on the Ulnar Collateral Ligament. The aim of the study is to contribute to elbow load monitoring by developing a prediction model based on the pelvis and trunk peak angular velocities and their separation time. Eleven male youth elite baseball pitchers (age 17 ± 2.2 years) threw 25 fastballs at full effort off a mound. Two-level varying-intercept, varying-slope Bayesian models were used to predict external valgus torque based on (inter)segmental rotation in fastball pitching with pitcher’s weight and height added to strengthen the individualisation of the prediction. The results revealed the high predictive performance of the models including a set of kinematic parameters trunk peak angular velocity and the separation time between the pelvis and trunk peak angular velocities. Such an approach allows individualised prediction of the external valgus torque for each pitcher, which has a great practical advantage compared to group-based predictions in terms of injury assessment and injury prevention.

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We construct a new class of efficient Monte Carlo methods based on continuous-time piecewise deterministic Markov processes (PDMPs) suitable for inference in high dimensional sparse models, i.e. models for which there is prior knowledge that many coordinates are likely to be exactly 0. This is achieved with the fairly simple idea of endowing existing PDMP samplers with “sticky” coordinate axes, coordinate planes etc. Upon hitting those subspaces, an event is triggered during which the process sticks to the subspace, this way spending some time in a sub-model. This results in non-reversible jumps between different (sub-)models. While we show that PDMP samplers in general can be made sticky, we mainly focus on the Zig-Zag sampler. Compared to the Gibbs sampler for variable selection, we heuristically derive favourable dependence of the Sticky Zig-Zag sampler on dimension and data size. The computational efficiency of the Sticky Zig-Zag sampler is further established through numerical experiments where both the sample size and the dimension of the parameter space are large.

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Coastal climate impact studies make increasing use of multi-source and multi-dimensional atmospheric and environmental datasets to investigate relationships between climate signals and the ecological response. The large quantity of numerically simulated data may, however, include redundancy, multi-colinearity and excess information not relevant to the studied processes. In such cases techniques for feature extraction and identification of latent processes prove useful. Using dimensionality reduction techniques this research provides a statistical underpinning of variable selection to study the impacts of atmospheric processes on coastal chlorophyll-a concentrations, taking the Dutch Wadden Sea as case study. Dimension reduction techniques are applied to environmental data simulated by the Delft3D coastal water quality model, the HIRLAM numerical weather prediction model and the Euro-CORDEX climate modelling experiment. The dimension reduction techniques were selected for their ability to incorporate (1) spatial correlation via multi-way methods (2), temporal correlation through Dynamic Factor Analysis, and (3) functional variability using Functional Data Analysis. The data reduction potential and explanatory value of these methods are showcased and important atmospheric variables affecting the chlorophyll-a concentration are identified. Our results indicate room for dimensionality reduction in the atmospheric variables (2 principle components can explain the majority of variance instead of 7 variables), in the chlorophyll-a time series at different locations (two characteristic patterns can describe the 10 locations), and in the climate projection scenarios of solar radiation and air temperature variables (a single principle component function explains 77% of the variation for solar radiation and 57% of the variation for air temperature). It was also found that solar radiation followed by air temperature are the most important atmospheric variables related to coastal chlorophyll-a concentration, noting that regional differences exist, for instance the importance of air temperature is greater in the Eastern Dutch Wadden Sea at Dantziggat than in the Western Dutch Wadden Sea at Marsdiep Noord. Common trends and different regional system characteristics have also been identified through dynamic factor analysis between the deeper channels and the shallower intertidal zones, where the onset of spring blooms occurs earlier. The functional analysis of climate data showed clusters of atmospheric variables with similar functional features. Moreover, functional components of Euro-CORDEX climate scenarios have been identified for radiation and temperature variables, which provide information on the dominant mode (pattern) of variation and its uncertainties. The findings suggest that radiation and temperature projections of different Euro-CORDEX scenarios share similar characteristics and mainly differ in their amplitudes and seasonal patterns, offering opportunities to construct statistical models that do not assume independence between climate scenarios but instead borrow information (“borrow strength”) from the larger pool of climate scenarios. The presented results were used in follow up studies to construct a Bayesian stochastic generator to complement existing Euro-CORDEX climate change scenarios and to quantify climate change induced trends and uncertainties in phytoplankton spring bloom dynamics in the Dutch Wadden Sea.@en

Stochastically evolving geometric systems are studied in shape analysis and computational anatomy for modeling random evolutions of human organ shapes. The notion of geodesic paths between shapes is central to shape analysis and has a natural generalization as diffusion bridges in a stochastic setting. Simulation of such bridges is key to solving inference and registration problems in shape analysis. We demonstrate how to apply state-of-the-art diffusion bridge simulation methods to recently introduced stochastic shape deformation models, thereby substantially expanding the appli-cability of such models. We exemplify these methods by estimating template shapes from observed shape configurations while simultaneously learning model parameters.

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In this work, we study the problem of learning the volatility under market microstructure noise. Specifically, we consider noisy discrete time observations from a stochastic differential equation and develop a novel computational method to learn the diffusion coefficient of the equation. We take a nonparametric Bayesian approach, where we a priori model the volatility function as piecewise constant. Its prior is specified via the inverse Gamma Markov chain. Sampling from the posterior is accomplished by incorporating the Forward Filtering Backward Simulation algorithm in the Gibbs sampler. Good performance of the method is demonstrated on two representative synthetic data examples. We also apply the method on a EUR/USD exchange rate dataset. Finally we present a limit result on the prior distribution.

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A continuous-time Markov process X can be conditioned to be in a given state at a fixed time T>0 using Doob's h-transform. This transform requires the typically intractable transition density of X. The effect of the h-transform can be described as introducing a guiding force on the process. Replacing this force with an approximation defines the wider class of guided processes. For certain approximations the law of a guided process approximates–and is equivalent to–the actual conditional distribution, with tractable likelihood-ratio. The main contribution of this paper is to prove that the principle of a guided process, introduced in [M. Schauer, F. van der Meulen, and H. van Zanten, Guided proposals for simulating multi-dimensional diffusion bridges, Bernoulli 23 (2017a), pp. 2917–2950. doi:10.3150/16-BEJ833] for stochastic differential equations, can be extended to a more general class of Markov processes. In particular we apply the guiding technique to jump processes in discrete state spaces. The Markov process perspective enables us to improve upon existing results for hypo-elliptic diffusions.

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In order to obtain valuable information from an Hull Structure Monitoring system, a large data set and consistent analysis of that data is required. The monitoring requires significant efforts over multiple years and as a result, uncertainties obtained from in-service measurements are rarely published. Instead, researchers have to rely on numerical simulations and conjecture to quantify certain parameters. In this article, two years of continuous monitoring data is used to quantify several sources of uncertainties of the hull structure of an FPSO. These sources include uncertainty related to the future extrapolation of loads and statistical uncertainty of the long-term sea states which is quantified using a Bayesian re-sampling scheme. Next, the uncertainty introduced through the use of analytical load distribution models is addressed. Finally, the uncertainty in the calculation method is quantified. These data are then used in a case study for the particular FPSO which has been monitored to demonstrate their practical application using a simple reliability model. Multiple stochastic models for the long-term description of loads are examined. Besides the traditional Weibull model, the less frequently used Pareto, Lognormal and Gumbel model were tested and compared against an uncertainty modal based on a spectral fatigue assessment. The Pareto and Weibull models are considered appropriate models and were compared against design stage analyses. Good design procedures adopt conservative parameters to describe the uncertainties. In the presented example, this was found to be true and therefore the inclusion of measurement data in Risk Based Inspection analysis for the presented case results in prolongation of the inspection interval.

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We consider the current status continuous mark model where, if an event takes place before an inspection time T a “continuous mark” variable is observed as well. A Bayesian nonparametric method is introduced for estimating the distribution function of the joint distribution of the event time (X) and mark variable (Y). We consider two histogram-type priors on the density of (Formula presented.). Our main result shows that under appropriate conditions, the posterior distribution function contracts pointwisely at rate (Formula presented.) if the true density is (Formula presented.) -Hölder continuous. In addition to our theoretical results we provide efficient computational methods for drawing from the posterior relying on a noncentered parameterization and Crank–Nicolson updates. The performance of the proposed methods is illustrated in several numerical experiments.

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We introduce the use of the Zig-Zag sampler to the problem of sampling conditional diffusion processes (diffusion bridges). The Zig-Zag sampler is a rejection-free sampling scheme based on a non-reversible continuous piecewise deterministic Markov process. Similar to the Lévy–Ciesielski construction of a Brownian motion, we expand the diffusion path in a truncated Faber–Schauder basis. The coefficients within the basis are sampled using a Zig-Zag sampler. A key innovation is the use of the fully local algorithm for the Zig-Zag sampler that allows to exploit the sparsity structure implied by the dependency graph of the coefficients and by the subsampling technique to reduce the complexity of the algorithm. We illustrate the performance of the proposed methods in a number of examples.

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Suppose X is a multivariate diffusion process that is observed discretely in time. At each observation time, a transformation of the state of the process is observed with noise. The smoothing problem consists of recovering the path of the process, consistent with the observations. We derive a novel Markov Chain Monte Carlo algorithm to sample from the exact smoothing distribution. The resulting algorithm is called the Backward Filtering Forward Guiding (BFFG) algorithm. We extend the algorithm to include parameter estimation. The proposed method relies on guided proposals introduced in [53]. We illustrate its efficiency in a number of challenging problems.

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Ball velocity is considered an important performance measure in baseball pitching. Proper pitching mechanics play an important role in both maximising ball velocity and injury-free participation of baseball pitchers. However, an individual pitcher’s characteristics display individuality and may contribute to velocity imparted to the ball. The aim of this study is to predict ball velocity in baseball pitching, such that prediction is tailored to the individual pitcher, and to investigate the added value of the individuality to predictive performance. Twenty-five youth baseball pitchers, members of a national youth baseball team and six baseball academies in The Netherlands, performed ten baseball pitches with maximal effort. The angular velocity of pelvis and trunk were measured with IMU sensors placed on pelvis and sternum, while the ball velocity was measured with a radar gun. We develop three Bayesian regression models with different predictors which were subsequently evaluated based on predictive performance. We found that pitcher’s height adds value to ball velocity prediction based on body segment rotation. The developed method provides a feasible and affordable method for ball velocity prediction in baseball pitching@en

Spring phytoplankton blooms in the southern North Sea substantially contribute to annual primary production and largely influence food web dynamics. Studying long-term changes in spring bloom dynamics is therefore crucial for understanding future climate responses and predicting implications on the marine ecosystem. This paper aims to study long term changes in spring bloom dynamics in the Dutch coastal waters, using historical coastal in-situ data and satellite observations as well as projected future solar radiation and air temperature trajectories from regional climate models as driving forces covering the twenty-first century. The main objective is to derive long-term trends and quantify climate induced uncertainties in future coastal phytoplankton phenology. The three main methodological steps to achieve this goal include (1) developing a data fusion model to interlace coastal in-situ measurements and satellite chlorophyll-a observations into a single multi-decadal signal; (2) applying a Bayesian structural time series model to produce long-term projections of chlorophyll-a concentrations over the twenty-first century; and (3) developing a feature extraction method to derive the cardinal dates (beginning, peak, end) of the spring bloom to track the historical and the projected changes in its dynamics. The data fusion model produced an enhanced chlorophyll-a time series with improved accuracy by correcting the satellite observed signal with in-situ observations. The applied structural time series model proved to have sufficient goodness-of-fit to produce long term chlorophyll-a projections, and the feature extraction method was found to be robust in detecting cardinal dates when spring blooms were present. The main research findings indicate that at the study site location the spring bloom characteristics are impacted by the changing climatic conditions. Our results suggest that toward the end of the twenty-first century spring blooms will steadily shift earlier, resulting in longer spring bloom duration. Spring bloom magnitudes are also projected to increase with a 0.4% year⁻¹ trend. Based on the ensemble simulation the largest uncertainty lies in the timing of the spring bloom beginning and-end timing, while the peak timing has less variation. Further studies would be required to link the findings of this paper and ecosystem behavior to better understand possible consequences to the ecosystem.

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Assume we observe a finite number of inspection times together with information on whether a specific event has occurred before each of these times. Suppose replicated measurements are available on multiple event times. The set of inspection times, including the number of inspections, may be different for each event. This is known as mixed case interval censored data. We consider Bayesian estimation of the distribution function of the event time while assuming it is concave. We provide sufficient conditions on the prior such that the resulting procedure is consistent from the Bayesian point of view. We also provide computational methods for drawing from the posterior and illustrate the performance of the Bayesian method in both a simulation study and two real datasets.

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Suppose X₁, …, X_n is a random sample from a bounded and decreasing density f₀ on [0, ∞). We are interested in estimating such f₀, with special interest in f₀ (0). This problem is encountered in various statistical applications and has gained quite some attention in the statistical literature. It is well known that the maximum likelihood estimator is inconsistent at zero. This has led several authors to propose alternative estimators which are consistent. As any decreasing density can be represented as a scale mixture of uniform densities, a Bayesian estimator is obtained by endowing the mixture distribution with the Dirichlet process prior. Assuming this prior, we derive contraction rates of the posterior density at zero by carefully revising arguments presented in Salomond (Electronic Journal of Statistics 8 (2014) 1380– 1404). Several choices of base measure are numerically evaluated and compared. In a simulation various frequentist methods and a Bayesian estimator are compared. Finally, the Bayesian procedure is applied to current durations data described in Slama et al. (Human Reproduction 27 (2012) 1489–1498).

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We consider a nonparametric Bayesian approach to estimate the diffusion coefficient of a stochastic differential equation given discrete time observations over a fixed time interval. As a prior on the diffusion coefficient, we employ a histogram-type prior with piecewise constant realisations on bins forming a partition of the time interval. Specifically, these constants are realizations of independent inverse Gamma distributed randoma variables. We justify our approach by deriving the rate at which the corresponding posterior distribution asymptotically concentrates around the data-generating diffusion coefficient. This posterior contraction rate turns out to be optimal for estimation of a Hölder-continuous diffusion coefficient with smoothness parameter 0<λ≤1. Our approach is straightforward to implement, as the posterior distributions turn out to be inverse Gamma again, and leads to good practical results in a wide range of simulation examples. Finally, we apply our method on exchange rate data sets.@en

In 1990, livestock grazing was introduced in Meijendel, a 1800 ha lime-rich coastal dune area, at a density of 0.06–0.07 LLU^.ha^-1.year⁻¹ (1:12–18 ha) to counteract encroachment of tall grasses and shrubland on dune grassland and increase the bare sand area. Monitoring was based on four digital orthophotos (1975–1990–2001-2009) with a high spatial resolution (pixel size 25 × 25 cm). The changes were tested using Generalized Estimating Equations. Habitat changes occurred, but contradicting our hypothesis, there was no significant impact from the grazing on bare sand, grassland or shrubland within 11 and 19 years post livestock introduction. (1) After several decennia of decreasing bare sand, there was a significant increase between 2001 and 2009, irrespective of livestock presence. (2) The changes in grasslands and shrublands are independent of the livestock, but dependent on distance to the coast. (3) Bare sand and shrub cover determine the space left for the dune grasslands. It appears other factors than livestock grazing must have induced the changes. Changes in climate conditions and nitrogen load might have stimulated bare sand. An interaction with the end of Marram planting in 1990 cannot be concluded from available data. The disease-led reduction of rabbit grazing from the mid-1950s led to an expansion of the dominant shrub Hippophae rhamnoides. However, Hippophae shrubland typically regresses to grasslands on its collapse after 25–40 years. Tree species like Crataegus, Betula and Quercus will gradually dominate the landscape for far longer. Active removal of these indigenous species is necessary to prevent future loss of dune grasslands.

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According to both domain expert knowledge and empirical evidence, wavelet coefficients of real signals tend to exhibit clustering patterns, in that they contain connected regions of coefficients of similar magnitude (large or small). A wavelet de-noising approach that takes into account such a feature of the signal may in practice outperform other, more vanilla methods, both in terms of the estimation error and visual appearance of the estimates. Motivated by this observation, we present a Bayesian approach to wavelet de-noising, where dependencies between neighbouring wavelet coefficients are a priori modelled via a Markov chain-based prior, that we term the caravan prior. Posterior computations in our method are performed via the Gibbs sampler. Using representative synthetic and real data examples, we conduct a detailed comparison of our approach with a benchmark empirical Bayes de-noising method (due to Johnstone and Silverman). We show that the caravan prior fares well and is therefore a useful addition to the wavelet de-noising toolbox.@en

Suppose X is a multidimensional diffusion process. Assume that at time zero the state of X is fully observed, but at time 0$ ]]> only linear combinations of its components are observed. That is, one only observes the vector for a given matrix L. In this paper we show how samples from the conditioned process can be generated. The main contribution of this paper is to prove that guided proposals, introduced in [35], can be used in a unified way for both uniformly elliptic and hypo-elliptic diffusions, even when L is not the identity matrix. This is illustrated by excellent performance in two challenging cases: a partially observed twice-integrated diffusion with multiple wells and the partially observed FitzHugh-Nagumo model.

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Available climate change projections, which can be used for quantifying future changes in marine and coastal ecosystems, usually consist of a few scenarios. Studies addressing ecological impacts of climate change often make use of a low- (RCP2.6), moderate- (RCP4.5) or high climate scenario (RCP8.5), without taking into account further uncertainties in these scenarios. In this research a methodology is proposed to generate further synthetic scenarios, based on existing datasets, for a better representation of climate change induced uncertainties. The methodology builds on Regional Climate Model scenarios provided by the EURO-CORDEX experiment. In order to generate new realizations of climate variables, such as radiation or temperature, a hierarchical Bayesian model is developed. In addition, a parameterized time series model is introduced, which includes a linear trend component, a seasonal shape with varying amplitude and time shift, and an additive residual term. The seasonal shape is derived with the non-parametric locally weighted scatterplot smoothing, and the residual term includes the smoothed variance of residuals and independent and identically distributed noise. The distributions of the time series model parameters are estimated through Bayesian parameter inference with Markov chain Monte Carlo sampling (Gibbs sampler). By sampling from the predictive distribution numerous new statistically representative synthetic scenarios can be generated including uncertainty estimates. As a demonstration case, utilizing these generated synthetic scenarios and a physically based ecological model (Delft3D-WAQ) that relates climate variables to ecosystem variables, a probabilistic simulation is conducted to further propagate the climate change induced uncertainties to marine and coastal ecosystem indicators.

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Suppose that a compound Poisson process is observed discretely in time and assume that its jump distribution is supported on the set of natural numbers. In this paper we propose a nonparametric Bayesian approach to estimate the intensity of the underlying Poisson process and the distribution of the jumps. We provide a Markov chain Monte Carlo scheme for obtaining samples from the posterior. We apply our method on both simulated and real data examples, and compare its performance with the frequentist plug-in estimator proposed by Buchmann and Grübel. On a theoretical side, we study the posterior from the frequentist point of view and prove that as the sample size n→∞, it contracts around the “true,” data-generating parameters at rate 1/√n, up to a n factor.

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