Consider an opaque medium that contains 3D particles. All particles are convex bodies of the same shape, but they vary in size. The particles are randomly positioned and oriented within the medium and cannot be observed directly. Taking a planar section of the medium we obtain a sample of observed 2D section profile areas of the intersected particles. In this paper, the distribution of interest is the underlying 3D particle size distribution for which an identifiability result is obtained. Moreover, a non-parametric estimator is proposed for this size distribution. The estimator is proven to be consistent and its performance is assessed in a simulation study.

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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.

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Background and Objectives Early neuroprognostication in children with reduced consciousness after cardiac arrest (CA) is a major clinical challenge. EEG is frequently used for neuroprognostication in adults, but has not been sufficiently validated for this indication in children. Using machine learning techniques, we studied the predictive value of quantitative EEG (qEEG) features for survival 12 months after CA, based on EEG recordings obtained 24 hours after CA in children. The results were confirmed through visual analysis of EEG background patterns. Methods This is a retrospective single-center study including children (0–17 years) with CA, who were subsequently admitted to the pediatric intensive care unit (PICU) of a tertiary care hospital between 2012 and 2021 after return of circulation (ROC) and were monitored using EEG at 24 hours after ROC. Signal features were extracted from a 30-minute EEG segment 24 hours after CA and used to train a random forest model. The background pattern from the same EEG fragment was visually classified. The primary outcome was survival or death 12 months after CA. Analysis of the prognostic accuracy of the model included calculation of receiver-operating characteristic and predictive values. Feature contribution to the model was analyzed using Shapley values. Results Eighty-six children were included (in-hospital CA 27%, out-of-hospital CA 73%). The median age at CA was 2.6 years; 53 (62%) were male. Mortality at 12 months was 56%; main causes of death on the PICU were withdrawal of life-sustaining therapies because of poor neurologic prognosis (52%) and brain death (31%). The random forest model was able to predict death at 12 months with an accuracy of 0.77 and positive predictive value of 1.0. Continuity and amplitude of the EEG signal were the signal parameters most contributing to the model classification. Visual analysis showed that no patients with a background pattern other than continuous with amplitudes exceeding 20 μV were alive after 12 months. Discussion Both qEEG and visual EEG background classification for registrations obtained 24 hours after ROC form a strong predictor of nonsurvival 12 months after CA in children.

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The prediction of remaining useful life (RUL) is a critical component of prognostic and health management for industrial systems. In recent decades, there has been a surge of interest in RUL prediction based on degradation data of a well-defined degradation index (DI). However, in many real-world applications, the DI may not be readily available and must be constructed from complex source data, rendering many existing methods inapplicable. Motivated by multivariate sensor data from industrial induction motors, this paper proposes a novel prognostic framework that develops a nonlinear DI, serving as an ensemble of representative features, and employs a similarity-based method for RUL prediction. The proposed framework enables online prediction of RUL by dynamically updating information from the in-service unit. Simulation studies and a case study on three-phase industrial induction motors demonstrate that the proposed framework can effectively extract reliability information from various channels and predict RUL with high accuracy.@en

We construct bootstrap confidence intervals for a monotone regression function. It has been shown that the ordinary nonparametric bootstrap, based on the nonparametric least squares estimator (LSE) (Formula presented.), is inconsistent in this situation. We show that an (Formula presented.) -consistent bootstrap can be based on the smoothed (Formula presented.), to be called the SLSE (Smoothed Least Squares Estimator). The asymptotic pointwise distribution of the SLSE is derived. The confidence intervals, based on the smoothed bootstrap, are compared to intervals based on the (not necessarily monotone) Nadaraya Watson estimator and the effect of Studentization is investigated. We also give a method for automatic bandwidth choice, correcting work in Sen and Xu (2015). Analogous methods for constructing confidence intervals in the current status model are discussed, improving on work in Groeneboom and Hendrickx (2018).

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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.

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In various stereological problems ann-dimensional convex body is intersected with an(n−1)-dimensionalIsotropic Uniformly Random (IUR) hyperplane. In this paper the cumulative distribution function associatedwith the(n−1)-dimensional volume of such a random section is studied. This distribution is also knownas chord length distribution and cross section area distribution in the planar and spatial case respectively.For various classes of convex bodies it is shown that these distribution functions are absolutely continuouswith respect to Lebesgue measure. A Monte Carlo simulation scheme is proposed for approximating thecorresponding probability density functions.@en

This study proposes a new approach to determine phenomenological or physical relations between microstructure features and the mechanical behavior of metals bridging advanced statistics and materials science in a study of the effect of hard precipitates on the hardening of metal alloys. Synthetic microstructures were created using multi-level Voronoi diagrams in order to control microstructure variability and then were used as samples for virtual tensile tests in a full-field crystal plasticity solver. A data-driven model based on Functional Principal Component Analysis (FPCA) was confronted with the classical Voce law for the description of uniaxial tensile curves of synthetic AISI 420 steel microstructures consisting of a ferritic matrix and increasing volume fractions of M23C6 carbides. The parameters of the two models were interpreted in terms of carbide volume fractions and texture using linear mixed-effects models. @en

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

Random forest is a popular prediction approach for handling high dimensional covariates. However, it often becomes infeasible to interpret the obtained high dimensional and non-parametric model. Aiming for an interpretable predictive model, we develop a forward variable selection method using the continuous ranked probability score (CRPS) as the loss function. eOur stepwise procedure selects at each step a variable that minimizes the CRPS risk and a stopping criterion for selection is designed based on an estimation of the CRPS risk difference of two consecutive steps. We provide mathematical motivation for our method by proving that in a population sense, the method attains the optimal set. In a simulation study, we compare the performance of our method with an existing variable selection method, for different sample sizes and correlation strength of covariates. Our method is observed to have a much lower false positive rate. We also demonstrate an application of our method to statistical post-processing of daily maximum temperature forecasts in the Netherlands. Our method selects about 10% covariates while retaining the same predictive power.

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The availability of multi-omics data has revolutionized the life sciences by creating avenues for integrated system-level approaches. Data integration links the information across datasets to better understand the underlying biological processes. However, high dimensionality, correlations and heterogeneity pose statistical and computational challenges. We propose a general framework, probabilistic two-way partial least squares (PO2PLS), that addresses these challenges. PO2PLS models the relationship between two datasets using joint and data-specific latent variables. For maximum likelihood estimation of the parameters, we propose a novel fast EM algorithm and show that the estimator is asymptotically normally distributed. A global test for the relationship between two datasets is proposed, specifically addressing the high dimensionality, and its asymptotic distribution is derived. Notably, several existing data integration methods are special cases of PO2PLS. Via extensive simulations, we show that PO2PLS performs better than alternatives in feature selection and prediction performance. In addition, the asymptotic distribution appears to hold when the sample size is sufficiently large. We illustrate PO2PLS with two examples from commonly used study designs: a large population cohort and a small case–control study. Besides recovering known relationships, PO2PLS also identified novel findings. The methods are implemented in our R-package PO2PLS.

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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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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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Investigating the main determinants of the mechanical performance of metals is not a simple task. Already known physically inspired qualitative relations between 2D microstructure characteristics and 3D mechanical properties can act as the starting point of the investigation. Isotonic regression allows to take into account ordering relations and leads to more efficient and accurate results when the underlying assumptions actually hold. The main goal in this paper is to test order relations in a model inspired by a materials science application. The statistical estimation procedure is described considering three different scenarios according to the knowledge of the variances: known variance ratio, completely unknown variances, and variances under order restrictions. New likelihood ratio tests are developed in the last two cases. Both parametric and non-parametric bootstrap approaches are developed for finding the distribution of the test statistics under the null hypothesis. Finally an application on the relation between geometrically necessary dislocations and number of observed microstructure precipitations is shown.

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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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Abstract: The relationship between microstructure features and mechanical properties plays an important role in the design of materials and improvement of properties. Hole expansion capacity plays a fundamental role in defining the formability of metal sheets. Due to the complexity of the experimental procedure of testing hole expansion capacity, where many influencing factors contribute to the resulting values, the relationship between microstructure features and hole expansion capacity and the complexity of this relation is not yet fully understood. In the present study, an experimental dataset containing the phase constituents of 55 microstructures as well as corresponding properties, such as hole expansion capacity and yield strength, is collected from the literature. Statistical analysis of these data is conducted with the focus on hole expansion capacity in relation to individual phases, combinations of phases and number of phases. In addition, different machine learning methods contribute to the prediction of hole expansion capacity based on both phase fractions and chemical content. Deep learning gives the best prediction accuracy of hole expansion capacity based on phase fractions and chemical composition. Meanwhile, the influence of different microstructure features on hole expansion capacity is revealed. Graphical abstract: [Figure not available: see fulltext.]

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Modeling microstructures is an interesting problem not just in materials science, but also in mathematics and statistics. The most basic model for steel microstructure is the Poisson-Voronoi diagram. It has mathematically attractive properties and it has been used in the approximation of single-phase steel microstructures. The aim of this article is to develop methods that can be used to test whether a real steel microstructure can be approximated by such a model. Therefore, a general framework for testing the Poisson-Voronoi assumption based on images of two-dimension sections of real metals is set out. Following two different approaches, according to the use or not of periodic boundary conditions, three different model tests are proposed. The first two are based on the coefficient of variation and the cumulative distribution function of the cells area. The third exploits tools from to topological data analysis, such as persistence landscapes.

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Understanding the relationship between microstructure features and mechanical properties is of great significance for the improvement and specific adjustment of steel properties. The relationship between mean grain size and yield strength is established by the well-known Hall-Petch equation. But due to the complexity of the grain configuration within materials, considering only the mean value is unlikely to give a complete representation of the mechanical behavior. The classical Taylor equation is often used to account for the effect of dislocation density, but not thoroughly tested in combination with grain size influence. In the present study, systematic heat treatment routes and cold rolling followed by annealing are designed for interstitial free (IF) steel to achieve ferritic microstructures that not only vary in mean grain size, but also in grain size distribution and in dislocation density, a combination that is rarely studied in the literature. Optical microscopy is applied to determine the grain size distribution. The dislocation density is determined through XRD measurements. The hardness is analyzed on its relation with the mean grain size, as well as with the grain size distribution and the dislocation density. With the help of the variable selection tool LASSO, it is shown that dislocation density, mean grain size and kurtosis of grain size distribution are the three features which most strongly affect hardness of IF steel.

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In the so-called rare type match problem, the discrete characteristics of a crime stain have not been observed in the set of background material. To assess the strength of evidence, two competing statistical hypotheses need to be considered. The formulation of the hypotheses depends on whichidentification of source question is of interest (Ommen, 2017, Approximate statistical solutions tothe forensic identification of source problem. (Phd thesis). South Dakota State University). Assuming that the evidence has been generated according to the beta-binomial model, two quantifications of the value of evidence can be found in the literature, but no clear indication is given when to use either of these. When the likelihood ratio is used to quantify the value of evidence, an estimateis needed for the frequency of the discrete characteristics. The central discussion is about whether or not one of the traces needs to be added to the background material when determining this estimate. In this article it is shown, using fully Bayesian methods, that one of the values of evidence from the literature corresponds to the so-called 'identification of common source' problem and the other to the 'identification of specific source' problem (Ommen, 2017, Approximate statistical solutions to the forensic identification of source problem. (Phd thesis). South Dakota State University). This means that the question whether or not one of the traces needs to be added to the background material reduces to the question whether a common source or specific source problem is under consideration. The distinction between the two values is especially important for the rare type match problem, since the values of evidence differ most in this situation.

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