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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., Comment: This preprint has not undergone peer review (when applicable) or any post-submission improvements or corrections. The Version of Record of this article is published in Statistical Methods & Applications, and is available online at https://doi.org/10.1007/s10260-023-00696-z

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

Kernel estimators are proposed for estimating the cumulative distribution functions and the probability density functions of several quantities of interest in a stereological oriented cylinder model. This oriented cylinder model was developed to represent anisotropic microstructural features in materials. The asymptotic properties of these estimators are studied, and the estimators are applied to two banded dual phase steel microstructures. The estimation method is quite general and can also be applied to distributions of other univariate quantities of interest.

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.

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.

Understanding the intricate and complex materials microstructure and how it is related to materials properties is an important problem in the Materials Science field. For a full comprehension of this relation, it is fundamental to be able to describe the main characteristics of the 3-dimensional microstructure. The most basic model used for approximating steel microstructure is the Poisson-Voronoi diagram. Poisson-Voronoi diagrams have interesting mathematical properties, and they are used as a good model for single-phase materials. In this paper we exploit the scaling property of the underlying Poisson process to derive the distribution of the main geometrical features of the grains for every value of the intensity parameter. Moreover, we use a sophisticated simulation program to construct a close Monte Carlo based approximation for the distributions of interest. Using this, we determine the closest approximating distributions within the mentioned frequently used parametric classes of distributions and conclude that these representations can be quite accurate. Finally we consider a 3D volume dataset and compare the real volume distribution to what is to be expected under the Poisson-Voronoi model.

In this paper we consider the current status continuous mark model where, if the 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 ($Y$). We consider a prior that is obtained by assigning a distribution on heights of cells, where cells are obtained from a partition of the support of the density of $(X, Y)$. As distribution on cell heights, we consider both a Dirichlet prior and a prior based on the graph-Laplacian on the specified partition. Our main result shows that under appropriate conditions, the posterior distribution function contracts pointwisely at rate $\left(n/\log n\right)^{-\frac{\rho}{3(\rho+2)}}$, where $\rho$ is the H\"older smoothness of the true density. In addition to our theoretical results, we provide computational methods for drawing from the posterior using probabilistic programming. The performance of our computational methods is illustrated in two examples.

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 paper 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 2D 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., 29 pages, 27 figures

Investigating the main determinants of the mechanical performance of metals is not a simple task. Already known physical 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, 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., 18 pages, 3 figures

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.

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 which identification of source question is of interest (Ommen, 2017, Approximate statistical solutions to the 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 estimate is 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.

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.

The majority of experimental data are obtained by destructive measuring techniques. Inevitably, in all these data variation is present, sometimes small and negligible, sometimes large, preventing proper analysis and extraction of meaningful information by traditional statistical techniques altogether. In this paper, three systems are presented to analyse destructive (cross-sectional) data, including biological as well as technical variation. The first system involves ranking the data per measuring point in time which provides a pseudo fruit number that can be used in non-linear indexed regression analysis similar as for non-destructive (longitudinal) data. The rationale behind this is that the individual with the highest value at some point in time will resemble the most another individual with the highest value at previous or future times, and the second highest the second highest at previous times, and so on. The second system also relies on this ranking number, but is now converted into a probability, which is used in non-linear regression analysis with quantile functions. The third system is based on optimising the log likelihood of the density function derived from the applied model (i.e., the expected distribution) over the measured data. Simulated data are used to elucidate the power of the three systems. A dataset on mango colour is used to validate the systems on a real-world data set. Although all three systems perform satisfactorily with percentages variability accounted for (R2 adj) well over 90%, a clear preference cannot be given since the choice of the proper analysis system depends on the experimental conditions (number of data, individuals and sampling points in time). Non-linear indexed and non-linear regression with quantile functions delivered the most reliable estimates. The three systems open up the possibility to analyse and reanalyse destructively measured data providing a sufficient large number of individuals and a clear indication of the kinetic model is available.

Luitzen Egbertus Jan (Bertus) Brouwer (27 February 1881–2 December 1966) was one of the world’s leading mathematicians and logicians, not afraid to be controversial. His revolutionary insights changed and enriched the landscape of mathematics, topology and logic in an ever-lasting way.

Petrus (Piet) Groeneboom was born in Scheveningen in 1941 and grew up in Voorburg. Both villages are located near The Hague in The Netherlands; Scheveningen actually being part of The Hague. He attended the gymnasium of the Huygens lyceum. In 1959, he entered the University of Amsterdam, where he studied psychology. After his “candidate” exam (comparable to BSc) in 1963, he worked at the psychological laboratory of the University of Amsterdam until 1966. In 1965, he took up mathematics as a part-time study. After having obtained his master’s degree in 1971, he had a position at the psychological laboratory again until 1973, when he was appointed to the Mathematical Center in Amsterdam. There, he wrote between 1975 and 1979 his Ph.D. thesis with Kobus Oosterhoff as advisor, graduating in 1979. After a period of two years as visiting professor at the University of Washington (UW) in Seattle, Piet moved back to the Mathematical Center until he was appointed full professor of statistics at the University of Amsterdam in 1984. Four years later, he moved to Delft University of Technology where he became professor of statistics and stayed until his retirement in 2006. Between 2000 and 2006 he also held a part-time professorship at the Vrije Universiteit in Amsterdam. From 1999 till 2013 he was Affiliate Professor at the statistics department of UW, Seattle. Apart from being visiting professor at the UW in Seattle, he was also visiting professor at Stanford University, Université Paris 6 and ETH Zürich. ¶ Piet is well known for his work on shape constrained statistical inference. He worked on asymptotic theory for these problems, created algorithms to compute nonparametric estimates in such models and applied these models to real data. He also worked on interacting particle systems, extreme value analysis and efficiency theory for testing procedures. Piet (co-)authored four books and 64 papers and served as promotor of 13 students. He is the recipient of the 1985 Rollo Davidson prize, a fellow of the IMS and elected member of the ISI. In 2015, he delivered the Wald lecture at the Joint Statistical Meeting in Montreal. ¶ Piet and his wife Marijke live in Naarden. He has two sons, Thomas and Tim, and (since June 12, 2018) one grandson, Tarik. This conversation was held at Piet’s house in Naarden, on February 28 and April 24, 2018.

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.

Shape constraints enter in many statistical models. Sometimes these constraints emerge naturally from the origin of the data. In other situations, they are used to replace parametric models by more versatile models retaining qualitative shape properties of the parametric model. In this paper, we sketch a part of the history of shape constrained statistical inference in a nutshell, using landmark results obtained in this area. For this, we mainly use the prototypical problems of estimating a decreasing probability density on $[0,\infty )$ and the estimation of a distribution function based on current status data as illustrations.

Background With the exponential growth in available biomedical data, there is a need for data integration methods that can extract information about relationships between the data sets. However, these data sets might have very different characteristics. For interpretable results, data-specific variation needs to be quantified. For this task, Two-way Orthogonal Partial Least Squares (O2PLS) has been proposed. To facilitate application and development of the methodology, free and open-source software is required. However, this is not the case with O2PLS. Results We introduce OmicsPLS, an open-source implementation of the O2PLS method in R. It can handle both low- and high-dimensional datasets efficiently. Generic methods for inspecting and visualizing results are implemented. Both a standard and faster alternative cross-validation methods are available to determine the number of components. A simulation study shows good performance of OmicsPLS compared to alternatives, in terms of accuracy and CPU runtime. We demonstrate OmicsPLS by integrating genetic and glycomic data. Conclusions We propose the OmicsPLS R package: a free and open-source implementation of O2PLS for statistical data integration. OmicsPLS is available at https://cran.r-project.org/package=OmicsPLS and can be installed in R via install.packages(“OmicsPLS”). Electronic supplementary material The online version of this article (10.1186/s12859-018-2371-3) contains supplementary material, which is available to authorized users.

Suppose X1,…,Xn 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).

The generalized Pareto distribution (GPD) is often used in the statistical analysis of climate extremes. For a sample of independent and identically distributed observations, the parameters of the GPD can be estimated by the maximum likelihood (ML) method. In this paper, we drop the assumption of identically distributed random variables. We consider independent observations from GPD distributions having a common shape parameter but possibly an increasing trend in the scale parameter. Such a model, with increasing scale parameter, can be used to describe a trend in the observed extremes as time progresses. Estimating an increasing trend in a distribution parameter is common in the field of isotonic regression. We use ideas and tools from that area to compute ML estimates of the GPD parameters. In a simulation experiment, we show that the iterative convex minorant (ICM) algorithm is much faster than the projected gradient (PG) algorithm. We apply the approach to the daily maxima of the central England temperature (CET) data. A clear positive trend in the GPD scale parameter is found, leading to an increase in the 100-year return level from about 31º in the 1880s to 34º in 2015.

A tutorial on using OmicsPLS. This pdf contains a case study illustrating the OmicsPLS package using freely available transcriptomics and metabolomics measurements from a Finnish population cohort. We discuss input and output of the main functions, interpret the analysis results and show how to generate publication-ready figures. (PDF 1172 kb)

With a rapid increase in volume and complexity of data sets, there is a need for methods that can extract useful information, for example the relationship between two data sets measured for the same persons. The Partial Least Squares (PLS) method can be used for this dimension reduction task. Within life sciences, results across studies are compared and combined. Therefore, parameters need to be identifiable, which is not the case for PLS. In addition, PLS is an algorithm, while epidemiological study designs are often outcome-dependent and methods to analyze such data require a probabilistic formulation. Moreover, a probabilistic model provides a statistical framework for inference. To address these issues, we develop Probabilistic PLS (PPLS). We derive maximum likelihood estimators that satisfy the identifiability conditions by using an EM algorithm with a constrained optimization in the M step. We show that the PPLS parameters are identifiable up to sign. A simulation study is conducted to study the performance of PPLS compared to existing methods. The PPLS estimates performed well in various scenarios, even in high dimensions. Most notably, the estimates seem to be robust against departures from normality. To illustrate our method, we applied it to IgG glycan data from two cohorts. Our PPLS model provided insight as well as interpretable results across the two cohorts., Comment: Accepted in Journal of Multivariate Analysis

Senior pre-university education (SPE) students experience difficulties applying mathematics to physics. This paper reports the outcome of an online explorative quantitative study of teachers' belief systems about improving transfer of algebraic skills from mathematics into physics, conducted among 503 mathematics and physics teachers working in SPE. We used a questionnaire with 16 beliefs about improving transfer, and asked teachers to select a top 5 and distribute 50 points among them. We used agglomerative hierarchical clustering to cluster qualified SPE teachers with more than 10 years of teaching experience. We found 3 large clusters, each containing naïve and desirable beliefs about transfer. These clusters turned out to be rather coherent sets of beliefs. Hence, these clusters can be interpreted as belief systems, to a certain extent justifying Ernest's [(1991). The philosophy of mathematics education. London: Falmer.] idea to cluster teachers based on their belief systems. We found relations between our groups and those of Ernest. Since naïve beliefs turn out to be weak in each cluster, science teacher educators can help science teachers to change their harmful naïve beliefs, into desirable transfer enhancing beliefs. Furthermore, we discuss some implications of our results for science teacher educators, curricula, teachers and textbooks.

Rainfall extremes are thought to have increased over recent years. Typically linear trends have been considered to describe the temporal evolution of high quantiles of the daily rainfall distribution. For long records it is important to allow more flexibility. Quantile regression methods are available to estimate monotone trends for single stations. Having multiple stations in a region, the significance of the trend at the regional scale is often of interest. From this perspective the authors propose a regression approach that can be used to estimate a common monotone trend for the site-specific quantiles. Moreover, the method allows for the construction of confidence bands and testing the hypothesis of an existing nondecreasing trend against the null hypothesis of no trend. The approach is applied to 102 series of daily rainfall over the Netherlands for the period 1910–2009. The results are compared with those from a (regional) Mann–Kendall test. Significantly increasing trends are found for the winter season and for the whole year. In the summer season trends are less consistent over the region and are only significant in the western part of the Netherlands. For the summer season, linearity of the trend seems less apparent than for winter and for the whole year. However, the deviation from linearity is not significant.

A hurdle in the peaks-over-threshold approach for analyzing extreme values is the selection of the threshold. A method is developed to reduce this obstacle in the presence of multiple, similar data samples. This is for instance the case in many environmental applications. The idea is to combine threshold selection methods into a regional method. Regionalized versions of the threshold stability and the mean excess plot are presented as graphical tools for threshold selection. Moreover, quantitative approaches based on the bootstrap distribution of the spatially averaged Kolmogorov–Smirnov and Anderson–Darling test statistics are introduced. It is demonstrated that the proposed regional method leads to an increased sensitivity for too low thresholds, compared to methods that do not take into account the regional information. The approach can be used for a wide range of univariate threshold selection methods. We test the methods using simulated data and present an application to rainfall data from the Dutch ...

A guide to include variation in statistical analysis of non-destructive data.Biological and technical variation are split up and estimated separately.Huge increase in reliability of the estimated parameters.Principles explained with simulated data on exponential decay.Applicability demonstrated on several examples from practise. More and more, the omnipresent variation between individual items in a batch is taken into account by using special analysing techniques like mixed effects and indexed regression. In this paper the assumptions upon which these techniques are based, are explained, based on a simulated data set. The most important issue is the separation of biological variation and the technical variation (or measuring error). The techniques are further elucidated with some examples from practise (skin colour apples in storage, softening of melons in storage and water loss in plums, melons and mandarins), to show the increased reliability of the analyses. Since variation is always present in any measured data set, the techniques are applicable in all fields working with living material.

Time-to-event data are collected and studied in many research fields, such as medical science and reliability theory. A complication often encountered with these data is censoring. The time of the actual event is not observed: for each subject, only an interval can be observed that contains this time. Parametric, as well as nonparametric estimation, procedures can be employed to estimate the relevant quantities of interest. Also, various models can be used to include explanatory variables in the model. In this paper the parametric and nonparametric approach to interval-censored data are described. The aim is to show a glimpse of the possibilities of stochastic modelling and stimulate discussion on the development of models specifically in the context of ageing.

In the evaluation of measurements on characteristics of forensic trace evidence, Aitken and Lucy (2004) model the data as a two-level model using assumptions of normality where likelihood ratios are used as a measure for the strength of evidence. A two-level model assumes two sources of variation: the variation within measurements in a group (first level) and the variation between different groups (second level). Estimates of the variation within groups, the variation between groups and the overall mean are required in this approach. This paper discusses three estimators for the overall mean. In forensic science, two of these estimators are known as the weighted and unweighted mean. For an optimal choice between these estimators, the within- and between-group covariance matrices are required. In this paper a generalization to the latter two mean estimators is suggested, which is referred to as the generalized weighted mean. The weights of this estimator can be chosen such that they minimize the variance of the generalized weighted mean. These optimal weights lead to a "toy estimator", because they depend on the unknown within- and between-group covariance matrices. Using these optimal weights with estimates for the within- and between-group covariance matrices leads to the third estimator, the optimal "plug-in" generalized weighted mean estimator. The three estimators and the toy estimator are compared through a simulation study. Under conditions generally encountered in practice, we show that the unweighted mean can be preferred over the weighted mean. Moreover, in these situations the unweighted mean and the optimal generalized weighted mean behave similarly. An artificial choice of parameters is used to provide an example where the optimal generalized weighted mean outperforms both the weighted and unweighted mean. Finally, the three mean estimators are applied to real XTC data to illustrate the impact of the choice of overall mean estimator.

Students in senior pre-university education encounter difficulties in the application of mathematics into physics. This paper presents the outcome of an explorative qualitative study of teachers’ beliefs about improving the transfer of algebraic skills from mathematics into physics. We interviewed 10 mathematics and 10 physics teachers using a semi-structured questionnaire that was based on an algebraic transfer problem. Almost all teachers acknowledged this transfer problem and considered it to be important. We found a continuum of teachers’ beliefs about aspects influencing transfer, including beliefs on improving this transfer. Together with identified improvement aspects about coherent mathematics education, these may help reduce physics teachers’ frustrations who spend extra time on re-teaching mathematics. Teachers think that transfer does not happen, because students see both subjects as separate disciplines. Contrary to most physics teachers, most mathematics teachers do not feel the need to collaborate with physics teachers. We found two extreme, opposite beliefs about the transfer of algebraic skills into physics. An intermediate group believes that only an integrated approach can solve the transfer problem. Some of the teachers’ beliefs could be organised into a beliefs system. Further research could investigate to which extent such beliefs systems exist and which beliefs these contain.

Projections of extreme precipitation are of great importance, considering the potential severe impacts on society. In this study a recently developed regional, non-stationary peaks-over-threshold approach is applied to two transient simulations of the RACMO2 regional climate model for the period 1950-2100, driven by two different general circulation models. The regional approach reduces the estimation uncertainty compared to at-site approaches. The selection of a threshold for the peaks-over-threshold model is tackled from a new perspective, taking advantage of the regional setting. Further, a regional quantile regression model using a common relative trend in the threshold is introduced. A considerable bias in the extreme return levels is found with respect to gridded observations. This bias is corrected for by adjusting the parameters in the peaks-over-threshold model. In summer a significant increase in extreme precipitation over the study area is found for both RACMO2 simulations, mainly as a result of an increase of the variability of the excesses over the threshold. However, the magnitude of this trend in extreme summer precipitation depends on the driving general circulation model. In winter an increase in extreme precipitation corresponding with an increase in mean precipitation is found for both simulations. This trend is due to an increase of the threshold. Keywords: Climate model data; Non-stationary; Peaks-over-threshold; Regional frequency analysis; Threshold choice

BackgroundRapid computational and technological developments made large amounts of omics data available in different biological levels. It is becoming clear that simultaneous data analysis methods are needed for better interpretation and understanding of the underlying systems biology. Different methods have been proposed for this task, among them Partial Least Squares (PLS) related methods. To also deal with orthogonal variation, systematic variation in the data unrelated to one another, we consider the Two-way Orthogonal PLS (O2PLS): an integrative data analysis method which is capable of modeling systematic variation, while providing more parsimonious models aiding interpretation.ResultsA simulation study to assess the performance of O2PLS showed positive results in both low and higher dimensions. More noise (50 % of the data) only affected the systematic part estimates. A data analysis was conducted using data on metabolomics and transcriptomics from a large Finnish cohort (DILGOM). A previous sequential study, using the same data, showed significant correlations between the Lipo-Leukocyte (LL) module and lipoprotein metabolites. The O2PLS results were in agreement with these findings, identifying almost the same set of co-varying variables. Moreover, our integrative approach identified other associative genes and metabolites, while taking into account systematic variation in the data. Including orthogonal components enhanced overall fit, but the orthogonal variation was difficult to interpret.ConclusionsSimulations showed that the O2PLS estimates were close to the true parameters in both low and higher dimensions. In the presence of more noise (50 %), the orthogonal part estimates could not distinguish well between joint and unique variation. The joint estimates were not systematically affected. Simultaneous analysis with O2PLS on metabolome and transcriptome data showed that the LL module, together with VLDL and HDL metabolites, were important for the metabolomic and transcriptomic relation. This is in agreement with an earlier study. In addition more gene expression and metabolites are identified being important for the joint covariation.

We consider the maximum likelihood estimator of a distribution function in a class of deconvolution models where the known density of the noise variable is of bounded variation. This class of noise densities contains in particular bounded, decreasing densities. The estimator is defined, characterized in terms of Fenchel optimality conditions and computed. Under appropriate conditions, various consistency results for are derived, including uniform strong consistency. The Canadian Journal of Statistics 41: 98–110; 2013 © 2012 Statistical Society of Canada Nous considerons l'estimateur du maximum de vraisemblance de la fonction de repartition dans une classe de modeles de deconvolution ou la densite du bruit est connue et est a variation bornee. Cette classe de densites pour le bruit contient en particulier les densites bornees et decroissantes. Nous definissons l'estimateur , nous le caracterisons en terme des conditions d'optimalite de Fenchel et nous l'evaluons. Sous des conditions appropriees, plusieurs resultats de coherence pour sont obtenus, incluant la coherence uniforme forte. La revue canadienne de statistique 41: 98–110; 2013 © 2012 Societe statistique du Canada

Two dual phase steels with markedly different microstructural banding have been serial sectioned for characterisation and quantification of the banding in three dimension (3D). Two parameters, bounded on a scale of zero to one, have been defined to quantify the amount of microstructural banding in two dimension (2D). The band continuity index Cb quantifies the continuity of each band within the band. The perpendicular continuity index Cp describes the continuity between adjacent bands. In the present work, these parameters are extended and applied to full 3D bands. The results show that while the connectivity of bands in 3D is different than what is observed in 2D, the quantification of banding with these parameters in 2D is sufficient to accurately represent the banding in 3D, thus validating these newly defined parameters.

In order to quantify the degree of banding in dual phase steel, optical micrographs of various dual phased steel microstructures have been analysed. From the binary images of the micrographs, greyscale profiles are created and used to define the bands within the image. Two parameters are calculated from the defined bands: band continuity index Cb and perpendicular continuity index Cp. The first parameter quantitatively describes the continuity of each band along the direction of banding, while the second parameter quantitatively describes the continuity of the bands perpendicular to the banding direction. Both parameters are bounded on [0,1], with 0 indicating no banding and 1 indicating strong banding.

We consider the problem of estimating the joint distribution function of the event time and a continuous mark variable when the event time is subject to interval censoring case 1 and the continuous mark variable is only observed in case the event occurred before the time of inspection. The non-parametric maximum likelihood estimator in this model is known to be inconsistent. We study two alternative smooth estimators, based on the explicit (inverse) expression of the distribution function of interest in terms of the density of the observable vector. We derive the pointwise asymptotic distribution of both estimators.

The need to identify toxicologically equivalent doses across different species is a major issue in toxicology and risk assessment. In this article, we investigate interspecies scaling based on the allometric equation applied to the single, oral LD (50) data previously analyzed by Rhomberg and Wolff. We focus on the statistical approach, namely, regression analysis of the mentioned data. In contrast to Rhomberg and Wolff's analysis of species pairs, we perform an overall analysis based on the whole data set. From our study it follows that if one assumes one single scaling rule for all species and substances in the data set, then β = 1 is the most natural choice among a set of candidates known in the literature. In fact, we obtain quite narrow confidence intervals for this parameter. However, the estimate of the variance in the model is relatively high, resulting in rather wide prediction intervals.

The standard isotonic regression of a vector in R n is the solution to a least squares projection problem on the cone C of vectors with ‘increasing components’ in R n . Generalized isotonic regression problems are isotonic optimization problems that seem to be quite different from isotonic regression problems, but in fact have the same solution. In problems of maximum smoothed likelihood estimation, often continuous versions of generalized isotonic regression problems emerge. In this paper we show that the solutions to such problems are often given by the relatively simple continuous isotonic regression of a function. We illustrate the result using the problem of maximum smoothed likelihood estimation of an increasing hazard function.

We consider deconvolution models with noise variables that have bounded, decreasing densities with compact support. The nonparametric maximum likelihood estimator of the distribution function is shown to converge globally at a rate n − 1 / 3 with respect to the L 2 -metric.

In a controlled multiple case design study, the development of a therapeutic relationship and its role in affect regulation were studied in 6 children with visual disabilities, severe intellectual disabilities, severe challenging behavior, and prolonged social deprivation. In the 1st phase, children had sessions with an experimental therapist stimulating therapeutic attachment, alternating with a control therapist providing positive personal attention only. In the 2nd phase, both therapists applied behavior therapy. Clients sought more proximity to the experimental therapist compared with the control therapist. Psychophysiological arousal (respiratory sinus arrhythmia and pre-ejection period) was lower when the experimental therapist applied behavior modification than when the control therapist did. Despite prolonged social deprivation, the attachment behavioral system appeared responsive to stimulation. The effects on affect regulation may explain the synergy between psychotherapy based on interpersonal and behavior modification approaches. © 2009 American Psychological Association.

We consider the classical problem of nonparametrically estimating a star-shaped distribution, i.e., a distribution function F on [0,∞) with the property that F(u)/u is nondecreasing on the set {u : F(u) < 1}. This problem is intriguing because of the fact that a well defined maximum likelihood estimator (MLE) exists, but this MLE is inconsistent. In this paper, we argue that the likelihood that is commonly used in this context is somewhat unnatural and propose another, so called ‘smoothed likelihood’. However, also the resulting MLE turns out to be inconsistent. We show that more serious smoothing of the likelihood yields consistent estimators in this model.

In this paper, we study an algorithm (which we call the support reduction algorithm) that can be used to compute non-parametric M-estimators in mixture models. The algorithm is compared with natural competitors in the context of convex regression and the 'Aspect problem' in quantum physics. © Board of the Foundation of the Scandinavian Journal of Statistics 2008.

We study nonparametric isotonic confidence intervals for monotone functions. In Banerjee and Wellner (2001) pointwise confidence intervals, based on likelihood ratio tests for the restricted and unrestricted MLE in the current status model, are introduced. We extend the method to the treatment of other models with monotone functions, and demonstrate our method by a new proof of the results in Banerjee and Wellner (2001) and also by constructing confidence intervals for monotone densities, for which still theory had to be developed. For the latter model we prove that the limit distribution of the LR test under the null hypothesis is the same as in the current status model. We compare the confidence intervals, so obtained, with confidence intervals using the smoothed maximum likelihood estimator (SMLE), using bootstrap methods. The `Lagrange-modified' cusum diagrams, developed here, are an essential tool both for the computation of the restricted MLEs and for the development of the theory for the confidence intervals, based on the LR tests., Comment: 31 pages, 13 figures

Key words and Phrases: cumulant, empirical characteristic function,Lévy process, self-decomposable distribution, stationary process.Consider a stationary sequence of random variables with infinitely divisiblemarginal law, characterized by its Lévy density. We analyze the behaviorof a so-called cumulant M-estimator, in case this Lévy density ischaracterized by a Euclidean (finite-dimensional) parameter. Under mildconditions, we prove consistency and asymptotic normality of the estimator.The estimator is considered in the situation where the data are incrementsof a subordinator as well as the situation where the data consist of adiscretely sampled Ornstein Uhlenbeck process induced by the subordinator.We illustrate our results for the Gamma-process and theInverse-Gaussian-OU-process. For these processes we also explain how theestimator can be computed numerically.