# ENBIS: European Network for Business and Industrial Statistics

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## ENBIS-14 in Linz

21 – 25 September 2014; Johannes Kepler University, Linz, Austria Abstract submission: 23 January – 22 June 2014

The following abstracts have been accepted for this event:

• Challenges of Virtual Testing in Statistical Quality Control of Railway Ballast

Authors: Vera Hofer (Department of Statistics, University of Graz), Holger Bach (Petromodel Ltd., Reykjavik)
Primary area of focus / application: Process
Secondary area of focus / application: Quality
Keywords: Change detection, Novelty detection, Statistical quality control, Machine learning
Submitted at 19-Jun-2014 09:26 by Vera Hofer
Accepted
22-Sep-2014 16:40 Challenges of Virtual Testing in Statistical Quality Control of Railway Ballast
Railway ballast is a natural product and as such it is subject to variation in petrographic composition. This results in variations in particle shape and resistance to attrition. As existing test methods are arduous and expensive, test intervals are typically fairly wide. As a consequence, short-term and mid-term fluctuations of ballast quality may not be detected. This results in increased costs for maintenance work such as tamping. Shorter test intervals would yield a better ballast quality and reduce ballast life-cycle costs. This can be achieved with acceptable effort only if new methods are taken into consideration. Against this background, a new statistical monitoring process for railway ballast is proposed which combines traditional test methods with an innovative measurement device, the Petroscope 4D®. Here, the geometrical parameters can be measured directly in a manner superior to that of traditional tests, and the mechanical properties
are statistically estimated based on geometric and spectrographic features. This procedure is referred to as virtual testing. However, replacing manual testing by virtual testing requires that distributions on which the prediction model is based remain unchanged. However, there is no guarantee that, for example, new rock types that were not included in the training phase emerge. Thus, statistical monitoring of samples from daily production requires a novelty detection step to guarantee a high prediction performance quality.
• Estimating Time to Failure Distribution by Functional Data Analysis

Authors: Kamyar Sabri-laghaie (Iran University of Science and Technology), Rassoul Noorossana (Iran University of Science and Technology)
Primary area of focus / application: Reliability
Keywords: Reliability, Degradation measure, Functional Data Analysis, Time to failure
Submitted at 20-Jun-2014 01:12 by Kamyar Sabri-laghaie
Accepted
In some cases, traditional life tests can’t provide enough information for reliability estimation. For some products, degradation measurements can be recorded over time. These information can be very useful in product reliability evaluations. Failure is usually defined in terms of a particular level of degradation. In this regard, degradation models can be used to obtain time to failure distribution of the products. We use a statistical method based on Functional Data Analysis (FDA) to estimate time to failure distribution of products. We compare the performance of the proposed method with the results of traditional methods. It's shown that using Functional Data analysis is advantageous in product reliability assessment.
• Minimum Volume Confidence Intervals under Prior Information for the Mean of a Poisson Distribution

Authors: Kristina Lurz (prognostica GmbH), Rainer Göb (University of Würzburg)
Primary area of focus / application: Reliability
Keywords: Confidence interval, Poisson distribution, Prior information, Count data
Submitted at 20-Jun-2014 10:24 by Kristina Krebs
Accepted
23-Sep-2014 09:20 Minimum Volume Confidence Intervals under Prior Information for the Mean of a Poisson Distribution
Confidence intervals for the mean of a Poisson distribution find application when it comes to analysing count data. Examples for fields of application are epidemiology, physics, accounting and auditing. Frequently, the confidence intervals are used as conservative approximations for estimating proportions by making use of the limiting characteristics of the Poisson distribution approximating the Binomial distribution. In many applications, prior knowledge about the unknown distribution parameter is available, but rarely made use of, unless in a Bayesian framework. Exact (frequentist) confidence intervals of minimal volume for a binomial proportion that exploit prior knowledge have been suggested by Göb & Lurz (2014). In this presentation, we investigate the concept of Göb & Lurz (2014) applied to the parameter of a Poisson distribution. Prior information is employed in a flexible way by means of the Gamma distribution. Important results that support an efficient calculation of these exact confidence intervals in real time are derived. The concept is compared with other confidence intervals for a Poisson parameter.

Göb, R., & Lurz, K. (2014). Design and analysis of shortest two-sided confidence intervals for a probability under prior information. Metrika, vol. 77, no. 3, pp. 389-413.
• A Study of the Copula Parameter Impact on Optimal Design of Experiments for Copula Models

Authors: Elisa Perrone (IFAS - Johannes Kepler University of Linz)
Primary area of focus / application: Design and analysis of experiments
Keywords: Design of Experiments, Copulas, Fisher information matrix, Equivalence theorem, Stochastic dependence
Submitted at 20-Jun-2014 12:45 by Elisa Perrone
Accepted
24-Sep-2014 09:40 A Study of the Copula Parameter Impact on Optimal Design of Experiments for Copula Models.
Copula modelling is largely employed in many areas of applied statistics. However, the design of related experiments is still a neglected aspect. In this work the relationship between optimal design theory and copula theory is analysed, with the goal of highlighting the influence of stochastic dependence in the optimal design domain. A framework is provided with an extension of the classical equivalence theorem. The main part of this work is a better understanding of the role played by the copula parameter. For this aim, a particular accent is put on specific investigations on the robustness of the method by introducing as copula parameter a function which depends upon the intercept . First investigations are focused just on Archimedean copulas. Later the analyzed case is when the dependence model is described by a combination of copulas which are linked by a parameter to be estimated. Comparisons are made on different examples in order to see when the impact stronger.
• Comparison of Different Approaches for the Prediction of Sugar Content in Whole Port Wine Grape Berries Using Hyperspectral Imaging

Authors: Véronique Gomes (CITAB-Centre for the Research and Technology of Agro-Environmental and Biological Sciences, Universidade de Trás-os-Montes e Alto Douro), Armando Fernandes (CITAB-Centre for the Research and Technology of Agro-Environmental and Biological Sciences, Universidade de Trás-os-Montes e Alto Douro; Center of Intelligent Systems, IDMEC/LAETA, Instituto Superior Técnico, Universidade de Lisboa), Arlete Faia (IBB–Institute for Biotechnology and Bioengineering, Centre of Genomics and Biotechnology, Universidade de Trás-os-Montes e Alto Douro), Pedro Melo-Pinto (CITAB-Centre for the Research and Technology of Agro-Environmental and Biological Sciences, Universidade de Trás-os-Montes e Alto Douro; Departamento de Engenharias, Escola de Ciências e Tecnologia, Universidade de Trás-os-Montes e Alto Douro)
Primary area of focus / application: Quality
Secondary area of focus / application: Modelling
Keywords: Prediction, Hyperspectral imaging, PLS-R, Neural networks, Grapes berries
Submitted at 20-Jun-2014 12:49 by Véronique Gomes
Accepted (view paper)
22-Sep-2014 12:35 Comparison of Different Approaches for the Prediction of Sugar Content in Whole Port Wine Grape Berries Using Hyperspectral Imaging
Douro region is famous for producing a unique fortified wine with renowned quality, Port wine. To assure their prominence in current markets it’s important to ensure the high-values of the wines produced as well as to improve winemaking process. Harvesting the wine grapes at the optimal point of maturity and selecting them according to their quality features has a strong impact on the quality of wines. In this context, hyperspectral imaging is becoming an important technique which integrates spectroscopy and digital imaging techniques to provide both spatial and spectral information and which allows the extraction of important information available and the development of useful models to estimate the enological parameters of the grapes. Given the large amount of information collected by this technology more flexible data analysis tools are required to deal with that complex data. In this work, we compare two different approaches, PLS regression and Neural Networks approaches, for supporting the proper monitoring of the quality of wine based on sugar content predictions. Prediction models were established upon application of each approach and both are validated through the n-fold cross-validation with test set. Comparing the results for validation data with PLS regression and Neural Networks, the root mean square error (RMSECV) were 1.10 ºBrix and 1.09 ºBrix and the squared correlation coefficients (R2) were 0.891 and 0.892, respectively for each approach. In the same order, but using test data fed in each developed approach, the RMSE values were 0.939 ºBrix and 0.955 ºBrix, and the R2 values were 0.929 and 0.924. The results obtained suggest that combining hyperspectral imaging with appropriate advanced multivariate statistical techniques or machine learning algorithms, allow us to achieve good prediction. In fact, both approaches are able to predict sugar content in whole Port wine grape berries without relevant differences.
• Bayesian Local Kriging

Authors: Luc Pronzato (CNRS), Joaõ Rendas (CNRS)
Primary area of focus / application: Design and analysis of experiments
Secondary area of focus / application: Modelling
Keywords: Gaussian process, Kriging, Prediction, Interpolation, Bayesian estimation
Submitted at 20-Jun-2014 14:41 by Luc Pronzato
Accepted
23-Sep-2014 09:40 Bayesian Local Kriging
The usual approach to Gaussian Process (GP) modeling and kriging prediction raises two major issues: (i) stationarity if often a too strong assumption but is hardly avoidable when one single realization of the random field is observed; (ii) the estimation of the kernel parameters that specify the correlation between distant observations is problematic, taking the uncertainty on these estimates into account in the construction of predictions is difficult and requires either heavy Monte-Carlo calculations or relies on some (sometimes crude) approximations based on the asymptotic behavior of estimators.

We propose a local-kriging approach that faces the two difficulties above. First, we consider a different local model at each point $t$ where prediction is required, which allows us to account for non stationarity. Second, for each prediction site $t$ we consider a finite set of $L$ localized correlation functions $C_{\ell|t}$, $\ell=1,\ldots,L$, and a local model $Z_{s(t)}$ with correlation function $C_{s(t)|t}$ such that $s(t)=\ell$ with some probability $w^\ell(t)$. Starting with some prior weights $w^\ell_0$, we can then update them into $w^\ell_n$ after $n$ observations $\zb_n=(Z(x_1),\ldots,Z(x_n))\TT$ have been collected, and hence construct a Bayesian predictor $x\in\SX\longmapsto\hat z_n(x|t)$ based on the $L$ local models. As shown below, due to the dependence of the $w^\ell_n$ in $\zb_n$, this predictor depends non linearly in $\zb_n$. By construction, $\hat z_n(x|t)$ is only valid locally, for $x$ close to $t$, but the predictor $t\in\SX \longmapsto \hat z_n(t)=\hat z_n(t|t)$, which we call Bayesian local kriging predictor, inherits continuity and interpolating properties from the properties of the correlation functions $C_{\ell|t}$. This prediction and its posterior squared error can be constructed explicitly when we assume a linear parametric trend $\gb\TT(x)\beta$, with $\gb(\cdot)$ a known vector of functions (the usual framework for universal kriging), and a hierarchical prior $\beta|\ms^2 \sim \SN(\beta_0,\ms^2 \Vb_0)$ and $\ms^2\sim$ inverse chi-squared, common to the $L$ models. Various examples, with and without non-stationarity, will be presented to compare the performance of this local-kriging method with that of universal kriging with maximum likelihood estimation of covariance parameters.