Looking for Validity or Testing It? The Perils of Stepwise Regression, Extreme-Scores Analysis, Heteroscedasticity, and Measurement Error

When researchers introduce a new test they have to demonstrate that it is valid, using unbiased designs and suitable statistical procedures. In this article we use Monte Carlo analyses to highlight how incorrect statistical procedures (i.e., stepwise regression, extreme scores analyses) or ignoring regression assumptions (e.g., heteroscedasticity) contribute to wrong validity estimates. Beyond these demonstrations, and as an example, we re-examined the results reported by Warwick, Nettelbeck, and Ward (2010) concerning the validity of the Ability Emotional Intelligence Measure (AEIM). Warwick et al. used the wrong statistical procedures to conclude that the AEIM was incrementally valid beyond intelligence and personality traits in predicting various outcomes. In our re-analysis, we found that the reliability-corrected multiple correlation of their measures with personality and intelligence was up to .69. Using robust statistical procedures and appropriate controls, we also found that the AEIM did not predict incremental variance in GPA, stress, loneliness, or well-being, demonstrating the importance for testing validity instead of looking for it.

Analysis of a finite volume element method for the Stokes problem

In this paper we propose a stabilized conforming finite volume element method for the Stokes equations. On stating the convergence of the method, optimal a priori error estimates in different norms are obtained by establishing the adequate connection between the finite volume and stabilized finite element formulations. A superconvergence result is also derived by using a postprocessing projection method. In particular, the stabilization of the continuous lowest equal order pair finite volume element discretization is achieved by enriching the velocity space with local functions that do not necessarily vanish on the element boundaries. Finally, some numerical experiments that confirm the predicted behavior of the method are provided.

The relationship between forensic science and judicial error: a study covering error sources, bias, and remedies

Summary : Forensic science - both as a source of and as a remedy for error potentially leading to judicial error - has been studied empirically in this research. A comprehensive literature review, experimental tests on the influence of observational biases in fingermark comparison, and semistructured interviews with heads of forensic science laboratories/units in Switzerland and abroad were the tools used. For the literature review, some of the areas studied are: the quality of forensic science work in general, the complex interaction between science and law, and specific propositions as to error sources not directly related to the interaction between law and science. A list of potential error sources all the way from the crime scene to the writing of the report has been established as well. For the empirical tests, the ACE-V (Analysis, Comparison, Evaluation, and Verification) process of fingermark comparison was selected as an area of special interest for the study of observational biases, due to its heavy reliance on visual observation and recent cases of misidentifications. Results of the tests performed with forensic science students tend to show that decision-making stages are the most vulnerable to stimuli inducing observational biases. For the semi-structured interviews, eleven senior forensic scientists answered questions on several subjects, for example on potential and existing error sources in their work, of the limitations of what can be done with forensic science, and of the possibilities and tools to minimise errors. Training and education to augment the quality of forensic science have been discussed together with possible solutions to minimise the risk of errors in forensic science. In addition, the time that samples of physical evidence are kept has been determined as well. Results tend to show considerable agreement on most subjects among the international participants. Their opinions on possible explanations for the occurrence of such problems and the relative weight of such errors in the three stages of crime scene, laboratory, and report writing, disagree, however, with opinions widely represented in existing literature. Through the present research it was therefore possible to obtain a better view of the interaction of forensic science and judicial error to propose practical recommendations to minimise their occurrence. Résumé : Les sciences forensiques - considérés aussi bien comme source de que comme remède à l'erreur judiciaire - ont été étudiées empiriquement dans cette recherche. Une revue complète de littérature, des tests expérimentaux sur l'influence du biais de l'observation dans l'individualisation de traces digitales et des entretiens semi-directifs avec des responsables de laboratoires et unités de sciences forensiques en Suisse et à l'étranger étaient les outils utilisés. Pour la revue de littérature, quelques éléments étudies comprennent: la qualité du travail en sciences forensiques en général, l'interaction complexe entre la science et le droit, et des propositions spécifiques quant aux sources d'erreur pas directement liées à l'interaction entre droit et science. Une liste des sources potentielles d'erreur tout le long du processus de la scène de crime à la rédaction du rapport a également été établie. Pour les tests empiriques, le processus d'ACE-V (analyse, comparaison, évaluation et vérification) de l'individualisation de traces digitales a été choisi comme un sujet d'intérêt spécial pour l'étude des effets d'observation, due à son fort recours à l'observation visuelle et dû à des cas récents d'identification erronée. Les résultats des tests avec des étudiants tendent à prouver que les étapes de prise de décision sont les plus vulnérables aux stimuli induisant des biais d'observation. Pour les entretiens semi-structurés, onze forensiciens ont répondu à des questions sur des sujets variés, par exemple sur des sources potentielles et existantes d'erreur dans leur travail, des limitations de ce qui peut être fait en sciences forensiques, et des possibilités et des outils pour réduire au minimum ses erreurs. La formation et l'éducation pour augmenter la qualité des sciences forensiques ont été discutées ainsi que les solutions possibles pour réduire au minimum le risque d'erreurs en sciences forensiques. Le temps que des échantillons sont gardés a été également déterminé. En général, les résultats tendent à montrer un grand accord sur la plupart des sujets abordés pour les divers participants internationaux. Leur avis sur des explications possibles pour l'occurrence de tels problèmes et sur le poids relatif de telles erreurs dans les trois étapes scène de crime;', laboratoire et rédaction de rapports est cependant en désaccord avec les avis largement représentés dans la littérature existante. Par cette recherche il était donc possible d'obtenir une meilleure vue de l'interaction des sciences forensiques et de l'erreur judiciaire afin de proposer des recommandations pratiques pour réduire au minimum leur occurrence. Zusammenfassung : Forensische Wissenschaften - als Ursache und als Hilfsmittel gegen Fehler, die möglicherweise zu Justizirrtümern führen könnten - sind hier empirisch erforscht worden. Die eingestzten Methoden waren eine Literaturübersicht, experimentelle Tests über den Einfluss von Beobachtungseffekten (observer bias) in der Individualisierung von Fingerabdrücken und halbstandardisierte Interviews mit Verantwortlichen von kriminalistischen Labors/Diensten in der Schweiz und im Ausland. Der Literaturüberblick umfasst unter anderem: die Qualität der kriminalistischen Arbeit im Allgemeinen, die komplizierte Interaktion zwischen Wissenschaft und Recht und spezifische Fehlerquellen, welche nicht direkt auf der Interaktion von Recht und Wissenschaft beruhen. Eine Liste möglicher Fehlerquellen vom Tatort zum Rapportschreiben ist zudem erstellt worden. Für die empirischen Tests wurde der ACE-V (Analyse, Vergleich, Auswertung und Überprüfung) Prozess in der Fingerabdruck-Individualisierung als speziell interessantes Fachgebiet für die Studie von Beobachtungseffekten gewählt. Gründe sind die Wichtigkeit von visuellen Beobachtungen und kürzliche Fälle von Fehlidentifizierungen. Resultate der Tests, die mit Studenten durchgeführt wurden, neigen dazu Entscheidungsphasen als die anfälligsten für Stimuli aufzuzeigen, die Beobachtungseffekte anregen könnten. Für die halbstandardisierten Interviews beantworteten elf Forensiker Fragen über Themen wie zum Beispiel mögliche und vorhandene Fehlerquellen in ihrer Arbeit, Grenzen der forensischen Wissenschaften und Möglichkeiten und Mittel um Fehler zu verringern. Wie Training und Ausbildung die Qualität der forensischen Wissenschaften verbessern können ist zusammen mit möglichen Lösungen zur Fehlervermeidung im selben Bereich diskutiert worden. Wie lange Beweismitten aufbewahrt werden wurde auch festgehalten. Resultate neigen dazu, für die meisten Themen eine grosse Übereinstimmung zwischen den verschiedenen internationalen Teilnehmern zu zeigen. Ihre Meinungen über mögliche Erklärungen für das Auftreten solcher Probleme und des relativen Gewichts solcher Fehler in den drei Phasen Tatort, Labor und Rapportschreiben gehen jedoch mit den Meinungen, welche in der Literatur vertreten werden auseinander. Durch diese Forschungsarbeit war es folglich möglich, ein besseres Verständnis der Interaktion von forensischen Wissenschaften und Justizirrtümer zu erhalten, um somit praktische Empfehlungen vorzuschlagen, welche diese verringern. Resumen : Esta investigación ha analizado de manera empírica el rol de las ciencias forenses como fuente y como remedio de potenciales errores judiciales. La metodología empleada consistió en una revisión integral de la literatura, en una serie de experimentos sobre la influencia de los sesgos de observación en la individualización de huellas dactilares y en una serie de entrevistas semiestructuradas con jefes de laboratorios o unidades de ciencias forenses en Suiza y en el extranjero. En la revisión de la literatura, algunas de las áreas estudiadas fueron: la calidad del trabajo en ciencias forenses en general, la interacción compleja entre la ciencia y el derecho, así como otras fuentes de error no relacionadas directamente con la interacción entre derecho y ciencia. También se ha establecido una lista exhaustiva de las fuentes potenciales de error desde la llegada a la escena del crimen a la redacción del informe. En el marco de los tests empíricos, al analizar los sesgos de observación dedicamos especial interés al proceso de ACE-V (análisis, comparación, evaluación y verificación) para la individualización de huellas dactilares puesto que este reposa sobre la observación visual y ha originado varios casos recientes de identificaciones erróneas. Los resultados de las experimentaciones realizadas con estudiantes sugieren que las etapas en las que deben tornarse decisiones son las más vulnerables a lös factores que pueden generar sesgos de observación. En el contexto de las entrevistas semi-estructuradas, once científicos forenses de diversos países contestaron preguntas sobre varios temas, incluyendo las fuentes potenciales y existehtes de error en su trabajo, las limitaciones propias a las ciencias forenses, las posibilidades de reducir al mínimo los errores y las herramientas que podrían ser utilizadas para ello. Se han sugerido diversas soluciones para alcanzar este objetivo, incluyendo el entrenamiento y la educación para aumentar la calidad de las ciencias forenses. Además, se ha establecido el periodo de conservación de las muestras judiciales. Los resultados apuntan a un elevado grado de consenso entre los entrevistados en la mayoría de los temas. Sin embargo, sus opiniones sobre las posibles causas de estos errores y su importancia relativa en las tres etapas de la investigación -la escena del crimen, el laboratorio y la redacción de informe- discrepan con las que predominan ampliamente en la literatura actual. De este modo, esta investigación nos ha permitido obtener una mejor imagen de la interacción entre ciencias forenses y errores judiciales, y comenzar a formular una serie de recomendaciones prácticas para reducirlos al minimo.

Cross-validation of bioelectrical impedance analysis for the assessment of body composition in a representative sample of 6- to 13-year-old children.

BACKGROUND/OBJECTIVES: (1) To cross-validate tetra- (4-BIA) and octopolar (8-BIA) bioelectrical impedance analysis vs dual-energy X-ray absorptiometry (DXA) for the assessment of total and appendicular body composition and (2) to evaluate the accuracy of external 4-BIA algorithms for the prediction of total body composition, in a representative sample of Swiss children. SUBJECTS/METHODS: A representative sample of 333 Swiss children aged 6-13 years from the Kinder-Sportstudie (KISS) (ISRCTN15360785). Whole-body fat-free mass (FFM) and appendicular lean tissue mass were measured with DXA. Body resistance (R) was measured at 50 kHz with 4-BIA and segmental body resistance at 5, 50, 250 and 500 kHz with 8-BIA. The resistance index (RI) was calculated as height(2)/R. Selection of predictors (gender, age, weight, RI4 and RI8) for BIA algorithms was performed using bootstrapped stepwise linear regression on 1000 samples. We calculated 95% confidence intervals (CI) of regression coefficients and measures of model fit using bootstrap analysis. Limits of agreement were used as measures of interchangeability of BIA with DXA. RESULTS: 8-BIA was more accurate than 4-BIA for the assessment of FFM (root mean square error (RMSE)=0.90 (95% CI 0.82-0.98) vs 1.12 kg (1.01-1.24); limits of agreement 1.80 to -1.80 kg vs 2.24 to -2.24 kg). 8-BIA also gave accurate estimates of appendicular body composition, with RMSE < or = 0.10 kg for arms and < or = 0.24 kg for legs. All external 4-BIA algorithms performed poorly with substantial negative proportional bias (r> or = 0.48, P<0.001). CONCLUSIONS: In a representative sample of young Swiss children (1) 8-BIA was superior to 4-BIA for the prediction of FFM, (2) external 4-BIA algorithms gave biased predictions of FFM and (3) 8-BIA was an accurate predictor of segmental body composition.

Measuring and Explaining the Increase of Travel Distance : A Multilevel Analysis Using Repeated Cross Sectional Travel Surveys

We want to shed some light on the development of person mobility by analysing the repeated cross-sectional data of the four National Travel Surveys (NTS) that were conducted in Germany since the mid seventies. The above mentioned driving forces operate on different levels of the system that generates the spatial behaviour we observe: Travel demand is derived from the needs and desires of individuals to participate in spatially separated activities. Individuals organise their lives in an interactive process within the context they live in, using given infrastructure. Essential determinants of their demand are the individual's socio-demographic characteristics, but also the opportunities and constraints defined by the household and the environment are relevant for the behaviour which ultimately can be realised. In order to fully capture the context which determines individual behaviour, the (nested) hierarchy of persons within households within spatial settings has to be considered. The data we will use for our analysis contains information on these three levels. With the analysis of this micro-data we attempt to improve our understanding of the afore subsumed macro developments. In addition we will investigate the prediction power of a few classic sociodemographic variables for the daily travel distance of individuals in the four NTS data sets, with a focus on the evolution of this predictive power. The additional task to correctly measure distances travelled by means of the NTS is threatened by the fact that although these surveys measure the same variables, different sampling designs and data collection procedures were used. So the aim of the analysis is also to detect variables whose control corrects for the known measurement error, as a prerequisite to apply appropriate models in order to better understand the development of individual travel behaviour in a multilevel context. This task is complicated by the fact that variables that inform on survey procedures and outcomes are only provided with the data set for 2002 (see Infas and DIW Berlin, 2003).

Meta-analysis of gene-level associations for rare variants based on single-variant statistics.

Meta-analysis of genome-wide association studies (GWASs) has led to the discoveries of many common variants associated with complex human diseases. There is a growing recognition that identifying "causal" rare variants also requires large-scale meta-analysis. The fact that association tests with rare variants are performed at the gene level rather than at the variant level poses unprecedented challenges in the meta-analysis. First, different studies may adopt different gene-level tests, so the results are not compatible. Second, gene-level tests require multivariate statistics (i.e., components of the test statistic and their covariance matrix), which are difficult to obtain. To overcome these challenges, we propose to perform gene-level tests for rare variants by combining the results of single-variant analysis (i.e., p values of association tests and effect estimates) from participating studies. This simple strategy is possible because of an insight that multivariate statistics can be recovered from single-variant statistics, together with the correlation matrix of the single-variant test statistics, which can be estimated from one of the participating studies or from a publicly available database. We show both theoretically and numerically that the proposed meta-analysis approach provides accurate control of the type I error and is as powerful as joint analysis of individual participant data. This approach accommodates any disease phenotype and any study design and produces all commonly used gene-level tests. An application to the GWAS summary results of the Genetic Investigation of ANthropometric Traits (GIANT) consortium reveals rare and low-frequency variants associated with human height. The relevant software is freely available.

L'erreur en médecine ambulatoire: comment l'aborder. [Error in ambulatory medicine: how to deal with it?]

Medical errors compromise patient safety in ambulatory practice. These errors must be faced in a framework that reduces to a minimum their consequences for the patients. This approach relies on the implementation of a new culture without stigmatization and where errors are disclosed to the patients; this culture implies the build up of a system for reporting errors associated to an in-depth analysis of the system, looking for root causes and insufficient barriers with the aim to fix them. A useful education tool is the "critical situations" meeting during which physicians are encouraged to openly present adverse events and "near misses". Their analysis, with supportive attitude towards involved staff members, allows to reveal systems failures within the institution or the private practice.

Random measurement error and regression dilution bias.

Summary points: - The bias introduced by random measurement error will be different depending on whether the error is in an exposure variable (risk factor) or outcome variable (disease) - Random measurement error in an exposure variable will bias the estimates of regression slope coefficients towards the null - Random measurement error in an outcome variable will instead increase the standard error of the estimates and widen the corresponding confidence intervals, making results less likely to be statistically significant - Increasing sample size will help minimise the impact of measurement error in an outcome variable but will only make estimates more precisely wrong when the error is in an exposure variable

Sample size and statistical power in the hierarchical analysis of variance: applications in morphometry of the nervous system.

Analysis of variance is commonly used in morphometry in order to ascertain differences in parameters between several populations. Failure to detect significant differences between populations (type II error) may be due to suboptimal sampling and lead to erroneous conclusions; the concept of statistical power allows one to avoid such failures by means of an adequate sampling. Several examples are given in the morphometry of the nervous system, showing the use of the power of a hierarchical analysis of variance test for the choice of appropriate sample and subsample sizes. In the first case chosen, neuronal densities in the human visual cortex, we find the number of observations to be of little effect. For dendritic spine densities in the visual cortex of mice and humans, the effect is somewhat larger. A substantial effect is shown in our last example, dendritic segmental lengths in monkey lateral geniculate nucleus. It is in the nature of the hierarchical model that sample size is always more important than subsample size. The relative weight to be attributed to subsample size thus depends on the relative magnitude of the between observations variance compared to the between individuals variance.

Validity of an arterial pressure waveform analysis device: does the puncture site play a role in the agreement with intermittent pulmonary artery catheter thermodilution measurements?

OBJECTIVE: The measurement of cardiac output is a key element in the assessment of cardiac function. Recently, a pulse contour analysis-based device without need for calibration became available (FloTrac/Vigileo, Edwards Lifescience, Irvine, CA). This study was conducted to determine if there is an impact of the arterial catheter site and to investigate the accuracy of this system when compared with the pulmonary artery catheter using the bolus thermodilution technique (PAC). DESIGN: Prospective study. SETTING: The operating room of 1 university hospital. PARTICIPANTS: Twenty patients undergoing cardiac surgery. INTERVENTIONS: CO was determined in parallel by the use of the Flotrac/Vigileo systems in the radial and femoral position (CO_rad and CO_fem) and by PAC as the reference method. Data triplets were recorded at defined time points. The primary endpoint was the comparison of CO_rad and CO_fem, and the secondary endpoint was the comparison with the PAC. MEASUREMENTS AND MAIN RESULTS: Seventy-eight simultaneous data recordings were obtained. The Bland-Altman analysis for CO_fem and CO_rad showed a bias of 0.46 L/min, precision was 0.85 L/min, and the percentage error was 34%. The Bland-Altman analysis for CO_rad and PAC showed a bias of -0.35 L/min, the precision was 1.88 L/min, and the percentage error was 76%. The Bland-Altman analysis for CO_fem and PAC showed a bias of 0.11 L/min, the precision was 1.8 L/min, and the percentage error was 69%. CONCLUSION: The FloTrac/Vigileo system was shown to not produce exactly the same CO data when used in radial and femoral arteries, even though the percentage error was close to the clinically acceptable range. Thus, the impact of the introduction site of the arterial catheter is not negligible. The agreement with thermodilution was low.

Measurement Errors Should Always Be Incorporated in Phylogenetic Comparative Analysis

The evolution of continuous traits is the central component of comparative analyses in phylogenetics, and the comparison of alternative models of trait evolution has greatly improved our understanding of the mechanisms driving phenotypic differentiation. Several factors influence the comparison of models, and we explore the effects of random errors in trait measurement on the accuracy of model selection. We simulate trait data under a Brownian motion model (BM) and introduce different magnitudes of random measurement error. We then evaluate the resulting statistical support for this model against two alternative models: Ornstein-Uhlenbeck (OU) and accelerating/decelerating rates (ACDC). Our analyses show that even small measurement errors (10%) consistently bias model selection towards erroneous rejection of BM in favour of more parameter-rich models (most frequently the OU model). Fortunately, methods that explicitly incorporate measurement errors in phylogenetic analyses considerably improve the accuracy of model selection. Our results call for caution in interpreting the results of model selection in comparative analyses, especially when complex models garner only modest additional support. Importantly, as measurement errors occur in most trait data sets, we suggest that estimation of measurement errors should always be performed during comparative analysis to reduce chances of misidentification of evolutionary processes.

Regression analysis of spatial data.

Many of the most interesting questions ecologists ask lead to analyses of spatial data. Yet, perhaps confused by the large number of statistical models and fitting methods available, many ecologists seem to believe this is best left to specialists. Here, we describe the issues that need consideration when analysing spatial data and illustrate these using simulation studies. Our comparative analysis involves using methods including generalized least squares, spatial filters, wavelet revised models, conditional autoregressive models and generalized additive mixed models to estimate regression coefficients from synthetic but realistic data sets, including some which violate standard regression assumptions. We assess the performance of each method using two measures and using statistical error rates for model selection. Methods that performed well included generalized least squares family of models and a Bayesian implementation of the conditional auto-regressive model. Ordinary least squares also performed adequately in the absence of model selection, but had poorly controlled Type I error rates and so did not show the improvements in performance under model selection when using the above methods. Removing large-scale spatial trends in the response led to poor performance. These are empirical results; hence extrapolation of these findings to other situations should be performed cautiously. Nevertheless, our simulation-based approach provides much stronger evidence for comparative analysis than assessments based on single or small numbers of data sets, and should be considered a necessary foundation for statements of this type in future.

Advanced geostatistical and machine-learning models for spatial data analysis of radioactively contaminated regions

Radioactive soil-contamination mapping and risk assessment is a vital issue for decision makers. Traditional approaches for mapping the spatial concentration of radionuclides employ various regression-based models, which usually provide a single-value prediction realization accompanied (in some cases) by estimation error. Such approaches do not provide the capability for rigorous uncertainty quantification or probabilistic mapping. Machine learning is a recent and fast-developing approach based on learning patterns and information from data. Artificial neural networks for prediction mapping have been especially powerful in combination with spatial statistics. A data-driven approach provides the opportunity to integrate additional relevant information about spatial phenomena into a prediction model for more accurate spatial estimates and associated uncertainty. Machine-learning algorithms can also be used for a wider spectrum of problems than before: classification, probability density estimation, and so forth. Stochastic simulations are used to model spatial variability and uncertainty. Unlike regression models, they provide multiple realizations of a particular spatial pattern that allow uncertainty and risk quantification. This paper reviews the most recent methods of spatial data analysis, prediction, and risk mapping, based on machine learning and stochastic simulations in comparison with more traditional regression models. The radioactive fallout from the Chernobyl Nuclear Power Plant accident is used to illustrate the application of the models for prediction and classification problems. This fallout is a unique case study that provides the challenging task of analyzing huge amounts of data ('hard' direct measurements, as well as supplementary information and expert estimates) and solving particular decision-oriented problems.

Analysis and spatial modeling of the indoor radon Swiss data

The present research deals with an important public health threat, which is the pollution created by radon gas accumulation inside dwellings. The spatial modeling of indoor radon in Switzerland is particularly complex and challenging because of many influencing factors that should be taken into account. Indoor radon data analysis must be addressed from both a statistical and a spatial point of view. As a multivariate process, it was important at first to define the influence of each factor. In particular, it was important to define the influence of geology as being closely associated to indoor radon. This association was indeed observed for the Swiss data but not probed to be the sole determinant for the spatial modeling. The statistical analysis of data, both at univariate and multivariate level, was followed by an exploratory spatial analysis. Many tools proposed in the literature were tested and adapted, including fractality, declustering and moving windows methods. The use of Quan-tité Morisita Index (QMI) as a procedure to evaluate data clustering in function of the radon level was proposed. The existing methods of declustering were revised and applied in an attempt to approach the global histogram parameters. The exploratory phase comes along with the definition of multiple scales of interest for indoor radon mapping in Switzerland. The analysis was done with a top-to-down resolution approach, from regional to local lev¬els in order to find the appropriate scales for modeling. In this sense, data partition was optimized in order to cope with stationary conditions of geostatistical models. Common methods of spatial modeling such as Κ Nearest Neighbors (KNN), variography and General Regression Neural Networks (GRNN) were proposed as exploratory tools. In the following section, different spatial interpolation methods were applied for a par-ticular dataset. A bottom to top method complexity approach was adopted and the results were analyzed together in order to find common definitions of continuity and neighborhood parameters. Additionally, a data filter based on cross-validation was tested with the purpose of reducing noise at local scale (the CVMF). At the end of the chapter, a series of test for data consistency and methods robustness were performed. This lead to conclude about the importance of data splitting and the limitation of generalization methods for reproducing statistical distributions. The last section was dedicated to modeling methods with probabilistic interpretations. Data transformation and simulations thus allowed the use of multigaussian models and helped take the indoor radon pollution data uncertainty into consideration. The catego-rization transform was presented as a solution for extreme values modeling through clas-sification. Simulation scenarios were proposed, including an alternative proposal for the reproduction of the global histogram based on the sampling domain. The sequential Gaussian simulation (SGS) was presented as the method giving the most complete information, while classification performed in a more robust way. An error measure was defined in relation to the decision function for data classification hardening. Within the classification methods, probabilistic neural networks (PNN) show to be better adapted for modeling of high threshold categorization and for automation. Support vector machines (SVM) on the contrary performed well under balanced category conditions. In general, it was concluded that a particular prediction or estimation method is not better under all conditions of scale and neighborhood definitions. Simulations should be the basis, while other methods can provide complementary information to accomplish an efficient indoor radon decision making.

A novel approach to reducing number of sensing units for wearable gait analysis systems.

Gait analysis methods to estimate spatiotemporal measures, based on two, three or four gyroscopes attached on lower limbs have been discussed in the literature. The most common approach to reduce the number of sensing units is to simplify the underlying biomechanical gait model. In this study, we propose a novel method based on prediction of movements of thighs from movements of shanks. Datasets from three previous studies were used. Data from the first study (ten healthy subjects and ten with Parkinson's disease) were used to develop and calibrate a system with only two gyroscopes attached on shanks. Data from two other studies (36 subjects with hip replacement, seven subjects with coxarthrosis, and eight control subjects) were used for comparison with the other methods and for assessment of error compared to a motion capture system. Results show that the error of estimation of stride length compared to motion capture with the system with four gyroscopes and our new method based on two gyroscopes was close ( -0.8 ±6.6 versus 3.8 ±6.6 cm). An alternative with three sensing units did not show better results (error: -0.2 ±8.4 cm). Finally, a fourth that also used two units but with a simpler gait model had the highest bias compared to the reference (error: -25.6 ±7.6 cm). We concluded that it is feasible to estimate movements of thighs from movements of shanks to reduce number of needed sensing units from 4 to 2 in context of ambulatory gait analysis.