Extreme Data Points Research Articles

Models…

The year 2016 was, especially for people who professionally deal with statistics, a very interesting year. Especially two events caused more than a bit of turmoil in our profession: the Brexit referendum and the recent US presidential elections. The most interesting observation was the response of the media “the day after the night before”: “this outcome was considered extremely unlikely even in the best models available”. People, in both cases, just showed a different behavior than that what was included in these models. This is an issue I have addressed also in earlier editorials in this journal: in many papers that are published in this journal (and in even more papers that do not make it to publication), often very sophisticated models are used as part of a prediction and/or optimization process without even remotely addressing possible underlying effects that can totally change the predicted outcome. As the two examples that were mentioned have illustrated, even models that have been used for decades can lose their validity because of, earlier unknown, mechanisms that can start play a role at unexpected/unanticipated moments. In teaching statistics and, especially, data analytics we are in our university therefore reconsidering our education methods in this field. The idea is to spend less time on the statistical details of various models but to teach students especially to look into the underlying mechanisms that determine a model. Are there (new) trends that can be of relevance and are these trends taken into account? Are there, especially, outliers in datasets that may require a more detailed analysis? Are there systematic/systemic effects that may be of relevance and how are these effects covered in the available models? The focus is here to teach students more to the extreme data points and their underlying mechanisms than to the “goodness of fit” of a given model to the majority of a set of data points. This is, at our university, not only new for students but often also for the lecturers involved. For many of them, it has been quite a while since they went out into the field looking into underlying phenomena instead of looking into clouds of data points on a computer screen. I do not say that with this approach we would have been able to better predict the outcome of the two stated events. But, at least, the outcome could have come with less surprises….

Identification of ringing operation for low temperature combustion engines

High-efficiency and low-emission low temperature combustion modes including homogeneous charge compression ignition (HCCI) are limited at high load conditions due to rapid pressure rise rate, short combustion duration and ringing operation. This study uses two different HCCI engines to investigate combustion-generated ringing at a number of HCCI engine operating points between misfire and ringing zones for ethanol and n-heptane fuels. Ringing intensity (RI) is investigated along with main HCCI combustion parameters and engine-out emissions. The results show the RI generally increases by advancing crank angle of 50% fuel burnt (CA50) and also decreasing burn duration (BD). It is found that adjusting CA50 can provide a control knob for the RI since all the extreme noisy data points have CA50<9 CAD aTDC. In-cylinder pressure at 5, 10, 15 CAD aTDC (P5,P10 and P15) and maximum in-cylinder pressure (Pmax) show strong correlation with RI. To this end, P5,P10 and P15 and Pmax are used to develop an artificial neural network (ANN) model to predict RI. Experimental data at 155 steady-state points are used to evaluate the ANN model for two totally different HCCI engines running with high and low octane fuels. The validation results indicate that the ANN model can predict RI with less than 4.2% error. The ANN model can be used to identify HCCI ringing operation for combustion control applications.

Resistant measures in assessing the adequacy of split-plot design models

This paper assesses the adequacy of model fit of the split-plot design models, that is the whole plot (WP) sub-design model with WP error and the split-plot (SP) sub-design model with SP error for comparing the effectiveness of resistant measures that use medians instead of means, resulting in a coefficient that is more resistant to outliers or extreme data points. This paper presents empirical application of four measures of model adequacy check and they are coefficient of determination (R2), modelling efficiency (MEF) statistic, prediction coefficient of determination (R2prod), and mean square error prediction (MSEP). These four measures were explored using their mean and median form. A 2(1+3) replicated two-level SP design and a 31 × 42 replicated mixed level SP design were used for computing the measures of model adequacy of fit for each WP and SP sub-design models. These measures in their median form described the predictive performance of each WP and SP sub-design models adequately.

Methods for identifying subject-specific abnormalities in neuroimaging data.

Algorithms that are capable of capturing subject-specific abnormalities (SSA) in neuroimaging data have long been an area of focus for diverse neuropsychiatric conditions such as multiple sclerosis, schizophrenia, and traumatic brain injury. Several algorithms have been proposed that define SSA in patients (i.e., comparison group) relative to image intensity levels derived from healthy controls (HC) (i.e., reference group) based on extreme values. However, the assumptions underlying these approaches have not always been fully validated, and may be dependent on the statistical distributions of the transformed data. The current study evaluated variations of two commonly used techniques ("pothole" method and standardization with an independent reference group) for identifying SSA using simulated data (derived from normal, t and chi-square distributions) and fractional anisotropy maps derived from 50 HC. Results indicated substantial group-wise bias in the estimation of extreme data points using the pothole method, with the degree of bias being inversely related to sample size. Statistical theory was utilized to develop a distribution-corrected z-score (DisCo-Z) threshold, with additional simulations demonstrating elimination of the bias and a more consistent estimation of extremes based on expected distributional properties. Data from previously published studies examining SSA in mild traumatic brain injury were then re-analyzed using the DisCo-Z method, with results confirming the evidence of group-wise bias. We conclude that the benefits of identifying SSA in neuropsychiatric research are substantial, but that proposed SSA approaches require careful implementation under the different distributional properties that characterize neuroimaging data.

Robust Ellipse Fitting Based on Sparse Combination of Data Points

Ellipse fitting is widely applied in the fields of computer vision and automatic industry control, in which the procedure of ellipse fitting often follows the preprocessing step of edge detection in the original image. Therefore, the ellipse fitting method also depends on the accuracy of edge detection besides their own performance, especially due to the introduced outliers and edge point errors from edge detection which will cause severe performance degradation. In this paper, we develop a robust ellipse fitting method to alleviate the influence of outliers. The proposed algorithm solves ellipse parameters by linearly combining a subset of ("more accurate") data points (formed from edge points) rather than all data points (which contain possible outliers). In addition, considering that squaring the fitting residuals can magnify the contributions of these extreme data points, our algorithm replaces it with the absolute residuals to reduce this influence. Moreover, the norm of data point errors is bounded, and the worst case performance optimization is formed to be robust against data point errors. The resulting mixed l1-l2 optimization problem is further derived as a second-order cone programming one and solved by the computationally efficient interior-point methods. Note that the fitting approach developed in this paper specifically deals with the overdetermined system, whereas the current sparse representation theory is only applied to underdetermined systems. Therefore, the proposed algorithm can be looked upon as an extended application and development of the sparse representation theory. Some simulated and experimental examples are presented to illustrate the effectiveness of the proposed ellipse fitting approach.

An Extreme Function Theory for Novelty Detection

We introduce an extreme function theory as a novel method by which probabilistic novelty detection may be performed with functions, where the functions are represented by time-series of (potentially multivariate) discrete observations. We set the method within the framework of Gaussian processes (GP), which offers a convenient means of constructing a distribution over functions. Whereas conventional novelty detection methods aim to identify individually extreme data points, with respect to a model of normality constructed using examples of “normal” data points, the proposed method aims to identify extreme functions, with respect to a model of normality constructed using examples of “normal” functions, where those functions are represented by time-series of observations. The method is illustrated using synthetic data, physiological data acquired from a large clinical trial, and a benchmark time-series dataset.

What makes a “research star”? Factors influencing the research productivity of business faculty

PurposeThe purpose of this paper is to identify factors influencing extremely high or low research productivity for business faculty members.Design/methodology/approachUsing data originating from a random sample of 236 faculty members across a wide range of accredited business schools and a web‐based survey, main effects are hypothesized and explored. The authors examine only extreme data points of high (and low) research productivity to focus on high‐performing research “stars.”FindingsIt is found that research “stars” hold higher academic rank, possess greater time management skills, individually place a high value on research, report higher time available to conduct research, enjoy higher institutional support in the form of graduate assistants and summer research support, have fewer course preparations, and work for departments with a similar priority placed on research.Research limitations/implicationsThe authors found that certain person‐ and situation‐level factors differentiate high and low performing faculty members’ research output.Practical implicationsThe paper has implications for university administrators regarding recruiting, selecting, and managing faculty members’ research performance.Originality/valueResearch productivity and intellectual contributions continue to dominate much of higher education as a primary measure of faculty members’ success. One area that remains under‐explored in the business literature is what “makes a research star” and, to the contrary, what factors predict extremely low faculty research productivity? Shedding light on this research question provides practical benefits for universities by enabling administrators to better recruit, select, motivate, and develop productive faculty members.

Information‐theoretic model selection affects home‐range estimation and habitat preference inference: a case study of male Reeves’s Pheasants Syrmaticus reevesii

Reeves’s Pheasant Syrmaticus reevesii is a vulnerable forest bird inhabiting broadleaved habitats dominated by oaks Quercus spp. in central China. Identifying home‐ranges and habitat associations is important for understanding the biology of this species and developing effective management and conservation plans. We used information‐theoretic criteria to evaluate the relative performance of four parametric (exponential power, one‐mode bivariate normal, two‐mode bivariate normal and two‐mode bivariate circle) and two non‐parametric models (adaptive and fixed kernel) for estimating home‐ranges and habitat associations of Reeves’s Pheasants. For parametric models, Akaike’s information criterion (AICc) and the likelihood cross‐validation criterion (CVC) were relatively consistent in ranking the bivariate exponential power model the least acceptable, whereas the two‐mode bivariate models performed better. The CVC suggested that kernel models, particularly the adaptive kernel, performed best among all six models evaluated. The average core area and 95% contour area based on the model with greatest support were 6.1 and 54.9 ha, respectively, and were larger than those estimated from other models. The discrepancy in estimates between models with highest and the lowest support decreased as the contour size increased; however, home‐range shapes differed between models. Minimum convex polygons that removed 5% of extreme data points (MCP95) were roughly half the size of home‐ranges based on kernel models. Estimates of home‐range and model evaluation were not affected by sample size (&gt; 50 observations for each bird). Inference about habitat preference based on composition analysis and home‐range overlap varied between models. That with strongest support suggested that Reeves’s Pheasants selected mature fir and mixed forest, avoided farmland, and had mean among‐individual home‐range overlaps of 20%. We recommend non‐parametric methods, particularly the adaptive kernel method, for estimating home‐ranges and core areas for species with complex multi‐polar habitat preferences in heterogeneous environments with large habitat patches. However, we caution against the traditional convenience of using a single model to estimate home‐ranges and recommend exploration of multiple models for describing and understanding the ecological processes underlying space use and habitat associations.

Asbestos fiber concentrations in the lungs of brake repair workers: commercial amphiboles levels are predictive of chrysotile levels

Objectives: To investigate the impact of extreme data points in Finkelstein’s 2009 findings of no association between lung levels of commercial and non-commercial amphiboles (principally tremolite as a marker for chrysotile asbestos) in brake repair workers with mesothelioma.Methods: We first identified potential outliers, high leverage points, and influential points among lung levels of commercial amphiboles and tremolite among 15 persons whose only known exposure to asbestos was through brake repair work. We used sensitivity analysis and quantile regression to account for extreme data points and model commercial amphibole levels as a predictor of tremolite levels. We also used quantile regression to evaluate whether case-reported duration of employment as a brake repair worker predicted lung levels of commercial amphiboles or tremolite.Results: We found lung levels of commercial amphiboles are a statistically significant predictor of tremolite levels via sensitivity analysis (r = 0.82, slope estimate P-value = 0.001, R2 = 0.68) and quantile regression (slope estimate P-value <0.0001). Our data provide no evidence that duration of employment as a brake repair worker was a predictor of lung levels of tremolite or commercial amphiboles.Conclusions: Our findings suggest that elevated lung levels of tremolite in the lungs of brake repair workers with elevated levels of amphiboles arose from concurrent exposures to commercial amphibole and chrysotile asbestos in occupational settings other than brake repair work. These findings are supported by five new cases. The weight of the scientific evidence does not support a role for occupational exposure to brake dust and other friction products in the development of mesothelioma.

662: Power spectral analysis of trans-abdominal fetal ECG at the beginning of labour as a predictor of adverse pregnancy outcome

To evaluate fetal heart rate, obtained by trans-abdominal ECG-RR intervals, by power spectral density (PSD) and compare normal values with findings obtained in acidemic fetuses Non invasive transabdominal fetal ECG with Monica AN24 device was performed in labour in uncomplicated term pregnancies. Thirty-six fetal ECG traces were collected at the beginning of labour from patients that delivered neonates with normal outcome (pH>7.20, BE<5, Apgar at 1 and 5min 10-10). Comparative analysis was performed with two cases with adverse outcome (pH<7.0, BE>12, Apgar at 5 min ≤7). Thirty minutes records were used for each patient. Due to non-uniformly sampled data a Lomb-Scargle periodogram was used to estimate the power spectral density at ultra low (0.00083 – 0.003), very low (0.003 – 0.04), low (0.04 – 0.15 Hz), high (0.15 – 0.4 Hz) and very high frequencies (0.4 – 0.92 Hz). The graph shows the data represented through box plots. The boxes represent the inter-quartile range and the whiskers represent the most extreme data points, which are not considered outliers. The two fetuses with an abnormal hypoxic outcome did not show any difference in power spectral analysis values since their findings fitted within the interquartile range of normal cases. This is the first reported PSD analysis in non-uniformly sampled data by means of Lomb-Scargle periodogram. We were able to define the relative power spectral analysis of ultra low, very low, low, high and very high frequencies of trans-abdominal fetal ECG in early labour in healthy fetuses. Two fetuses that subsequently developed acidemia did not show any difference in power spectral densities in early stages of labour. This finding suggests that possible changes of the autonomous nervous system balance may not present early in labour in cases where intrapartum asphyxia, confirmed at birth, develops progressively during the labour.

Game-Miners Grapple With Massive Data

Researchers have been using massively multiplayer online games as natural laboratories, but the data are a challenge to interpret. At the meeting, a computer scientist presented results obtained using a mathematical tool called archetype analysis that works by identifying the most extreme data points and describes the rest as combinations of these archetypes.

Absence of Evidence for MHC–Dependent Mate Selection within HapMap Populations

The major histocompatibility complex (MHC) of immunity genes has been reported to influence mate choice in vertebrates, and a recent study presented genetic evidence for this effect in humans. Specifically, greater dissimilarity at the MHC locus was reported for European-American mates (parents in HapMap Phase 2 trios) than for non-mates. Here we show that the results depend on a few extreme data points, are not robust to conservative changes in the analysis procedure, and cannot be reproduced in an equivalent but independent set of European-American mates. Although some evidence suggests an avoidance of extreme MHC similarity between mates, rather than a preference for dissimilarity, limited sample sizes preclude a rigorous investigation. In summary, fine-scale molecular-genetic data do not conclusively support the hypothesis that mate selection in humans is influenced by the MHC locus.

Data boundary fitting using a generalized least-squares method

In many astronomical problems one often needs to determine the upper and/or lower boundary of a given data set. An automatic and objective approach consists in fitting the data using a generalised least-squares method, where the function to be minimized is defined to handle asymmetrically the data at both sides of the boundary. In order to minimise the cost function, a numerical approach, based on the popular downhill simplex method, is employed. The procedure is valid for any numerically computable function. Simple polynomials provide good boundaries in common situations. For data exhibiting a complex behaviour, the use of adaptive splines gives excellent results. Since the described method is sensitive to extreme data points, the simultaneous introduction of error weighting and the flexibility of allowing some points to fall outside of the fitted frontier, supplies the parameters that help to tune the boundary fitting depending on the nature of the considered problem. Two simple examples are presented, namely the estimation of spectra pseudo-continuum and the segregation of scattered data into ranges. The normalisation of the data ranges prior to the fitting computation typically reduces both the numerical errors and the number of iterations required during the iterative minimisation procedure.

Genetic evaluation of growth of Kenya Boran cattle using random regression models

Data consisting of 18 884 weight records collected from 1273 Boran cattle from birth to 24 months of age were used to estimate covariance functions and genetic parameters for growth of Boran cattle using random regression (RR) models under a situation of small herd size and inconsistent recording. The RR model fitted quadratic Legendre polynomials of age at recording for additive genetic and permanent environmental effects. Genetic variance increased from birth, reaching an asymptotic value at 455 days and was maximum at 525 days of age after which it gradually dropped. Permanent environmental variance increased throughout the trajectory. Estimates of temporary environmental variance were heterogeneous across ages. Direct heritability and permanent environmental variance as a proportion of phenotypic variance fluctuated greatly during the early ages but later stabilized at intermediate to later ages; the estimates ranged from 0.11 to 0.33 and from 0.18 to 0.83, respectively. Genetic correlation estimates were positive, ranging from 0.10 to unity. The estimates declined with increasing in lag between the age points. Phenotypic correlation pattern was erratic between early ages, negatively low (-0.02) between the extreme data points and moderate to highly positive (>0.50) between intermediate and later points, with prominent spikes along the diagonal. It is concluded that RR models have potential for modelling growth of Boran cattle, notwithstanding conditions of small herd sizes and inconsistent recording.

Is there a positive association between mammographic density and bone mineral density? Authors' response

We read with interest the issues raised by Dite and coworkers [1] in their response to our recent research article [2], and we are pleased to address them. In their letter, Dite and colleagues present previously unpublished results that reveal no association between bone mineral density and mammographic density in female twins. Relevant information about the characteristics of the study participants, the methods of measuring mammographic density, and the timing of the mammograms in relation to the bone density assessment are not supplied. Differences in study samples, methods, and sample size could account for the difference between their results and ours. Dite and coworkers [1] posit several explanations for the apparent discrepancy between their study and ours. First, they suggest that our results were an artefact of our performance of multiple analyses. In fact, we performed only three regression analyses, and these analyses were based on clearly stipulated a priori hypotheses. We believe that a strict Bonferroni adjustment for multiple testing would have been overly conservative. Second, they argue that we might have been misled by outliers or influential points. However, we performed outlier analyses using the dfBeta approach [3], which confirmed that our results were not unduly influenced by extreme data points. It is impossible to rule out chance as a possible explanation for our results, but with a few exceptions this criticism applies to all studies. Finally, Dite and colleagues state that we might have assumed effect modification without testing for it. We tested for effect modification between recent use of hormone therapy and lumbar bone mineral density by adding an interaction term to the linear regression model that included age, body mass index, smoking, lumbar bone mineral density, and recent hormone therapy as covariates, and mammographic density as the outcome. The P value for the lumbar bone mineral density-recent hormone therapy interaction term was 0.0583 at the lumbar spine. Similar results were apparent at the hip (P = 0.094 for the interaction term). On this basis, we conclude that recent hormone therapy modifies the association between bone mineral density and mammographic density. We stand by our results and hope to elucidate what biologic factors may be responsible for the association between mammographic density and bone mineral density in our study.

On-line signal quality estimation of multichannel surface electromyograms

When multichannel surface-electromyography (MCSEMG) systems are used, there is a risk of recording low-quality signals. Such signals can be confusing for analysis and interpretation and can be caused by power-line interference, motion artifacts or poor electrode-skin contact. Usually, the electrode-skin impedance is measured to estimate the quality of the contact between the electrodes and the skin. However, this is not always practical, and the contact can change over short time-scales. A fast method is described to estimate the quality of individual signals of monopolar MCSEMG recordings based on volume conduction of myo-electric signals. The characteristics of the signals were described using two descriptor variables. Outliers (extreme data points) were detected in the two-dimensional distributions of the descriptor variables using a non-parametric technique, and the quality of the signals was estimated by their outlier probabilities. The method's performance was evaluated using 1 s long signals visually classified as very poor (G 1), poor (G2) or good quality (G3). Recordings from different subjects, contraction levels and muscles were used. An optimum threshold at 0.05 outlier probability was proposed and resulted in classification accuracies of 100% and > 70% for G I and G2 signals, respectively, whereas <5% of the G3 signals were classified as poor. In conclusion, the proposed method estimated MCSEMG signal quality with high accuracy, compared with visual assessment, and is suitable for on-line implementation. The method could be applied to other multichannel sensor systems, with an arbitrary number of descriptor variables, when their distributions can be assumed to lie within a certain range.

Metal content of surface soils in parks and allotments from three European cities: initial pilot study results

A pilot study of metal content and basic soil properties was undertaken in a number of parks and allotments in the cities of Glasgow, UK, Torino, Italy, and Sevilla, Spain. Between 40 and 60 samples were collected from each city, with soil from two depths. The maximum metal contents (aqua regia) found were 698 mg/kg Cu; 1004 mg/kg Zn; 300 mg/kg Ni; 356 mg/kg Cr and 7051 mg/kg Pb. Variability of metal content showed similar patterns across all cities, with a number of outlier data points. Surface and subsurface samples were comparable within sites. Cu, Zn and Pb levels appeared to contain most variability and extreme data points, while Ni and Cr were more homogeneous. The data support previously published observations of anthropogenic association (Cu, Zn and Pb) and natural sources (Ni and Cr), found in urban environments influenced by diffuse pollution. Within the Glasgow data, differences in the variability of metal content in park and allotment soil are not dramatic, but do reflect the influence of different agronomic activities. The study has provided baseline information for ongoing pan-European urban soil research funded through the EU.

Production dynamics of intensively managed loblolly pine stands in the southern United States: a synthesis of seven long-term experiments

Results from seven long-term experiments in the southern US were summarized to understand production dynamics of intensively managed loblolly pine plantations. Replicated studies that spanned a wide range of soil and climatic conditions were established (North Carolina—NC; Georgia—GA (three sites); Florida—FL; Louisiana—LA; Oklahoma—OK). All experiments received some combination of silvicultural treatments, including fertilizer application, understory competition control, irrigation, and thinning. Accumulation of stemwood biomass at age 15 years varied among sites and ranged from 70 Mg ha −1 (NC) to 180 Mg ha −1 (GA). All sites that received fertilizer and weed control applications were responsive to treatments, and growth responses ranged from about 2-fold (GA) to 3.5-fold (FL) at age 15 years. Variation in fertilizer responses among sites reflected differences in soil types, inherent site quality, and stages of stand development. Site carrying capacity, expressed as maximum basal area attained in closed canopy stands, was surprisingly consistent among sites and climatic conditions, reaching 45–48 m 2 ha −1 under the most intensive silvicultural treatments. Across studies, competition-related mortality was initiated as stand basal areas approached 30–35 m 2 ha −1, and annual stemwood biomass increment peaked as basal areas reached about 20–35 m 2 ha −1. These data suggest that a regional maximum in stand density occurs for loblolly pine when regular fertilizer additions are made or inherent soil nutrient supply is high. Periodic density management will be required to minimize reductions in individual tree and net stand growth. Wood specific gravity at a standard ring age of 10–11 years varied both among sites and by treatment within sites, and ranged from approximately 0.45 (OK site) to 0.56 (GA sites). Maximum leaf area index (LAI) among sites varied from about 2.5 to 6.5. The relationship between stemwood biomass increment and LAI across sites was strong at LAI levels <3.0, but was considerably more variable at higher LAIs. Variation in stemwood increment at higher LAIs was substantially reduced, however, when extreme data points were removed; a logistic function explained 75% of the variation in stemwood increment across all sites. Differences in productivity among sites were not strongly related to site water balance. Taken together, these results support other work which suggests that soil nutrient availability is the dominant driver of loblolly pine productivity across its natural range. Future research should seek to better understand the mechanisms of nutrient demand, uptake and utilization efficiency in developing stands, as well as the factors controlling intraspecific tree competition.

Detecting outliers in frontier models : a simple approach.

In frontier analysis, most of the nonparametric approaches (DEA, FDH) are based on envelopment ideas which suppose that with probability one, all the observed units belong to the attainable set. In these "deterministic'' frontier models, statistical theory is now mostly available (Simar and Wilson, 2000a). In the presence of superefficient outliers, envelopment estimators could behave dramatically since they are very sensitive to extreme observations. Some recent results from Cazals et al. (2002) on robust nonparametric frontier estimators may be used in order to detect outliers by de. ning a new DEA/FDH "deterministic'' type estimator which does not envelop all the data points and so is more robust to extreme data points. In this paper, we summarize the main results of Cazals et al. (2002) and we show how this tool can be used for detecting outliers when using the classical DEA/FDH estimators or any parametric techniques. We propose a methodology implementing the tool and we illustrate through some numerical examples with simulated and real data. The method should be used in a first step, as an exploratory data analysis, before using any frontier estimation.

Teaching the concept of breakdown point in simple linear regression

Most introductory textbooks on simple linear regression analysis mention the fact that extreme data points have a great influence on ordinary least-squares (OLS) regression estimation. However, not many textbooks provide a rigorous mathematical explanation of this phenomenon. In this note a way is suggested to fill this gap by teaching students the concept of breakdown point.