When zero doesn't mean it and other geomathematical mischief

There is almost not a case in exploration geology, where the studied data doesn’tincludes below detection limits and/or zero values, and since most of the geological dataresponds to lognormal distributions, these “zero data” represent a mathematicalchallenge for the interpretation.We need to start by recognizing that there are zero values in geology. For example theamount of quartz in a foyaite (nepheline syenite) is zero, since quartz cannot co-existswith nepheline. Another common essential zero is a North azimuth, however we canalways change that zero for the value of 360°. These are known as “Essential zeros”, butwhat can we do with “Rounded zeros” that are the result of below the detection limit ofthe equipment?Amalgamation, e.g. adding Na2O and K2O, as total alkalis is a solution, but sometimeswe need to differentiate between a sodic and a potassic alteration. Pre-classification intogroups requires a good knowledge of the distribution of the data and the geochemicalcharacteristics of the groups which is not always available. Considering the zero valuesequal to the limit of detection of the used equipment will generate spuriousdistributions, especially in ternary diagrams. Same situation will occur if we replace thezero values by a small amount using non-parametric or parametric techniques(imputation).The method that we are proposing takes into consideration the well known relationshipsbetween some elements. For example, in copper porphyry deposits, there is always agood direct correlation between the copper values and the molybdenum ones, but whilecopper will always be above the limit of detection, many of the molybdenum values willbe “rounded zeros”. So, we will take the lower quartile of the real molybdenum valuesand establish a regression equation with copper, and then we will estimate the“rounded” zero values of molybdenum by their corresponding copper values.The method could be applied to any type of data, provided we establish first theircorrelation dependency.One of the main advantages of this method is that we do not obtain a fixed value for the“rounded zeros”, but one that depends on the value of the other variable.Key words: compositional data analysis, treatment of zeros, essential zeros, roundedzeros, correlation dependency

U.S. subprime financial crisis contagion on BRIC and European Union stock markets

ABSTRACTThe Copula Theory was used to analyze contagion among the BRIC (Brazil, Russia, India and China) and European Union stock markets with the U.S. Equity Market. The market indexes used for the period between January 01, 2005 and February 27, 2010 are: MXBRIC (BRIC), MXEU (European Union) and MXUS (United States). This article evaluated the adequacy of the main copulas found in the financial literature using log-likelihood, Akaike information and Bayesian information criteria. This article provides a groundbreaking study in the area of contagion due to the use of conditional copulas, allowing to calculate the correlation increase between indexes with non-parametric approach. The conditional Symmetrized Joe-Clayton copula was the one that fitted better to the considered pairs of returns. Results indicate evidence of contagion effect in both markets, European Union and BRIC members, with a 5% significance level. Furthermore, there is also evidence that the contagion of U.S. financial crisis was more pronounced in the European Union than in the BRIC markets, with a 5% significance level. Therefore, stock portfolios formed by equities from the BRIC countries were able to offer greater protection during the subprime crisis. The results are aligned with recent papers that present an increase in correlation between stock markets, especially in bear markets.

A note on schooling in development accounting

How much would output increase if underdeveloped economies were to increase their levels of schooling? We contribute to the development accounting literature by describing a non-parametric upper bound on the increase in output that can be generated by more schooling. The advantage of our approach is that the upper bound is valid for any number of schooling levels with arbitrary patterns of substitution/complementarity. Another advantage is that the upper bound is robust to certain forms of endogenous technology response to changes in schooling. We also quantify the upper bound for all economies with the necessary data, compare our results with the standard development accounting approach, and provide an update on the results using the standard approach for a large sample of countries.

Detection of Optimal Models in Parameter Space with Support Vector Machines

The paper proposes an approach aimed at detecting optimal model parameter combinations to achieve the most representative description of uncertainty in the model performance. A classification problem is posed to find the regions of good fitting models according to the values of a cost function. Support Vector Machine (SVM) classification in the parameter space is applied to decide if a forward model simulation is to be computed for a particular generated model. SVM is particularly designed to tackle classification problems in high-dimensional space in a non-parametric and non-linear way. SVM decision boundaries determine the regions that are subject to the largest uncertainty in the cost function classification, and, therefore, provide guidelines for further iterative exploration of the model space. The proposed approach is illustrated by a synthetic example of fluid flow through porous media, which features highly variable response due to the parameter values' combination.

Myocardial flow reserve by Rb-82 cardiac PET improves the selection of patients eligible for invasive coronary angiography

Aim: We asked whether myocardial flow reserve (MFR) by Rb-82 cardiac PET improve the selection of patients eligible for invasive coronary angiography (ICA). Material and Methods: We enrolled 26 consecutive patients with suspected or known coronary artery disease who performed dynamic Rb-82 PET/CT and (ICA) within 60 days; 4 patients who underwent revascularization or had any cardiovascular events between PET and ICA were excluded. Myocardial blood flow at rest (rMBF), at stress with adenosine (sMBF) and myocardial flow reserve (MFR=sMBF/rMBF) were estimated using the 1-compartment Lortie model (FlowQuant) for each coronary arteries territories. Stenosis severity was assessed using computer-based automated edge detection (QCA). MFR was divided in 3 groups: G1:MFR<1.5, G2:1.5≤MFR<2 and G3:2≤MFR. Stenosis severity was graded as non-significant (<50% or FFR ≥0.8), intermediate (50%≤stenosis<70%) and severe (≥70%). Correlation between MFR and percentage of stenosis were assessed using a non-parametric Spearman test. Results: In G1 (44 vessels), 17 vessels (39%) had a severe stenosis, 11 (25%) an intermediate one, and 16 (36%) no significant stenosis. In G2 (13 vessels), 2 (15%) vessels presented a severe stenosis, 7 (54%) an intermediate one, and 4 (31%) no significant stenosis. In G3 (9 vessels), 0 vessel presented a severe stenosis, 1 (11%) an intermediate one, and 8 (89%) no significant stenosis. Of note, among 11 patients with 3-vessel low MFR<1.5 (G1), 9/11 (82%) had at least one severe stenosis and 2/11 (18%) had at least one intermediate stenosis. There was a significant inverse correlation between stenosis severity and MFR among all 66 territories analyzed (rho= -0.38, p=0.002). Conclusion: Patients with MFR>2 could avoid ICA. Low MFR (G1, G2) on a vessel-based analysis seems to be a poor predictor of severe stenosis severity. Patients with 3-vessel low MFR would benefit from ICA as they are likely to present a significant stenosis in at least one vessel.

The contribution of schooling in development accounting: Results from a nonparametric upper bound

How much would output increase if underdeveloped economies were toincrease their levels of schooling? We contribute to the development accounting literature by describing a non-parametric upper bound on theincrease in output that can be generated by more schooling. The advantage of our approach is that the upper bound is valid for any number ofschooling levels with arbitrary patterns of substitution/complementarity.Another advantage is that the upper bound is robust to certain forms ofendogenous technology response to changes in schooling. We also quantify the upper bound for all economies with the necessary data, compareour results with the standard development accounting approach, andprovide an update on the results using the standard approach for a largesample of countries.

Forecasting with missing data: Application to a real case

This paper presents a comparative analysis of linear and mixed modelsfor short term forecasting of a real data series with a high percentage of missing data. Data are the series of significant wave heights registered at regular periods of three hours by a buoy placed in the Bay of Biscay.The series is interpolated with a linear predictor which minimizes theforecast mean square error. The linear models are seasonal ARIMA models and themixed models have a linear component and a non linear seasonal component.The non linear component is estimated by a non parametric regression of dataversus time. Short term forecasts, no more than two days ahead, are of interestbecause they can be used by the port authorities to notice the fleet.Several models are fitted and compared by their forecasting behavior.

Adaptive model selection using empirical complexities

Given $n$ independent replicates of a jointly distributed pair $(X,Y)\in {\cal R}^d \times {\cal R}$, we wish to select from a fixed sequence of model classes ${\cal F}_1, {\cal F}_2, \ldots$ a deterministic prediction rule $f: {\cal R}^d \to {\cal R}$ whose risk is small. We investigate the possibility of empirically assessingthe {\em complexity} of each model class, that is, the actual difficulty of the estimation problem within each class. The estimated complexities are in turn used to define an adaptive model selection procedure, which is based on complexity penalized empirical risk.The available data are divided into two parts. The first is used to form an empirical cover of each model class, and the second is used to select a candidate rule from each cover based on empirical risk. The covering radii are determined empirically to optimize a tight upper bound on the estimation error. An estimate is chosen from the list of candidates in order to minimize the sum of class complexity and empirical risk. A distinguishing feature of the approach is that the complexity of each model class is assessed empirically, based on the size of its empirical cover.Finite sample performance bounds are established for the estimates, and these bounds are applied to several non-parametric estimation problems. The estimates are shown to achieve a favorable tradeoff between approximation and estimation error, and to perform as well as if the distribution-dependent complexities of the model classes were known beforehand. In addition, it is shown that the estimate can be consistent,and even possess near optimal rates of convergence, when each model class has an infinite VC or pseudo dimension.For regression estimation with squared loss we modify our estimate to achieve a faster rate of convergence.

Obesity-related phenotypes are associated to parental longevity in a Swiss population-based study

PURPOSE. Longevity has been attributed to decreased cardiovascular mortality. Subjects with long-lived parents may represent a valuable group to study cardiovascular risk factors (CVRF) associated with longevity, possibly leading to new ways of preventing cardiovascular disease. Purpose: Longevity has been attributed to decreased cardiovascular mortality. Subjects with long-lived parents may represent a valuable group to study cardiovascular risk factors (CVRF) associated with longevity, possibly leading to new ways of preventing cardiovascular disease. Methods: We analyzed data from a population-based sample of 2561 participants (1163 men and 1398 women) aged 55--75 years from the city of Lausanne, Switzerland (CoLaus study). Participants were stratified by the number of parents (0, 1, 2) who survived to 85 years or more. Trend across these strata was assessed using a non-parametric kmean test. The associations of parental age (independent covariate used as a proxy for longevity) with fasting blood glucose, blood pressures, blood lipids, body mass index (BMI), weight, height or liver enzymes (continuous dependent variables) were analyzed using multiple linear regressions. Models were adjusted for age, sex, alcohol consumption, smoking and educational level, and BMI for liver enzymes. Results: For subjects with 0 (N=1298), 1 (N=991) and 2 (N=272) long-lived parents, median BMI (interquartile range) was 25.4 (6.5), 24.9 (6.1) and 23.7 (4.8) kg/m2 in women (P<0.001), and 27.3 (4.8), 27.0 (4.5) and 25.9 (4.9) kg/m2 in men (P=0.04), respectively; median weight was 66.5 (16.1), 65.0 (16.4) and 63.4 (13.7) kg in women (P=0.003), and 81.5 (17.0), 81.4 (16.4) and 80.3 (17.1) kg in men (P=0.36). Median height was 161 (8), 162 (9) and 163 (8) cm in women (P=0.005), and 173 (9), 174 (9) and 174 (11) cm in men (P=0.09). The corresponding medians for AST (Aspartate Aminotransferase) were 31 (13), 29 (11) and 28 (10) U/L (P=0.002), and 28 (17), 27 (14) and 26 (19) U/L for ALT (Alanin Aminotransferase, P=0.053) in men. In multivariable analyses, greater parental longevity was associated with lower BMI, lower weight and taller stature in women (P<0.01) and lower AST in men (P=0.011). No significant associations were observed for the other variables analyzed. Sensitivity analyses restricted to subjects whose parents were dead (N=1844) led to similar results, with even stronger associations of parental longevity with liver enzymes in men. Conclusion: In women, increased parental longevity was associated with smaller BMI, attributable to lower weight and taller stature. In men, the association of increased parental longevity with lower liver enzymes, independently of BMI, suggests that parental longevity may be associated with decreased nonalcoholic fatty liver disease.

Radial measures of public services deficit for regional allocation of public funds

The goal of this paper is to present an optimal resource allocation model for the regional allocation of public service inputs. Theproposed solution leads to maximise the relative public service availability in regions located below the best availability frontier, subject to exogenous budget restrictions and equality ofaccess for equal need criteria (equity-based notion of regional needs). The construction of non-parametric deficit indicators is proposed for public service availability by a novel application of Data Envelopment Analysis (DEA) models, whose results offer advantages for the evaluation and improvement of decentralised public resource allocation systems. The method introduced in this paper has relevance as a resource allocation guide for the majority of services centrally funded by the public sector in a given country, such as health care, basic and higher education, citizen safety, justice, transportation, environmental protection, leisure, culture, housing and city planning, etc.

Detection of moving groups among early type stars

Our procedure to detect moving groups in the solar neighbourhood (Chen et al., 1997) in the four-dimensional space of the stellar velocity components and age has been improved. The method, which takes advantadge of non-parametric estimators of density distribution to avoid any a priori knowledge of the kinematic properties of these stellar groups, now includes the effect of observational errors on the process to select moving group stars, uses a better estimation of the density distribution of the total sample and field stars, and classifies moving group stars using all the available information. It is applied here to an accurately selected sample of early-type stars with known radial velocities and Strömgren photometry. Astrometric data are taken from the HIPPARCOS catalogue (ESA, 1997), which results in an important decrease in the observational errors with respect to ground-based data, and ensures the uniformity of the observed data. Both the improvement of our method and the use of precise astrometric data have allowed us not only to confirm the existence of classical moving groups, but also to detect finer structures that in several cases can be related to kinematic properties of nearby open clusters or associations.

A limited area model intercomparison on the "Montserrat-2000" flash-flood event using statistical and deterministic methods

In the scope of the European project Hydroptimet, INTERREG IIIB-MEDOCC programme, limited area model (LAM) intercomparison of intense events that produced many damages to people and territory is performed. As the comparison is limited to single case studies, the work is not meant to provide a measure of the different models' skill, but to identify the key model factors useful to give a good forecast on such a kind of meteorological phenomena. This work focuses on the Spanish flash-flood event, also known as "Montserrat-2000" event. The study is performed using forecast data from seven operational LAMs, placed at partners' disposal via the Hydroptimet ftp site, and observed data from Catalonia rain gauge network. To improve the event analysis, satellite rainfall estimates have been also considered. For statistical evaluation of quantitative precipitation forecasts (QPFs), several non-parametric skill scores based on contingency tables have been used. Furthermore, for each model run it has been possible to identify Catalonia regions affected by misses and false alarms using contingency table elements. Moreover, the standard "eyeball" analysis of forecast and observed precipitation fields has been supported by the use of a state-of-the-art diagnostic method, the contiguous rain area (CRA) analysis. This method allows to quantify the spatial shift forecast error and to identify the error sources that affected each model forecasts. High-resolution modelling and domain size seem to have a key role for providing a skillful forecast. Further work is needed to support this statement, including verification using a wider observational data set.

Effect of once-yearly zoledronic acid on the spine and hip as measured by quantitative computed tomography: results of the HORIZON Pivotal Fracture Trial.

Changes in bone mineral density and bone strength following treatment with zoledronic acid (ZOL) were measured by quantitative computed analysis (QCT) or dual-energy X-ray absorptiometry (DXA). ZOL treatment increased spine and hip BMD vs placebo, assessed by QCT and DXA. Changes in trabecular bone resulted in increased bone strength. INTRODUCTION: To investigate bone mineral density (BMD) changes in trabecular and cortical bone, estimated by quantitative computed analysis (QCT) or dual-energy X-ray absorptiometry (DXA), and whether zoledronic acid 5 mg (ZOL) affects bone strength. METHODS: In 233 women from a randomized, controlled trial of once-yearly ZOL, lumbar spine, total hip, femoral neck, and trochanter were assessed by DXA and QCT (baseline, Month 36). Mean percentage changes from baseline and between-treatment differences (ZOL vs placebo, t-test) were evaluated. RESULTS: Mean between-treatment differences for lumbar spine BMD were significant by DXA (7.0%, p < 0.01) and QCT (5.7%, p < 0.0001). Between-treatment differences were significant for trabecular spine (p = 0.0017) [non-parametric test], trabecular trochanter (10.7%, p < 0.0001), total hip (10.8%, p < 0.0001), and compressive strength indices at femoral neck (8.6%, p = 0.0001), and trochanter (14.1%, p < 0.0001). CONCLUSIONS: Once-yearly ZOL increased hip and spine BMD vs placebo, assessed by QCT vs DXA. Changes in trabecular bone resulted in increased indices of compressive strength.

Benchmarking therapeutic drug monitoring software: A systematic evaluation of available computer tools

Introduction: Therapeutic drug monitoring (TDM) aims at optimizing treatment by individualizing dosage regimen based on measurement of blood concentrations. Maintaining concentrations within a target range requires pharmacokinetic and clinical capabilities. Bayesian calculation represents a gold standard in TDM approach but requires computing assistance. In the last decades computer programs have been developed to assist clinicians in this assignment. The aim of this benchmarking was to assess and compare computer tools designed to support TDM clinical activities.¦Method: Literature and Internet search was performed to identify software. All programs were tested on common personal computer. Each program was scored against a standardized grid covering pharmacokinetic relevance, user-friendliness, computing aspects, interfacing, and storage. A weighting factor was applied to each criterion of the grid to consider its relative importance. To assess the robustness of the software, six representative clinical vignettes were also processed through all of them.¦Results: 12 software tools were identified, tested and ranked. It represents a comprehensive review of the available software's characteristics. Numbers of drugs handled vary widely and 8 programs offer the ability to the user to add its own drug model. 10 computer programs are able to compute Bayesian dosage adaptation based on a blood concentration (a posteriori adjustment) while 9 are also able to suggest a priori dosage regimen (prior to any blood concentration measurement), based on individual patient covariates, such as age, gender, weight. Among those applying Bayesian analysis, one uses the non-parametric approach. The top 2 software emerging from this benchmark are MwPharm and TCIWorks. Other programs evaluated have also a good potential but are less sophisticated (e.g. in terms of storage or report generation) or less user-friendly.¦Conclusion: Whereas 2 integrated programs are at the top of the ranked listed, such complex tools would possibly not fit all institutions, and each software tool must be regarded with respect to individual needs of hospitals or clinicians. Interest in computing tool to support therapeutic monitoring is still growing. Although developers put efforts into it the last years, there is still room for improvement, especially in terms of institutional information system interfacing, user-friendliness, capacity of data storage and report generation.

Pericardial fat volume correlates with coronary vasomotion

Purpose: Recent studies showed that pericardial fat was independently correlated with the development of coronary artery disease (CAD). The mechanism remains unclear. We aimed at assessing a possible relationship between pericardial fat volume and endothelium-dependent coronary vasomotion, a surrogate of future cardiovascular events.Methods: Fifty healthy volunteers without known CAD or cardiovascular risk factors (CRF) were enrolled. They all underwent a dynamic Rb- 82 cardiac PET/CT to quantify myocardial blood flow (MBF) at rest, during MBF response to cold pressure test (CPT-MBF) and adenosine stress. Pericardial fat volume (PFV) was measured using a 3D volumetric CT method and common biological CRF (glucose and insulin levels, HOMA-IR, cholesterol, triglyceride, hs-CRP). Relationships between MBF response to CPT, PFV and other CRF were assessed using non-parametric Spearman correlation and multivariate regression analysis of variables with significant correlation on univariate analysis (Stata 11.0).Results: All of the 50 participants had normal MBF response to adenosine (2.7±0.6 mL/min/g; 95%CI: 2.6−2.9) and myocardial flow reserve (2.8±0.8; 95%CI: 2.6−3.0) excluding underlying CAD. Simple regression analysis revealed a significant correlation between absolute CPTMBF and triglyceride level (rho = −0.32, p = 0.024) fasting blood insulin (rho = −0.43, p = 0.0024), HOMA-IR (rho = −0.39, p = 0.007) and PFV (rho = −0.52, p = 0.0001). MBF response to adenosine was only correlated with PFV (rho = −0.32, p = 0.026). On multivariate regression analysis PFV emerged as the only significant predictor of MBF response to CPT (p = 0.002).Conclusion: PFV is significantly correlated with endothelium-dependent coronary vasomotion. High PF burden might negatively influence MBF response to CPT, as well as to adenosine stress, even in persons with normal hyperemic myocardial perfusion imaging, suggesting a link between PF and future cardiovascular events. While outside-to-inside adipokines secretion through the arterial wall has been described, our results might suggest an effect upon NO-dependent and -independent vasodilatation. Further studies are needed to elucidate this mechanism.