Sources Of Imprecision Research Articles

Backtesting and estimation error: value-at-risk overviolation rate

Financial institutions and regulators use value-at-risk (VaR) and related measures as a tool for financial risk management. It is therefore critical to appropriately assess the quality of VaR forecasts and reporting. The VaR estimation error creates an additional source of imprecision. We show that even an unbiased estimator of VaR is likely to produce a systematic overviolation. We then propose an adjustment to account for the issue. A Monte Carlo study illustrates the overviolation problem and the effectiveness of the adjustment. An application to Fama–French portfolios returns series highlights the need to further account for tail behavior in the data. Applying the adjustment to the normal distribution performs relatively well for a less prudential level (5% VaR), but is unable to provide enough buffer to overcome the overviolation for more prudential levels (1% or 0.5%VaR). Using the empirical distribution for more prudential levels improves risk forecasts.

Validation Methods for Aggregate-Level Test Scale Linking: A Case Study Mapping School District Test Score Distributions to a Common Scale

Linking score scales across different tests is considered speculative and fraught, even at the aggregate level. We introduce and illustrate validation methods for aggregate linkages, using the challenge of linking U.S. school district average test scores across states as a motivating example. We show that aggregate linkages can be validated both directly and indirectly under certain conditions such as when the scores for at least some target units (districts) are available on a common test (e.g., the National Assessment of Educational Progress). We introduce precision-adjusted random effects models to estimate linking error, for populations and for subpopulations, for averages and for progress over time. These models allow us to distinguish linking error from sampling variability and illustrate how linking error plays a larger role in aggregates with smaller sample sizes. Assuming that target districts generalize to the full population of districts, we can show that standard errors for district means are generally less than .2 standard deviation units, leading to reliabilities above .7 for roughly 90% of districts. We also show how sources of imprecision and linking error contribute to both within- and between-state district comparisons within versus between states. This approach is applicable whenever the essential counterfactual question—“what would means/variance/progress for the aggregate units be, had students taken the other test?”—can be answered directly for at least some of the units.

An Interval-Based Evolutionary Approach to Portfolio Optimization of New Product Development Projects

The growth of large enterprises in the manufacturing market commonly depends on good New Product Development (NPD) projects; these projects represent a strategy to overcome competitors inside a competitive environment. The management of such projects is usually complex and involves risk due to the changing and conflicting environment. The approaches that tackle the problem lack an explicit consideration of the DM’s attitude facing uncertainty and imprecision related to the risk and particularly in the presence of time-interdependencies. This paper proposes a model of the time-related effects, under imperfect knowledge, and their influence in choosing optimal NPD portfolios. The proposed approach is an interval-based method to solve NPD portfolio optimization problems under different forms of imperfect knowledge. This approach has the advantage of a unified and simple way to model the different sources of imprecision, vagueness, uncertainty, and arbitrariness. The attitude of the DM facing the imperfect knowledge is adjusted by using some meaningful parameters. The research focuses particularly in creating a method useful for risk-averse DMs. The proposal was tested through an experimental design that compared the results achieved by the new method against the expected value in portfolios. The results revealed that high levels of conservatism might prevent wasting resources in failed projects.

Fundamentals of Counting Statistics in Digital PCR: I Just Measured Two Target Copies-What Does It Mean?

Current commercially available digital PCR (dPCR) systems and assays are capable of detecting individual target molecules with considerable reliability. As tests are developed and validated for use on clinical samples, the need to understand and develop robust statistical analysis routines increases. This chapter covers the fundamental processes and limitations of detecting and reporting on single molecule detection. We cover the basics of quantification of targets and sources of imprecision. We describe the basic test concepts: sensitivity, specificity, limit of blank, limit of detection, and limit of quantification in the context of dPCR. We provide basic guidelines how to determine those, how to choose and interpret the operating point, and what factors may influence overall test performance in practice.

A fuzzy regression model based on finite fuzzy numbers and its application to real-world financial data

Different sources of imprecision and uncertainty are encountered in practical problems and, thus, many elements may need to be imprecisely observed, defined or treated. In this setting, one of the most successfully applied techniques to describe possible relationships between fuzzy variables is the regression methodology. In this paper, we introduce a fuzzy regression procedure involving a class a fuzzy numbers defined by some level sets called finite fuzzy numbers. We give a characterization of the image of a finite fuzzy number in terms of the extremes of its level sets and we present a parametric family of fuzzy semidistances between them that let us to consider a total fuzzy error of estimation (described as a fuzzy sum of squares of residuals in particular cases). The estimation process consists in finding a regression model that minimizes, in a fuzzy sense, such fuzzy error. Although spreads of finite fuzzy numbers can take some values very close to zero, which complicate the task of finding nonnegative models, the presented algorithm is able to guarantee that the predicted response is a fuzzy variable. Finally a numerical example based on fuzzy economic data of China is given to illustrate the use of the proposed method.

Time Resolved Dynamic Measurements at THz Frequencies Using a Rotary Optical Delay Line

Fabrication, characterization, and applications of a fast rotary linear optical delay line (FRLODL) for THz time-domain spectroscopy are presented. The FRLODL features two reflective surfaces with spatially separated incoming and outgoing beams. It has been manufactured using CNC machining. A linear dependence of the optical delay on the rotation angle allows a straightforward extraction of the conversion factor between the acquisition time (in ms) and the terahertz pulse time (in ps). We also discuss the accuracy of the rotary delay line detailing the possible sources of imprecision. The FRLODL has been tested using rotation speeds of up to 48 Hz, corresponding to an acquisition rate of up to 192 Hz with four blades incorporated on the same disk. At high speeds we observe a decrease of the bandwidth due to the limitations of the electronics, in particular, the transimpedance amplifier. An error analysis is performed by experimentally evaluating the signal-to-noise ratio and the dynamic range. With regard to the applications of the FRLODL, we first present observation of the evaporation of liquids, namely water, acetone and methanol. We then demonstrate monitoring of the spray painting process. Finally, detection of fast moving objects at 1 m/s and their thickness characterization are presented.

IMP: A decision aid for multiattribute evaluation using imprecise weight estimates

In multicriteria analysis, weights are inferred from judgements. Judgements are subject to uncertainty and the weights found depend on the method used so that weights must necessarily be imprecise. Describing weights by a suitable probability distribution captures this imprecision and leads to correspondingly imprecise estimates of the multiattribute scores given to alternatives. A method is described which enables the parameters of a Dirichlet distribution to be found from three point weight estimates and for this to be used to determine whether or not alternatives may justifiably be differentiated by their scores. A simple chart shows this information and permits easy interaction. An illustration shows the effects of different sources of imprecision and of aggregating individual assessments in a group.

Uncertainties of the 137Cs technique for validation of soil redistribution modelling in a semiarid meso-scale watershed

Scarcity of long-term series of sediment-related variables has led watershed managers to apply mathematical models to simulate sediment fluxes. Due to the high efforts for installation and maintenance of sedimentological gauges, tracers have been pointed out as an alternative to validate soil redistribution modelling. In this study, the 137Cs technique was used to assess the WASA-SED model performance at the Benguê watershed (933 km²), in the Brazilian semiarid. Qualitatively, good agreement was found among the 137Cs technique and the WASA-SED model results. Nonetheless, quantitatively great differences, up to two orders of magnitude, were found between the two methods. Among the uncertainties inherent to the 137Cs technique, definition of the reference inventory seems to be a major source of imprecision. In addition, estimations of water and sediment fluxes with mathematical models usually also present high uncertainty, contributing to the quantitative differences of the soil redistribution estimates with the two methods.

How to fully represent expert information about imprecise properties in a computer system: random sets, fuzzy sets, and beyond: an overview

To help computers make better decisions, it is desirable to describe all our knowledge in computer-understandable terms. This is easy for knowledge described in terms on numerical values: we simply store the corresponding numbers in the computer. This is also easy for knowledge about precise (well-defined) properties which are either true or false for each object: we simply store the corresponding “true” and “false” values in the computer. The challenge is how to store information about imprecise properties. In this paper, we overview different ways to fully store the expert information about imprecise properties. We show that in the simplest case, when the only source of imprecision is disagreement between different experts, a natural way to store all the expert information is to use random sets; we also show how fuzzy sets naturally appear in such random set representation. We then show how the random set representation can be extended to the general (“fuzzy”) case when, in addition to disagreements, experts are also unsure whether some objects satisfy certain properties or not.

A new 3-D modelling method to extract subtransect dimensions from underwater videos

Abstract. Underwater video transects have become a common tool for quantitative analysis of the seafloor. However a major difficulty remains in the accurate determination of the area surveyed as underwater navigation can be unreliable and image scaling does not always compensate for distortions due to perspective and topography. Depending on the camera set-up and available instruments, different methods of surface measurement are applied, which make it difficult to compare data obtained by different vehicles. 3-D modelling of the seafloor based on 2-D video data and a reference scale can be used to compute subtransect dimensions. Focussing on the length of the subtransect, the data obtained from 3-D models created with the software PhotoModeler Scanner are compared with those determined from underwater acoustic positioning (ultra short baseline, USBL) and bottom tracking (Doppler velocity log, DVL). 3-D model building and scaling was successfully conducted on all three tested set-ups and the distortion of the reference scales due to substrate roughness was identified as the main source of imprecision. Acoustic positioning was generally inaccurate and bottom tracking unreliable on rough terrain. Subtransect lengths assessed with PhotoModeler were on average 20% longer than those derived from acoustic positioning due to the higher spatial resolution and the inclusion of slope. On a high relief wall bottom tracking and 3-D modelling yielded similar results. At present, 3-D modelling is the most powerful, albeit the most time-consuming, method for accurate determination of video subtransect dimensions.

A river stage correction approach using Fourier series

One-dimensional hydrodynamic models based on the Saint-Venant equations (the SVN model) are used widely for river stage prediction. Errors that originate from simplifying assumptions, improper specification of initial and boundary conditions, uncertainty in parameters, channel geometry, observed data, and solution methods produce the inconsistencies between actual flow and that represented by the SVN model; this problem is especially apparent in tidal rivers. All of these simplifications and sources of imprecision can accumulate and introduce substantial errors in application. Total errors due to the causes mentioned above are treated as an error function, which is introduced as an additive term in the SVN model momentum equation. The function is constructed using a Fourier series approximation of discrepancies between simulated and observed flow. By combining the SVN model with the error function, a river stage correction approach (the ISV model) is proposed to take account of unconsidered errors in application. The tidal reach of the Qiantang River is selected as the study case and results based on a classification of flood events show that the ISV model generally performs better than the SVN model alone. It indicates that the approach could help guide improvements on the SVN model performance.

Optimal experimental designs for partial likelihood information

In a follow-up study the time-to-event may be censored either because of dropouts or the end of study is earlier. This situation is frequently modeled through a Cox-proportional hazards model including covariates, some of which are under the control of the experimenter. When the model is to be fitted to n observed times these are known and for each of them it is also known whether that time is censored or not. When the experiment is to be designed neither the observed times nor the information about whether a particular unit will be censored are known. For censoring some additional prior probability distribution has to be assumed. Thus, the design problem faces two sources of imprecision when the experiment is to be scheduled. On the one hand, the censored times are not known. On the other hand, there is uncertainty about occurrence of censoring. A prior probability distribution is needed for this. Moreover, the Cox partial likelihood instead of the full likelihood is usually considered for these models. A partial information matrix is built in this case and optimal designs are computed and compared with the optimal designs for the full likelihood information. The usual tools for computing optimal designs with full likelihood are no longer valid for partial information. Some general results are provided in order to deal with this new approach. An application to a simple case with two possible treatments is used to illustrate it. The partial information matrix depends on the parameters and therefore a sensitivity analysis is conducted in order to check the robustness of the designs for the choice of the nominal values of the parameters.

The limits of precision in conventionally instrumented computer-navigated total knee arthroplasty

Computer-navigated total knee arthroplasty (TKA) improves the accuracy of component implantation. However, the final implant alignment may not match planned alignment. The hypothesis of this study is that although computer navigation improves alignment, imprecision may not be completely eliminated. The aim of the study was to establish the incidence and sources of imprecision during TKA using computer navigation to measure deviations from planned alignment. Computer navigation was used to quantify changes in planned alignment at four steps during 136 TKA's: application of cutting blocks, addition of definitive pin fixation, bone cuts and after prosthesis application. Mean changes in alignment deviation at each step in each plane were measured and the number of significant outliers (>3° from the planned resection plane) were assessed in each plane. Overall changes in planned alignment were small and non-cumulative between steps but the incidence of outliers (cuts measured as >3° from planned alignment at each step) increased through the steps, with 21.3 % (n = 29) of final implants outlying in the tibial sagittal plane, which was the least precise plane. The highest number of outliers occurred after bone resection and the addition of pins to cutting blocks was also identified as a source of imprecision. Despite improved accuracy of bone resection with computer-navigated TKA, the precision of bone cuts may be affected at several steps of the procedure. Cutting block application, bone resection and prosthesis application may all affect accuracy. Bone cuts should be made with meticulous care, whether navigated or not, and navigated cuts should be checked and corrected, particularly in the tibial sagittal plane. IV.

W09-02 - Statistical solutions for the evaluation of reliability in-study

One principal characteristic of an outcome measure in a clinical trial is reliability. The reliability of a measurement is an important consideration in the choice of the outcome measure for a clinical trial and in the choice of measures used for eligibility and exclusion. Just as the power of a study is reported in a final publication, so also should the reliability of the outcome and eligibility measurements so as to allow the authors to better describe, and readers to better understand, the sources of imprecision in study results, and to improve the design of future trials. The precision of measurements will be discussed, as the lower the precision, the more subjects will be needed for the clinical trial, which can affect outcomes and increase cost. The speaker will address the main components of measurement error, including systematic bias (general learning or fatigue effects), and random error due to biological or mechanical variation (including administration of study efficacy measures). In a clinical trial, error components should be meaningfully quantified for the researcher and physician to relate the described error to judgments regarding analytical goals (rather than just the statistical significance of the reliability indicators). Researchers should be cautious in (1) concluding acceptable reliability even if a correlation is high; (2) extrapolating the results of to a new sample; and (3) comparing reliability results between studies. From this workshop, clinicians and statisticians in industry and academia will learn: Understanding reliability to assess how precise are measurements. To identify graphical, numerical methods to a range of models encountered in clinical trials.

Clinician's Commentary on Dang et al.

Clinician's Commentary on Dang et al.

A reliability model for friction and wear experimental data

Tribology experimental research has been a considerable improvement during the last years, leading to a significant amount of results and consequently an increasing number of papers appear every month. Unfortunately, in spite of this development, the obtained results usually are characterized by big scatter and significant discrepancies can be founded for the same materials if tested by different research teams. The scatter found in the data has been frequently attributed to many variables involved in the experiments, namely: environment (especially humidity), contaminant layers, differences on test conditions, uncertainty on the results evaluation and rarely on the experimental equipment response. The control of the test variables, the atmosphere and also the test procedure can play an important role on the results reliability but accurate equipments and careful laboratory practices certainly could improve the quality of the results. However, the basic problem remains and even taking into account all that statements, the results could have significant scatter. This work aims to discuss several sources of imprecision which lead to scatter of the experimental tribology results. The usual experimental procedure used to calculate performance parameters, namely wear and friction coefficients will be compared to other solutions, including energy approaches. A reliability method will be proposed to characterize friction and wear data. Experimental results obtained by unidirectional sliding and by micro-abrasion will be used to support the discussion.

A Fast Onboard Relative Positioning Module for Multirobot Systems

We present an onboard robotic module that can determine relative positions among miniature robots. The module uses high-frequency-modulated infrared emissions to enable nearby robots to determine the range, bearing, and message of the sender with a rapid update rate. A carrier sense multiple access protocol is employed for scalable operation. We describe a technique for calculating the range and bearing between robots, which can be generalized for use with more sophisticated relative positioning systems. Using this method, we characterize the accuracy of positioning between robots and identify different sources of imprecision. Finally, the utility of this module is clearly demonstrated with several robotic formation experiments, where precise multirobot formations are maintained throughout difficult maneuvers.

A Recommended Improvement for Specifying and Estimating Serum Creatinine Performance

Myers et al. (1) discuss the importance of creatinine analytical performance in the estimation of the glomerular filtration rate. They correctly specify a model of assay performance but subsequently do not seem to use that model. I suggest a variation of their model that is less subject to misinterpretation. The Myers et al. (1) model is: \batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \[Y {=} \mathrm{bias} {+} \mathrm{imprecision},\] \end{document} where Y is a result of a field creatinine assay, bias is the average bias between Y and a reference method for creatinine measurement, and imprecision includes imprecision sources from short-term (within-run or repeatability) and long-term (within-laboratory or reproducibility) and random patient interferences [called specimen-specific effects by Myers et al. (1)]. Here we refer to the 1st 2 sources of imprecision as total imprecision …

Analytical Validation of the Oncotype DX Genomic Diagnostic Test for Recurrence Prognosis and Therapeutic Response Prediction in Node-Negative, Estrogen Receptor–Positive Breast Cancer

Oncotype DX is a clinically validated, high-complexity, multianalyte reverse transcription-PCR genomic test that predicts the likelihood of breast cancer recurrence in early-stage, node-negative, estrogen receptor-positive breast cancer. The Recurrence Score (RS) provides a more accurate, reproducible measure of breast cancer aggressiveness and therapeutic responsiveness than standard measures. Individualized patient management requires strict performance criteria for clinical laboratory tests. We therefore investigated the analytical performance of the assay. Assays used a pooled RNA sample from fixed paraffin-embedded tissues to evaluate the analytical performance of a 21-gene panel with respect to amplification efficiency, precision, linearity, and dynamic range, as well as limits of detection and quantification. Performance variables were estimated from assays carried out with sample dilutions. In addition, individual patient samples were used to test the optimized assay for reproducibility and sources of imprecision. Assay results defined acceptable operational performance ranges, including an estimated maximum deviation from linearity of <1 cycle threshold (C(T)) units over a > or =2000-fold range of RNA concentrations, with a mean quantification bias of 0.3% and CVs of 3.2%-5.7%. An analysis of study design showed that assay imprecision contributed by instrument, operator, reagent, and day-to-day baseline variation was low, with SDs of <0.5 C(T). The analytical and operational performance specifications defined for the Oncotype DX assay allow the reporting of quantitative RS values for individual patients with an SD within 2 RS units on a 100-unit scale.

Mass appraisal with genetic fuzzy rule‐based systems

PurposeThe traditional models of real estate market have several sources of imprecision, such as transitions between submarkets, generating difficulties in property valuation. The purpose of this paper is to examine an alternative to improve mass appraisal models, using fuzzy rules.Design/methodology/approachFuzzy rule‐based systems (FRBS) are able to generate flexible systems and may be useful in considering vagueness or imprecision presents in real estate market. An application to the housing market of Porto Alegre (Brazil), with more than 30,000 apartments, transacted in 1998‐2001, illustrates the fuzzy system, comparing with traditional hedonic regression model.FindingsThe results have indicated the potential of fuzzy rules to use in mass appraisal.Originality/valueThis paper presents a procedure to develop mass appraisal models using FRBS.