Deviation Criterion Research Articles

Statistical modeling of ecosystem respiration using eddy covariance data: Maximum likelihood parameter estimation, and Monte Carlo simulation of model and parameter uncertainty, applied to three simple models

Whether the goal is to fill gaps in the flux record, or to extract physiological parameters from eddy covariance data, researchers are frequently interested in fitting simple models of ecosystem physiology to measured data. Presently, there is no consensus on the best models to use, or the ideal optimization criteria. We demonstrate that, given our estimates of the distribution of the stochastic uncertainty in nighttime flux measurements at the Howland (Maine, USA) AmeriFlux site, it is incorrect to fit ecosystem respiration models using ordinary least squares (OLS) optimization. Results indicate that the flux uncertainty follows a double-exponential (Laplace) distribution, and the standard deviation of the uncertainty ( σ( δ)) follows a strong seasonal pattern, increasing as an exponential function of temperature. These characteristics both violate OLS assumptions. We propose that to obtain maximum likelihood estimates of model parameters, fitting should be based on minimizing the weighted sum of the absolute deviations: ∑ | measured − modeled | / σ ( δ ) . We examine in detail the effects of this fitting paradigm on the parameter estimates and model predictions for three simple but commonly used models of ecosystem respiration. The exponential Lloyd & Taylor model consistently provides the best fit to the measured data. Using the absolute deviation criterion reduces the estimated annual sum of respiration by about 10% (70–145 g C m −2 y −1) compared to OLS; this is comparable in magnitude but opposite in sign to the effect of filtering nighttime data using a range of plausible u * thresholds. The weighting scheme also influences the annual sum of respiration: specifying σ( δ) as a function of air temperature consistently results in the smallest totals. However, annual sums are, in most cases, comparable (within uncertainty estimates) regardless of the model used. Monte Carlo simulations indicate that a 95% confidence interval for the annual sum of respiration is about ±20–40 g C m −2 y −1, but varies somewhat depending on model, optimization criterion, and, most importantly, weighting scheme.

Multi-criterion optimization for heel–toe running

This paper presents an optimization procedure for multi-criterion analysis essential in many biomechanical studies. The optimization is illustrated with a heel–toe running analysis wherein the rate of load and the passive load on support leg are minimized concurrently. The goal of multi-criterion optimization is achieved by incorporating the criterion of Pareto optimality in the genetic algorithm. The proposed procedure can replace the popular weighted-sum approach for problems with multiple objectives. The selection of a final design from the Pareto optimum points (non-dominated designs) can be determined, based on the min–max objective deviation criterion. Nevertheless, a different decision can be made in the final selection without incurring recalculations. The scheme is readily adoptable for parallel computing, which deserves further study to reduce the execution time in a complex biomechanical analysis.

Targacept Active Conformation Search: A New Method for Predicting the Conformation of a Ligand Bound to Its Protein Target

Targacept active conformation search (TACS) is a novel variation of well-established three-dimensional quantitative structure--activity relationship methodologies that seeks to determine probable conformation(s) of ligands bound to their protein targets. A combination of affinity or activity data and energetically accessible conformational ensembles, each conformer described by three-dimensional (3-D) sensitive descriptors, forms the basis of the TACS data model. Recursive pruning is used to reduce the size of both the conformational ensemble and the descriptor space until the TACS data model contains just enough information to determine probable conformation(s) of ligands bound to their protein targets. The TACS algorithm is comprised of five components: (1) conformational ensemble generation, (2) 3-D sensitive descriptor calculation, (3) ensemble descriptor preprocessing, (4) model generation, and (5) prediction of bound conformation(s). Significantly, this method precludes the need for subjective or objective molecular alignment. We report the application of this technique to five benchmark protein-ligand couples where the conformation of a bound ligand has been previously established using X-ray crystallography: 9-cis-retinoic (1) and 9-trans-retinoic acid (2), both agonists for the retinoic acid receptor gamma, compounds KH1060 (3) and MC1288 (4), which bind to the vitamin D3 receptor, and R04 (5), an inhibitor bound to human rhinovirus 14 thermolysin. The binding conformations predicted by TACS were compared to the crystallographic structures extracted from their respective binding sites using root-mean-squared deviation (rmsd) criteria. Three of the conformations found using TACS were within crystallographic error. 9-cis-Retinoic acid, 9-trans-retinoic acid, and MC1288, when superimposed on their crystallographic structures, gave rmsd values of 0.22, 0.17, and 0.34 A, respectively. The rmsd values for KH1060 (1.54 A) and R04 (1.01 A) were larger but still reasonable.

Automatic real‐time surveillance of eye position and gating for stereotactic radiotherapy of uveal melanoma

A new prototype (hardware and software) for monitoring eye movements using a noninvasive technique for gated linac-based stereotactic radiotherapy (SRT) of uveal melanoma was developed. The prototype was tested within the scope of a study for 11 patients. Eye immobilization was achieved by having the patient fixate a light source integrated into the system. The system is used in conjunction with a Head&Neck mask system for immobilization, and uses infrared tracking technology for positioning (both BrainLAB AG Heimstetten/Germany). It was used during CT and MR image acquisition as well as during all of five treatment fractions (6 MeV, 5 x 12 Gy to 80% isodose) to guarantee identical patient setup and eye rotational state during treatment planning and treatment delivery. Maximum temporal and angular deviations tolerated during treatment delivery can be chosen by the physician, the radiation then being interrupted automatically and instantaneously if those criteria are being exceeded during irradiation. A graphical user interface displays life video images of the treated eye and information about the current and previous rotational deviation of the eye from its reference treatment position. The physician thus has online access to data directly linked to the success of the treatment and possible side effects. Mean angular deviations during CT/MR scans and treatment deliveries ranged from 1.61 degrees to 3.64 degrees (standard deviations 0.87 degrees to 2.09 degrees ) which is in accordance with precision requirements for SRT. Typical situations when preset deviation criteria were exceeded are slow drifts (fatigue), sudden large eye movements (irritation), or if patients closed their eyes (fatigue). In these cases radiation was reliably interrupted by the gating system. In our clinical setup the novel system for computer-controlled eye movement gated treatments was well tolerated by all patients. The system yields quantitative real-time information about the eye's rotational state with respect to a reference position (treatment planning situation). Together with the possibility of performing movement-gated treatments of uveal melanoma, the system thus greatly improves the quality of this treatment.

Speciation analysis of mercury by solid-phase microextraction and multicapillary gas chromatography hyphenated to inductively coupled plasma–time-of-flight-mass spectrometry

This paper reports the development of an analytical approach for speciation analysis of mercury at ultra-trace levels on the basis of solid-phase microextraction and multicapillary gas chromatography hyphenated to inductively coupled plasma–time-of-flight mass spectrometry. Headspace solid-phase microextraction with a carboxen/polydimethylsyloxane fiber is used for extraction/preconcentration of mercury species after derivatization with sodium tetraethylborate and subsequent volatilization. Isothermal separation of methylmercury (MeHg), inorganic mercury (Hg 2+) and propylmercury (PrHg) used as internal standard is achieved within a chromatographic run below 45 s without the introduction of spectral skew. Method detection limits (3 × standard deviation criteria) calculated for 10 successive injections of the analytical reagent blank are 0.027 pg g −1 (as metal) for MeHg and 0.27 pg g −1 for Hg 2+. The repeatability (R.S.D., %) is 3.3% for MeHg and 3.8% for Hg 2+ for 10 successive injections of a standard mixture of 10 pg. The method accuracy for MeHg and total mercury is validated through the analysis of marine and estuarine sediment reference materials. A comparison of the sediment data with those obtained by a purge-and-trap injection (PTI) method is also addressed. The analytical procedure is illustrated with some results for the ultra-trace level analysis of ice from Antarctica for which the accuracy is assessed by spike recovery experiments.

Application of the Genetic Algorithm to the Multi-Objective Optimization of Air Bearings

A feasible solution must be obtained in a reasonable time with high probability of global optimum for a complex tribological design problem. To meet this decisive requirement in a multi-objective optimization problem, the popular and powerful genetic algorithms (GAs) are adopted in an illustrated air bearing design. In this study, the goal of multi-objective optimization is achieved by incorporating the criterion of Pareto optimality in the selection of mating groups in the GAs. In the illustrated example the diversity of group members in the evolution process is much better maintained by using Pareto ranking method than that with the roulette wheel selection scheme. The final selection of the optimal point of the points satisfied the Pareto optimality is based on the minimum–maximum objective deviation criterion. It is shown that the application of the GA with the Pareto ranking is especially useful in dealing with multi-objective optimizations. A hybrid selection scheme combining the Pareto ranking and roulette wheel selections is also presented to deal with a problem with a combined single objective. With the early generations running the Pareto ranking criterion, the resultant divergence preserved in the population benefits the overall GA's performance. The presented procedure is readily adoptable for parallel computing, which deserves further study in tribological designs to improve the computational efficiency.

Homogeneity analysis using absolute deviations

Homogeneity analysis is a technique for making graphical representations of categorical multivariate data sets. Such data sets can also be represented by the adjacency matrix of a bipartite graph. Homogeneity analysis optimizes a weighted least-squares criterion and the optimal graph layout is computed by an alternating least squares algorithm. Heiser Comput. Statist. Data Anal. (1987) 337, looked at homogeneity analysis under a more robust to outliers criterion, namely a weighted least absolute deviations criterion. In this paper, we take an in-depth look at the mathematical structure of this problem and show that the graph drawings are created by reciprocal computation of multivariate medians. Several algorithms for computing the solution are investigated and applications to actual data suggest that the resulting p-dimensional drawings ( p⩾2) are degenerate, in the sense that all object points are clustered in p+1 locations. We also examine some variations of the criterion used and conclude that the generate solutions observed are a consequence of the normalization constraint employed in this class of problems.

Choosing the Best Volatility Models: The Model Confidence Set Approach*

AbstractThis paper applies the model confidence set (MCS) procedure of Hansen, Lunde and Nason (2003) to a set of volatility models. An MCS is analogous to the confidence interval of a parameter in the sense that it contains the best forecasting model with a certain probability. The key to the MCS is that it acknowledges the limitations of the information in the data. The empirical exercise is based on 55 volatility models and the MCS includes about a third of these when evaluated by mean square error, whereas the MCS contains only a VGARCH model when mean absolute deviation criterion is used. We conduct a simulation study which shows that the MCS captures the superior models across a range of significance levels. When we benchmark the MCS relative to a Bonferroni bound, the latter delivers inferior performance.

Choosing the Best Volatility Models: The Model Confidence Set Approach

This paper applies the model confidence sets (MCS) procedure to a set of volatility models. A MSC is analogous to a confidence interval of parameter in the sense that the former contains the best forecasting model with a certain probability. The key to the MCS is that it acknowledges the limitations of the information in the data. The empirical exercise is based on fifty-five volatility models, and the MCS includes about a third of these when evaluated by mean square error, whereas the MCS contains only a VGARCH model when mean absolute deviation criterion is used. We conduct a simulation study that shows the MCS captures the superior models across a range of significance levels. When we benchmark the MCS relative to a Bonferroni bound, this bound delivers inferior performance.

Practical Guidelines for Assessing the Clinical Significance of Health-Related Quality of Life Changes within Clinical Trials

Health-related quality of life (HRQOL) assessment is becoming common practice in many clinical trials. There is much debate over how to determine the clinical significance of changes in HRQOL scores. A number of techniques have been used to address this issue. This paper reviews the most popular of these approaches for use in a clinical trial setting. More specifically, the anchor-based “minimal clinically important difference” technique is described and critiqued, as is the more traditional distribution-based effect size technique. A novel application of effect size, which applies a common statistical premise known as the empirical rule, is also presented. The review of these techniques indicates that there is no single, optimal solution to determining clinical significance of changes in HRQOL scores. However, it is encouraging to note that they ail suggest a similar criterion of a half-standard deviation for whether or not a change in HRQOL score is clinically significant. Recommendations are given for reporting the clinical significance of HRQOL assessments in clinical trials.

The least square deviations criterion and inverse-source magnetostatic problems

A procedure for the determination of the distribution of magnetization in an object of interest using measured disturbances of external magnetic field is described in this paper. The object is divided into a finite number of brick-shaped elements and we prescribe uniform distribution of magnetization within each element. The contribution of each element to the total magnetic field may be calculated analytically in terms of unknown coefficients of magnetization distribution. These coefficients are determined from a set of measured magnetic field values by application of the least square deviations criterion. Such an approach enables a priori analysis of stability of computation. The application of the procedure is illustrated by an example.

Automated segmentation of point data in a feature-based reverse engineering system

This paper proposes a novel methodology for robust segmentation of scanned point data that has been implemented in the feature-based reverse engineering system (FBRES). In the proposed method, firstly triangle meshes are generated from the input point data. The normal and the area of generated meshes are checked to find boundary meshes using the angle deviation criterion and the area criterion based upon a region-growing technique. Boundary meshes of each segmented region are connected into loops. Then, the meshes closed by each boundary loop are segmented into a single distinctive region. Finally, all segmented regions are mapped into a single feature using an artificial neural network (ANN) based feature recognizer. The FBRES is currently dedicated for reconstructing prismatic features such as a block, pocket, step, slot, hole and boss, which are very common and crucial in mechanical engineering products. The effectiveness of the proposed segmentation method is validated with experimental results.

Fracture surface of plastic materials: the roughness exponent

In order to provide more evidence concerning the controversial topic, conjectured for the first time in the early 90's, that the roughness exponent of the self-affine fracture surfaces has a value close to 0.8, the self-affine behavior of fracture surfaces of both, semi-crystalline polypropylene (PP) and amorphous polystyrene (PS) was analyzed. The topography of polymeric fracture surfaces was obtained using atomic force microscopy, AFM, and the corresponding height profiles were processed using the variable bandwidth method (standard deviation criteria) to obtain the roughness exponent of the surfaces. Prior to that, the appropriate AFM operating conditions, in contact mode, were found. The average roughness exponent was 0.770±0.09 for the fracture surfaces of polypropylene and 0.707±0.07 for polystyrene. These results agree with values for different materials often reported in the literature that support 0.8 has a possible ‘universal’ value. Hence, it is considered that our results are in good agreement with the conjectured value even for polymeric materials.

Optimal polygonal approximation of digitized curves using the sum of square deviations criterion

We address the problem of finding an optimal polygonal approximation of digitized curves. Several optimal algorithms have already been proposed to determine the minimum number of points that define a polygonal approximation of the curve, with respect to a criterion error. We present a new algorithm with reasonable complexity to determine the optimal polygonal approximation using the mean square error norm. The idea is to estimate the remaining number of segments and to integrate the cost in the A * algorithm. The solution is optimal in the minimum number of segments.

Boiling points for five binary systems of sulfolane with aromatic hydrocarbons at 101.33 kPa

Boiling points have been determined at 101.33 kPa for the binary mixtures of sulfolane+ o-xylene, sulfolane+ m-xylene, sulfolane+ p-xylene, sulfolane+ethylbenzene and sulfolane+1,2,4-trimethylbenzene. Calculations of the non-ideality of the vapor phase were made with the second virial coefficients evaluated from the Hayden–O’Connell method. The binary parameters for five activity coefficient models (Margules, van Laar, Wilson, NRTL and UNIQUAC) have been fitted with the experimental boiling points measured in this work. A comparison of model performances has been carried out using the criterion of the average absolute deviations in boiling point. The activity coefficient of the component in the liquid phase is discussed based on the UNIFAC model with the consideration of the dipole–dipole interactions.

EPR tooth enamel dosimetry: optimization of the automated spectra deconvolution routine.

A computer routine was developed for automatic deconvolution of electron paramagnetic resonance spectra of tooth enamel samples for individual radiation dose reconstruction in the low dose region. The deconvolution routine uses the non-linear least square fit of a model simulating a tooth enamel spectrum by superposition of derivative Gaussian functions to obtain the amplitude of the dosimetric radiation induced signal. The parameters of the model and of the routine were optimized on a dose response level using a criterion of the least standard deviation of the derived radiation induced signal amplitude from the regression line vs. the nominal doses for the series of spectra of samples irradiated in known doses in the range 0-500 mGy. It was found that for the series of spectra of the heterogeneous samples (every sample is prepared from different teeth of different persons), it is essential to vary in the least square fit the parameters describing the shape of the native background signal in order to obtain the best accuracy. In the case of the series of spectra of the homogeneous (pooled) samples, almost the same accuracy of the results was obtained using the procedures with varied and fixed background signal parameters. The standard error of the dose reconstruction by the optimized deconvolution procedure was estimated as about 30 mGy for heterogeneous samples and 20 mGy for homogeneous samples.

Least absolute deviation estimation for all-pass time series models

An autoregressive moving average model in which all of the roots of the autoregressive polynomial are reciprocals of roots of the moving average polynomial and vice versa is called an all-pass time series model. All-pass models generate uncorrelated (white noise) time series, but these series are not independent in the non-Gaussian case. An approximation to the likelihood of the model in the case of Laplacian (two-sided exponential) noise yields a modified absolute deviations criterion, which can be used even if the underlying noise is not Laplacian. Asymptotic normality for least absolute deviation estimators of the model parameters is established under general conditions. Behavior of the estimators in finite samples is studied via simulation. The methodology is applied to exchange rate returns to show that linear all-pass models can mimic “nonlinear” behavior, and is applied to stock market volume data to illustrate a two-step procedure for fitting noncausal autoregressions.

Building cost functions minimizing to some summary statistics

A learning machine--or a model--is usually trained by minimizing a given criterion (the expectation of the cost function), measuring the discrepancy between the model output and the desired output. As is already well known, the choice of the cost function has a profound impact on the probabilistic interpretation of the output of the model, after training. In this work, we use the calculus of variations in order to tackle this problem. In particular, we derive necessary and sufficient conditions on the cost function ensuring that the output of the trained model approximates 1) the conditional expectation of the desired output given the explanatory variables; 2) the conditional median (and, more generally, the q-quantile); 3) the conditional geometric mean; and 4) the conditional variance. The same method could be applied to the estimation of other summary statistics as well. We also argue that the least absolute deviations criterion could, in some cases, act as an alternative to the ordinary least squares criterion for nonlinear regression. In the same vein, the concept of "regression quantile" is briefly discussed.

Band partitioning algorithm for surface reconstructionfrom planar contours

A heuristic contour triangulation method is proposed for reconstructing a facet model from a set of wire-frame contours. The proposed band partitioning algorithm (BPA) compensates for the disadvantages of optimal and heuristic methods, and produces an improved reconstructed surface. Furthermore, the maximum deviation criterion in span selection prohibits drastic error propagation in the surface definition procedure. Experimental results show that the proposed method is very stable and efficient, making it suitable for a wide range of applications.

Discordance in Patient Classification Using T-Scores

In their original study report, "Assessment of Fracture Risk and Its Application to Screening for Postmenopausal Osteoporosis," the World Health Organization (WHO) explicitly stated that any T-score criterion for osteoporosis is sensitive to bone mineral density (BMD) measurement site and technique, as well as the young adult reference population. Yet, the T = -2.5 criterion introduced by WHO is used for many different BMD techniques, despite the fact that it was based primarily on the relationship between forearm measurements and prevalent hip fracture in postmenopausal Caucasian females. It is reasonable to expect that a T-score threshold of -2.5 may be inappropriate for different skeletal sites and measurement techniques. This may explain the large variation in osteoporosis prevalence observed when different skeletal sites are measured. In this study, we compared the prevalence of osteoporosis (based on the T = -2.5 criterion) at different skeletal sites using the manufacturer's normative data. We determined the expected mean T-score for a 60-yr-old Caucasian female at the heel (ultrasound), hip (dual X-ray absorptiometry [DXA]), spine (PA DXA, lateral DXA, and quantitative computed tomography [QCT]), and forearm (DXA). Assuming a normal distribution of T-scores at a fixed age, we computed the expected percentage of 60-yr-old Caucasian women that would be classified as osteoporotic using the -2.5 standard deviation criterion for each technique. At age 60 yr, the expected mean T-score ranged from -2.5 (spine QCT) to -0.7 (heel). Prevalence estimates ranged from 3% at the heel to 50% for spinal QCT. It was also noted that the sites with the strongest relationship to hip fracture risk (the hip and heel) showed the least age-related T-score decline and lowest estimated prevalence. We conclude that a single T-score criterion cannot be universally applied to all BMD measurements. The discrepancies in the prevalence of osteoporosis are the result of several factors, including differences in age-related bone loss at different skeletal sites, differences in the young adult reference populations used by the various bone densitometry devices, and technology-related differences. Using estimated BMD by heel ultrasound, few patients will have T-scores below -2.5, whereas most postmenopausal women will fall below this level for spine bone density measurements performed by lateral DXA or QCT. Based on these data, it may be necessary to provide a T-score criterion specific to the type of densitometric evaluation performed.