Classification of experimental designs relative to polynomial spline regression functions
Classification of experimental designs relative to polynomial spline regression functions
Van Arman, D. J.↗
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Cortical localization of cognitive function by regression of performance on event-related potentials
This paper demonstrates a new method of mapping cortical localization of cognitive function, using electroencephalographic data. Cross-subject regression analyses are used to identify cortical sites and post-stimulus latencies where there is a high correlation between subjects' performance and their cognitive event-related potential amplitude. The procedure was tested using a mental arithmetic task and was found to identify essentially the same cortical regions that have been associated with such tasks on the basis of research with patients suffering localized cortical lesions. Thus, it appears to offer an inexpensive, noninvasive tool for exploring the dynamics of localization in neurologically normal subjects.
Montgomery, R. W.↗
Analysis of a Split-Plot Experimental Design Applied to a Low-Speed Wind Tunnel Investigation
A procedure to analyze a split-plot experimental design featuring two input factors, two levels of randomization, and two error structures in a low-speed wind tunnel investigation of a small-scale model of a fighter airplane configuration is described in this report. Standard commercially-available statistical software was used to analyze the test results obtained in a randomization-restricted environment often encountered in wind tunnel testing. The input factors were differential horizontal stabilizer incidence and the angle of attack. The response variables were the aerodynamic coefficients of lift, drag, and pitching moment. Using split-plot terminology, the whole plot, or difficult-to-change, factor was the differential horizontal stabilizer incidence, and the subplot, or easy-to-change, factor was the angle of attack. The whole plot and subplot factors were both tested at three levels. Degrees of freedom for the whole plot error were provided by replication in the form of three blocks, or replicates, which were intended to simulate three consecutive days of wind tunnel facility operation. The analysis was conducted in three stages, which yielded the estimated mean squares, multiple regression function coefficients, and corresponding tests of significance for all individual terms at the whole plot and subplot levels for the three aerodynamic response variables. The estimated regression functions included main effects and two-factor interaction for the lift coefficient, main effects, two-factor interaction, and quadratic effects for the drag coefficient, and only main effects for the pitching moment coefficient.
Erickson, Gary E.↗
Regression Bias in using Solar Wind Measurements
Simultaneous solar wind measurements from the solar wind monitors, WIND and ACE, differ due to the spatial and temporal structure of the solar wind. Correlation studies that use these measurements as input may infer an incorrect correlation due to uncertainties arising from this spatial and temporal structure, especially at extreme and rare solar wind values. In particular, regression analysis will lead to a regression function whose slope is biased towards the mean value of the measurement parameter. This article demonstrates this regression bias by comparing simultaneous ACE and WIND solar wind measurements. A non-linear regression analysis between them leads to a perception of underestimation of extreme values of one measurement on average over the other. Using numerical experiments, we show that popular regression analysis techniques such as linear least-squares, orthogonal least-squares, and non-linear regression are not immune to this bias. Hence while using solar wind parameters as an independent variable in a correlation or regression analysis, random uncertainty in the independent variable can create unintended biases in the response of the dependent variable. More generally, the regression to the mean effect can impact both event-based, statistical studies of magnetospheric response to solar wind forcing.
magnetosphere↗
Multidimensional stochastic approximation using locally contractive functions
A Robbins-Monro type multidimensional stochastic approximation algorithm which converges in mean square and with probability one to the fixed point of a locally contractive regression function is developed. The algorithm is applied to obtain maximum likelihood estimates of the parameters for a mixture of multivariate normal distributions.
Lawton, W. M.↗
Comparison of some biased estimation methods (including ordinary subset regression) in the linear model
Ridge, Marquardt's generalized inverse, shrunken, and principal components estimators are discussed in terms of the objectives of point estimation of parameters, estimation of the predictive regression function, and hypothesis testing. It is found that as the normal equations approach singularity, more consideration must be given to estimable functions of the parameters as opposed to estimation of the full parameter vector; that biased estimators all introduce constraints on the parameter space; that adoption of mean squared error as a criterion of goodness should be independent of the degree of singularity; and that ordinary least-squares subset regression is the best overall method.
Sidik, S. M.↗
Regression methods for spatial data
The kriging approach, a parametric regression method used by hydrologists and mining engineers, among others also provides an error estimate the integral of the regression function. The kriging method is explored and some of its statistical characteristics are described. The Watson method and theory are extended so that the kriging features are displayed. Theoretical and computational comparisons of the kriging and Watson approaches are offered.
Yakowitz, S. J.↗
Anuglar distribution of shower particles produced in the collisions of 20-GeV/c and 300-GeV negative pions with emulsion nuclei
For 435 accelerator produced antipions jets of 20 GeV/c and 300 GeV, in nuclear emulsion, eta(theta)'s have been individually calculated for each jet, where eta(theta) is a kinematic parameter introduced in order to approximate the LS (laboratory system) rapidity, eta = arctan h (beta cos theta). By taking further averages by dividing the samples into groupings of the LS energy E sub pi = m cos h eta sub pi N sub h, the number of heavy prongs with LS velocity beta 0.7, and n , the number of charged shower particles with LS velocity beta 0.7, much less than eta (theta) much greater than are obtained. By use of the KNO (Koba-Nielsen-Olesen) scaling variable, xi = n sub s/,n sub s. good fit is found of data to regression function.
Kim, C. O.↗
Optimization of the information content of multitemporal Landsat TM data sets for monitoring forest cover disturbance
Procedures that were developed to optimize the information content of multitemporal thematic mapper (TM) data sets for forest cover disturbance monitoring in Minnesota are described. TM imagery from three different years was calibrated to exoatmospheric reflectance. An atmospheric correction routine was applied combining two major components, atmospheric normalization over time and transformation to ground reflectance. Atmospheric conditions were modeled over time using regression functions derived from five ground features known to be unchanged over the time interval of interest and spanning the entire image reflectance range. The correlation between digital data and the forest cover was subsequently maximized and irrelevant information content was reduced by converting the band-specific reflectances into seven vegetation indices that were assumed to carry unique information. The application of two change detection algorithms to these seven indices ultimately resulted in 14 change features for each time interval of interest. Results show that the preprocessing sequence is vital to forest cover monitoring methodology.
Coppin, Pol R.↗
Dynamic Ensemble Prediction of Cognitive Performance in Space
Astronauts are exposed to a unique set of stressors in spaceflight. Microgravity, isolation, confinement, and environmental and operational hazards: all of these can impact sleep, vigilant attention, and alertness, which are critical to mission success. In this paper, we seek to understand the most important predictors of alertness over the course of a space mission, using self-reported, cognitive, and environmental data collected from 24 astronauts on 6-month missions to the International Space Station (ISS). Alertness was repeatedly and objectively assessed on the ISS with a brief 3-minute Psychomotor Vigilance Test (PVT) that is highly sensitive to sleep deprivation. To relate PVT performance to time-varying and sparsely-measured environmental, operational, and psychological covariates, we propose a n ensemble prediction model comprising of linear mixed effects regression, random forest, and functional concurrent regression models. An extensive cross-validation procedure reveals that this ensemble outperforms any one of its components alone. We also discover that a participant’s past performance, reported fatigue and stress, and temperature and radiation exposure were among the most important variables associated with alertness. This method is broadly applicable to environmental studies where the main goal is accurate, individualized prediction involving a mixture of person-level traits and irregularly measured time series.
Danni Tu↗
Bounds Estimation Via Regression with Asymmetric Cost Functions
This paper addresses a significant but mostly-neglected class of problems that we call bounds estimation. This includes learning empirical best-case and worst-case algorithmic complexity bounds and red-line bounds on sensor data.
regression-based learning algorithm bounds estimat↗
Ballistic limit regression analysis for Space Station Freedom meteoroid and space debris protection system
Relationships defining the ballistic limit of Space Station Freedom's (SSF) dual wall protection systems have been determined. These functions were regressed from empirical data found in Marshall Space Flight Center's (MSFC) Hypervelocity Impact Testing Summary (HITS) for the velocity range between three and seven kilometers per second. A stepwise linear least squares regression was used to determine the coefficients of several expressions that define a ballistic limit surface. Using statistical significance indicators and graphical comparisons to other limit curves, a final set of expressions is recommended for potential use in Probability of No Critical Flaw (PNCF) calculations for Space Station. The three equations listed below represent the mean curves for normal, 45 degree, and 65 degree obliquity ballistic limits, respectively, for a dual wall protection system consisting of a thin 6061-T6 aluminum bumper spaced 4.0 inches from a .125 inches thick 2219-T87 rear wall with multiple layer thermal insulation installed between the two walls. Normal obliquity is d(sub c) = 1.0514 v(exp 0.2983 t(sub 1)(exp 0.5228). Forty-five degree obliquity is d(sub c) = 0.8591 v(exp 0.0428) t(sub 1)(exp 0.2063). Sixty-five degree obliquity is d(sub c) = 0.2824 v(exp 0.1986) t(sub 1)(exp -0.3874). Plots of these curves are provided. A sensitivity study on the effects of using these new equations in the probability of no critical flaw analysis indicated a negligible increase in the performance of the dual wall protection system for SSF over the current baseline. The magnitude of the increase was 0.17 percent over 25 years on the MB-7 configuration run with the Bumper II program code.
Jolly, William H.↗
Modeling the effects of exercise during 100% oxygen prebreathe on the risk of hypobaric decompression sickness
BACKGROUND: Several previous studies indicated that exercise during prebreathe with 100% O2 decreased the incidence of hypobaric decompression sickness (DCS). We report a meta-analysis of these investigations combined with a new study in our laboratory to develop a statistical model as a predictive tool for DCS. HYPOTHESIS: Exercise during prebreathe increases N2 elimination in a theoretical 360-min half-time compartment decreasing the incidence of DCS. METHODS: A dose-response probability tissue ratio (TR) model with 95% confidence limits was created for two groups, prebreathe with exercise (n = 113) and resting prebreathe (n = 113), using nonlinear regression analysis with maximum likelihood optimization. RESULTS: The model predicted that prebreathe exercise would reduce the residual N2 in a 360-min half-time compartment to a level analogous to that in a 180-min compartment. This finding supported the hypothesis. The incidence of DCS for the exercise prebreathe group was significantly decreased (Chi-Square = 17.1, p < 0.0001) from the resting prebreathe group. CONCLUSIONS: The results suggested that exercise during prebreathe increases tissue perfusion and N2 elimination approximately 2-fold and markedly lowers the risk of DCS. Based on the model, the prebreathe duration may be reduced from 240 min to a predicted 91 min for the protocol in our study, but this remains to be verified. The model provides a useful planning tool to develop and test appropriate prebreathe exercise protocols and to predict DCS risks for astronauts.
NASA Program Environmental Health↗
Statistical distribution sampling
Determining the distribution of statistics by sampling was investigated. Characteristic functions, the quadratic regression problem, and the differential equations for the characteristic functions are analyzed.
Johnson, E. S.↗
Embedded Sensors for Measuring Surface Regression
The development and evaluation of new hybrid and solid rocket motors requires accurate characterization of the propellant surface regression as a function of key operational parameters. These characteristics establish the propellant flow rate and are prime design drivers affecting the propulsion system geometry, size, and overall performance. There is a similar need for the development of advanced ablative materials, and the use of conventional ablatives exposed to new operational environments. The Miniature Surface Regression Sensor (MSRS) was developed to serve these applications. It is designed to be cast or embedded in the material of interest and regresses along with it. During this process, the resistance of the sensor is related to its instantaneous length, allowing the real-time thickness of the host material to be established. The time derivative of this data reveals the instantaneous surface regression rate. The MSRS could also be adapted to perform similar measurements for a variety of other host materials when it is desired to monitor thicknesses and/or regression rate for purposes of safety, operational control, or research. For example, the sensor could be used to monitor the thicknesses of brake linings or racecar tires and indicate when they need to be replaced. At the time of this reporting, over 200 of these sensors have been installed into a variety of host materials. An MSRS can be made in either of two configurations, denoted ladder and continuous (see Figure 1). A ladder MSRS includes two highly electrically conductive legs, across which narrow strips of electrically resistive material are placed at small increments of length. These strips resemble the rungs of a ladder and are electrically equivalent to many tiny resistors connected in parallel. A substrate material provides structural support for the legs and rungs. The instantaneous sensor resistance is read by an external signal conditioner via wires attached to the conductive legs on the non-eroding end of the sensor. The sensor signal can be transmitted from inside a high-pressure chamber to the ambient environment, using commercially available feedthrough connectors. Miniaturized internal recorders or wireless data transmission could also potentially be employed to eliminate the need for producing penetrations in the chamber case. The rungs are designed so that as each successive rung is eroded away, the resistance changes by an amount that yields a readily measurable signal larger than the background noise. (In addition, signal-conditioning techniques are used in processing the resistance readings to mitigate the effect of noise.) Hence, each discrete change of resistance serves to indicate the arrival of the regressing host material front at the known depth of the affected resistor rung. The average rate of regression between two adjacent resistors can be calculated simply as the distance between the resistors divided by the time interval between their resistance jumps. Advanced data reduction techniques have also been developed to establish the instantaneous surface position and regression rate when the regressing front is between rungs.
Gramer, Daniel J.↗
Application of remote sensing for fishery resources assessment and monitoring
The author has identified the following significant results. The distribution and abundance of white marlin correlated with the chlorophyll, water temperature, and Secchi depth sea truth measurements. Results of correlation analyses for dolphin were inconclusive. Predicition models for white marlin were developed using stepwise multiple regression and discriminant function analysis techniques which demonstrated a potential for increasing the probability of game fishing success. The S190A and B imagery was density sliced/color enhanced with white marlin location superimposed on the image, but no density/white marlin relationship could be established.
Savastano, K. J.↗
TPSAS-NF1676L-18357-DND
High-spectral resolution measurements (in the IR region) from space born infrared sensors can provide sufficient spectral information about cloud properties like cloud top pressure, cloud particle size and cloud optical thickness. Empirical orthogonal function (EOF) based regression scheme was used to retrieve cloud properties along with atmospheric state profiles. A channel based physical inversion scheme was also tried on cloud-contaminated radiances to improve retrieval accuracy achieved by regression scheme. Recently developed principle component (PC) based physical retrieval algorithm utilized the EOF transformation to compress both hyperspectral radiance spectra and atmospherical profiles into PC scores to greatly boost the computational speed while maintaining the information content. The accuracy of the (PC) based radiation transfer model (PCRTM) to simulate top-of the atmosphere(TOA) high-spectral resolution radiance spectra for both clear and cloudy sky conditions has been well tested by comparing with the other line-by-line radiation transfer model and using the observation data. The application of the PCRTM based physical inversion method on simulated IASI radiance under 'cloudy' conditions will be a good integrity test for the new algorithm.
X Liu↗
Precision Interval Estimation of the Response Surface by Means of an Integrated Algorithm of Neural Network and Linear Regression
The integration of Radial Basis Function Networks and Back Propagation Neural Networks with the Multiple Linear Regression has been accomplished to map nonlinear response surfaces over a wide range of independent variables in the process of the Modem Design of Experiments. The integrated method is capable to estimate the precision intervals including confidence and predicted intervals. The power of the innovative method has been demonstrated by applying to a set of wind tunnel test data in construction of response surface and estimation of precision interval.
Lo, Ching F.↗