On non-central chi-squared and non-central F distributions.
Differential difference equations for decision procedure risk function based on noncentral chi squared and F distributions in multivariate statistical analysis
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Differential difference equations for decision procedure risk function based on noncentral chi squared and F distributions in multivariate statistical analysis
Comparison of multivariate statistical analysis techniques for multinomial selection indices
The author has identified the following significant results. The ability to read the 24-channel MSS CCT tapes, select specified agricultural land use areas from the CCT, and perform multivariate statistical and pattern recognition analyses has been demonstrated. The 5 optimum channels chosen for classifying an agricultural scene were, in the order of their selection the far red visible, short reflective IR, visible blue, thermal infrared, and ultraviolet portions of the electromagnetic spectrum, respectively. Although chosen by a training set containing only vegetal categories, the optimum 4 channels discriminated pavement, water, bare soil, and building roofs, as well as the vegetal categories. Among the vegetal categories, sugar cane and cotton had distinctive signatures that distinguished them from grass and citrus. Acreages estimated spectrally by the computer for the test scene were acceptably close to acreages estimated from aerial photographs for cotton, sugar cane, and water. Many nonfarmable land resolution elements representing drainage ditch, field road, and highway right-of-way as well as farm headquarters area fell into the grass, bare soil plus weeds, and citrus categories and lessened the accuracy of the farmable acreage estimates in these categories. The expertise developed using the 24-channel data will be applied to the ERTS-1 data.
Research has focused on the design and partial implementation of a comprehensive ILLIAC software system for computer-assisted interpretation of multispectral earth resources data such as that now collected by the Earth Resources Technology Satellite. Research suggests generally that the ILLIAC 4 should be as much as two orders of magnitude more cost effective than serial processing computers for digital interpretation of ERTS imagery via multivariate statistical classification techniques. The potential of the ARPA Network as a mechanism for interfacing geographically-dispersed users to an ILLIAC 4 image processing facility is discussed.
Computer program applies chi-square Pearson test to multivariate statistics for application in any field in which data of two or more variables (dimensions) are sampled for statistical purposes. Program handles dimensions two through five, with up to thousand data sets.
Energetic analyses of the NMC initial conditions and NMC six-layer primitive equation operational prediction model 12-hr forecast for a developing cyclone are presented. Consideration is given to the total kinetic energy, the energetics of the divergent and nondivergent flows and the baroclinic (vertical shear flow) and barotropic (vertical mean flow) components of the kinetic energy. It is found that the model initial conditions lose 10-15% of the kinetic energy at various levels compared to a limited-area multivariate statistical analysis of the observational data, leading to a decrease in the horizontal kinetic energy flux, a misrepresentation of the synoptic scale wave system in the 12-hr forecast. Similar results are obtained for the nondivergent flow, while the divergent flow energetics are not reproduced accurately by the model. The horizontal flux terms of the vertical mean and vertical shear energetics are also not found to be reproduced in the upper levels, although horizontal flux contributions to the baroclinic component are improved at middle and lower levels. Finally, vertical shear kinetic energy generation is found to be well represented in the model prediction, however kinetic energy conversion between vertical shear and mean flow is not reproduced in the lower layer.
The benefits of changes in management organization and facilities for the Center for Remote Sensing and Cartography in Utah are reported as well as interactions with and outreach to state and local agencies. Completed projects are described which studied (1) Unita Basin wetland/land use; (2) Davis County foothill development; (3) Farmington Bay shoreline fluctuation; (4) irrigation detection; and (5) satellite investigation of snow cover/mule deer relationships. Techniques developed for composite computer mapping, contrast enhancement, U-2 CIR/LANDSAT digital interface; factor analysis, and multivariate statistical analysis are described.
A digital computer and multivariate statistical techniques were used to analyze 4-band multispectral data. A representation of the original data for each of the four bands allows a certain degree of terrain interpretation; however, variations in appearance of sites within and between bands, without additional criteria for deciding which representation should be preferred, create difficulties for classification. Investigation of the video data groups produced by principal components analysis and cluster analysis techniques shows that effective correlations with classifications of terrain produced by conventional methods could be carried out. The analyses also highlighted underlying relationships between the various elements. The approach used allows large areas (185 cm by 185 cm) to be classified into fundamental units within a matter of hours and can be applied to those parts of the Earth where facilities for conventional studies are poor or lacking.
An estimated cost savings of 30% to 50% was realized from using LANDSAT-derived data as input into a program which simulates hydrologic and water quality processes in natural and man-made water systems. Data from the satellite were used in conjunction with EPA's 11-channel multispectral scanner to obtain maps for characterizing the distribution of turbidity plumes in Flathead Lake and to predict the effect of increasing urbanization in Montana's Flathead River Basin on the lake's trophic state. Multispectral data are also being studied as a possible source of the parameters needed to model the buffering capability of lakes in an effort to evaluate the effect of acid rain in the Adirondacks. Water quality in Lake Champlain, Vermont is being classified using data from the LANDSAT and the EPA MSS. Both contact-sensed and MSS data are being used with multivariate statistical analysis to classify the trophic status of 145 lakes in Illinois and to identify water sampling sites in Appalachicola Bay where contaminants threaten Florida's shellfish.
Multivariate statistical analysis and imaging processing techniques are being applied to the study of arid/semiarid environments, with emphasis on desertification. Field level indicators of land-soil biota degradation are being sifted out with staging up to the low aircraft reconnaissance level, to LANDSAT TM & MSS, and even to the AVHRR level. Three completed projects are reviewed: riparian habitat on the Humboldt River floodplain, Salt Lake County Urban expansion detection, and salinization/desertification detection in the delta area. Beginning projects summarized include: comparative condition of rangeland in Rush Valley; modeling a GIS/remote sensing data base for Cache County; universal soil loss equation applied to Pinyon-Juniper; relating MSS to ground radiometry near Battle Mountain; and riparian habitat mapping on Mary's River, Nevada.
The papers presented at the Fifth Conference on the Meteorology of the Stratosphere and Mesosphere held on April 23-26, 1985, are reviewed. The observational aspects of large-scale circulation, such as summer and winter circulation in the Southern Hemisphere, and analysis schemes, like the multivariate statistical analysis scheme, are discussed. The topics of numerical simulations of the general circulation and sudden-warming are examined. Papers concerning processes of O3, NO2, H2, and HNO3 are described. Research on large-scale mixing processes in the stratosphere is presented. The topic of equatorial dynamics and stability is analyzed. Papers focusing on the effect of gravity waves on the general circulation are studied.
The application of satellite data to the study of synoptic characteristics is analyzed. A radiative transfer model is used to generate a database of satellite information on synoptic features. Canonical discriminant analysis is employed to reveal the differences among synoptic sounding classes; and the fine structures within each sounding class are examined with rotated factor analysis. Diagrams of wind and frontal inversions are presented. It is noted that the applicability of satellite data depends on the method used to analyze it and multivariable statistical techniques may be useful for deriving additional information from satellite data.
The spatial and phenological distribution of vegetation was examined in a remote sensing geobotanical study of the East Africa Rift region. Six normalized difference vegetation index (NDVI) AVHRR (advanced very high resolution radiometer) scenes (February, June, and September of both 1984 and 1987) were used as a measure of vegetation presence. NOAA ETOPO-5 elevation and geographic coordinate data were coregistered with the multitemporal NDVI images. Univariate and multivariate statistics indicate that the NDVI values are significantly associated with elevation, latitude, and longitude. This supports the concept of quantifiable, regional gradients that affect large-scale geobotanical studies. A quadratic regression line was fitted to the NDVI, elevation, latitude, and longitudinal data. In this way a regional trend, as affected by elevation, was determined. The deviation of the actual data from this regional trend was displayed as an image, and shows the local climatic and geological influences.
The aircraft cockpit ambient lighting simulation system (ACALSS) has been developed to study display readability and associated pilot/vehicle performance effects in a part-task simulator cockpit. In the study reported here, the ACALSS was used to determine the illumination levels at which subjects lose the ability to maintain aircraft states when using three display technologies as display media for primary flight displays: a standard monochrome EL (electroluminescent) flat-panel, a laboratory-class monochrome CRT, and an enhanced-brightness EL flat-panel. The multivariate statistical technique of modified profile analysis was used to test for performance differences between display devices as functions of illumination levels. The standard monochrome EL flat-panel display began to washout after the 2500 foot-candle level of illumination. The monochrome CRT began to washout after the 5500 foot-candle level of illumination. No performance decrements by increased illumination up to the 12,000 foot-candle level were found for the enhanced-brightness EL flat-panel display. What was not anticipated was that half the subjects would subjectively prefer the CRT over the enhanced-brightness EL, even though their performance errors would have indicated the opposite.
Data exploration systems apply machine learning techniques, multivariate statistical methods, information theory, and database theory to databases to identify significant relationships among the data and summarize information. The result of applying data exploration systems should be a better understanding of the structure of the data and a perspective of the data enabling an analyst to form hypotheses for interpreting the data. This paper argues that data exploration systems need a minimum amount of domain knowledge to guide both the statistical strategy and the interpretation of the resulting patterns discovered by these systems.
Multivariate statistical techniques and fundamental plane fits are used here to study possible systematic differences between field ellipticals (FEs) and cluster ellipticals (CEs). The FEs show more intrinsic scatter in their properties, especially when stellar population variables are included. Pairwise correlations for the two samples are different; the correlations are systematically better for the cluster sample, meaning that ellipticals in the two samples populate their fundamental planes in different ways. Bivariate correlations are different for the two samples, implying that they have different fundamental planes. This is especially true for the correlations which include the population variables Mg2 and (B-V), which are sensitive both to the enrichment history and the storm formation history.
Multivariate statistical analysis is used to correlate the estimated total numbers of globular clusters in elliptical galaxies (N sub gc), and the numbers per unit luminosity (S sub N), with a variety of observed properties of the host galaxies. Both N sub gc and S sub N are correlated with the so-called fundamental plane of elliptical galaxies, suggesting that the processes which determine global properties of ellipticals also largely determine their globular cluster content, although a considerable residual scatter remians. The redder (presumably more metal-rich) galaxies were found to have more globular clusters, implying that a dissipative formation mechanism was involved. Galaxies which have more anisotropic velocity distributions were also found to have more clusters, suggesting that mergers may have been important in the production of globular systems.
Implementation of computer programs based on multivariate statistical algorithms makes possible obtaining reliable information from long data vectors that contain large amounts of extraneous information, for example, noise and/or analytes that we do not wish to control. Three examples are described. Each of these applications requires the use of techniques characteristic of modern analytical chemistry. The first example, using a quantitative or analytical model, describes the determination of the acid dissociation constant for 2,2'-pyridyl thiophene using archived data. The second example describes an investigation to determine the active biocidal species of iodine in aqueous solutions. The third example is taken from a research program directed toward advanced fiber-optic chemical sensors. The second and third examples require heuristic or empirical models.