Statistical decision problems in large scale biological experiments Final report
Statistical decision theory applied to problems associated with Martian biological exploration program
BIOLOGY↗
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Data Mining Methods Applied to Flight Operations Quality Assurance Data: A Comparison to Standard Statistical Methods
In a previous study, multiple regression techniques were applied to Flight Operations Quality Assurance-derived data to develop parsimonious model(s) for fuel consumption on the Boeing 757 airplane. The present study examined several data mining algorithms, including neural networks, on the fuel consumption problem and compared them to the multiple regression results obtained earlier. Using regression methods, parsimonious models were obtained that explained approximately 85% of the variation in fuel flow. In general data mining methods were more effective in predicting fuel consumption. Classification and Regression Tree methods reported correlation coefficients of .91 to .92, and General Linear Models and Multilayer Perceptron neural networks reported correlation coefficients of about .99. These data mining models show great promise for use in further examining large FOQA databases for operational and safety improvements.
Stolzer, Alan J.↗
Statistics of close approaches between asteroids and planets - Project Spaceguard
A data base of close approaches to the major planets has been generated via numerical integrations for a large number of planet-crossing asteroid orbits over the course of 200,000 yr; these data are then applied to such statistical theories as those of Kessler (1981) and Wetherill (1967). Attention is given to the orbits of the Toro-class asteroids, which violate the assumption of a lack of mean motion resonance locking between target planet and asteroid. A modified form of the Kessler theory is proposed which can address the problem of approaches between orbits that are either nearly coplanar or nearly tangent. A correlation analysis is used to test the assumption that the orbital elements of a planet-crossing orbit change solely due to close approaches.
Milani, A.↗
TRMM Fire Algorithm, Product and Applications
Land fires are frequent menaces to human lives and property. They also change the state of the vegetation and contribute to the climate forcing by releasing large amount of aerosols and greenhouse gases into the atmosphere. This paper summarizes methodologies of detecting global land fires from the Tropical Rainfall Measuring Mission (TRMM) Visible Infrared Scanner FIRS) measurements. The TRMM Science Data and Information System (TSDIS) fire products include global images of daily hot spots and monthly fire counts at 0.5 deg. x 0.5 deg. resolution, as well as text fiies that details necessary information of all fire pixels. The information includes date, orbit number, pixel number, local time, solar zenith angle, latitude, longitude, reflectance of visible/near infrared channels, brightness temperatures of infrared channels, as well as background brightness temperatures of infrared channels. These products have been archived since January 1998. The TSDIS fire products are compared with the coincidental European Commission (EC) Joint Research Center (JRC) 1 km AVHRR fire products. Analyses of the TSDIS monthly fire products during the period from 1998 to 2003 manifested seasonal cycles of biomass fires over Southeast Asia, Africa, North America and South America. The data also showed interannual variations associated with the 98/99 ENS0 cycle in Central America and the Indonesian region. In order to understand the variability of global land fires and their effects on the distribution of atmospheric aerosols, statistical methods were applied to the TSDIS fire products as well as to the Total Ozone Mapping Spectrometer (TOMS) aerosol index products for a period of five years from January 1998 to December 2002. The variability of global atmospheric aerosol is consistent with the fire variations over these regions during this period. The correlation between fire count and TOMS aerosol index is about 0.55 for fire pixels in Southeast Asia, Indonesia, and Africa. Parallel statistical analyses such as Empirical Orthogonal Function (EOF) analysis and Singular Spectrum Analysis (SSA) methods were applied to pentad TRMM fire data and TOMS aerosol data. The EOF analyses showed contrast between North and South hemispheres and also inter- continental transitions in Africa and America. EOF and SSA analyses also identified 25-60 day intra-seasonal oscillations that were superimposed on the annual cycles of both fire and aerosol data. The intra-seasonal variability of fires showed similarity of tropical rainfall oscillation modes. The TRMM fire products were also compared to the coincident TRMh4 rainfall and other rainfall products to investigate the interaction between rainfall and fire. The results indicate that the annual, interannual and intraseasonal variability of fire are dominated by global rainfall variations. However, the feedback of fire to the rainfall occurrence at regional scale for certain regions is also evident.
Ji, Yi-Min↗
Statistical Analysis of Factors Riving Surface Ozone Variability over Continental South Africa
Statistical relationships between surface ozone (O3) concentration, precursor species and meteorological conditions in continental South Africa were examined from data obtained from measurement stations in north-eastern South Africa. Three multivariate statistical methods were applied in the investigation, i.e. multiple linear regression (MLR), principal component analysis (PCA) and –regression (PCR), and generalised additive model (GAM) analysis. The daily maximum 8-h moving average O3 concentrations were considered in these statistical models (dependent variable). MLR models indicated that meteorology and precursor species concentrations are able to explain ~50% of the variability in daily maximum O3 levels. MLR analysis revealed that atmospheric carbon monoxide (CO), temperature and relative humidity were the strongest factors affecting the daily O3 variability. In summer, daily O3 variances were mostly associated with relative humidity, while winter O3 levels were mostly linked to temperature and CO. PCA indicated that CO, temperature and relative humidity were not strongly collinear. GAM also identified CO, temperature and relative humidity as the strongest factors affecting the daily variation of O3. Partial residual plots found that temperature, radiation and nitrogen oxides most likely have a non-linear relationship with O3,while the relationship with relative humidity and CO is probably linear. An inter-comparison between O3 levels modelled with the three statistical models compared to measured O3 concentrations showed that the GAM model offered a slight improvement over the MLR model. These findings emphasise the critical role of regional-scale O3 precursors coupled with meteorological conditions in daily variances of O3 levels in continental South Africa.
multiple linear regression (MLR)↗
JIGSAW: Preference-directed, co-operative scheduling
Techniques that enable humans and machines to cooperate in the solution of complex scheduling problems have evolved out of work on the daily allocation and scheduling of Tactical Air Force resources. A generalized, formal model of these applied techniques is being developed. It is called JIGSAW by analogy with the multi-agent, constructive process used when solving jigsaw puzzles. JIGSAW begins from this analogy and extends it by propagating local preferences into global statistics that dynamically influence the value and variable ordering decisions. The statistical projections also apply to abstract resources and time periods--allowing more opportunities to find a successful variable ordering by reserving abstract resources and deferring the choice of a specific resource or time period.
Linden, Theodore A.↗
Recent Development on O(+)-O Collision Frequency and Ionosphere-Middle Atmosphere Coupling
The collision frequency between an oxygen atom and its singly charged ion controls the transfer of energy between the solar radiation and the thermosphere. There were a long standing discrepancy, extending over a decade, between the theoretical and empirical determination of this frequency, and the empirical value of this frequency exceeded the theoretical value by a factor of 1.7. Recent improvements in theory were obtained by using accurate oxygen ion-oxygen atom potential energy curves, and partial wave quantum mechanical calculations. Similarly, recently three independent statistical methods were applied to the empirical determination of this frequency. These methods give results consistent with each other, and together with the recent theoretical improvements, bring the ratio close to unity, as it should be. It will be shown that the old statistical method for this determination contained accumulative errors, leading to a larger value for this ratio. The recent improvements lead to an average value of the empirical to the theoretical ratio equal to 0.98, with an uncertainty of +/- 8%, resolving the old discrepancy between theory and observations. The main source of uncertainties are errors in the profile of the oxygen atom density, which is of the order of 11 %. An alternative method to find the oxygen atom density is being suggested.
Omidvar, K.↗
Failure Bounding And Sensitivity Analysis Applied To Monte Carlo Entry, Descent, And Landing Simulations
In the study of entry, descent, and landing, Monte Carlo sampling methods are often employed to study the uncertainty in the designed trajectory. The large number of uncertain inputs and outputs, coupled with complicated non-linear models, can make interpretation of the results difficult. Three methods that provide statistical insights are applied to an entry, descent, and landing simulation. The advantages and disadvantages of each method are discussed in terms of the insights gained versus the computational cost. The first method investigated was failure domain bounding which aims to reduce the computational cost of assessing the failure probability. Next a variance-based sensitivity analysis was studied for the ability to identify which input variable uncertainty has the greatest impact on the uncertainty of an output. Finally, probabilistic sensitivity analysis is used to calculate certain sensitivities at a reduced computational cost. These methods produce valuable information that identifies critical mission parameters and needs for new technology, but generally at a significant computational cost.
Gaebler, John A.↗
Implementation of pattern recognition techniques as applied to geoscience interpretation
Statistical system using statistical decision theory for data interpretation
Dolke, G. W.↗
VISSR Atmospheric Sounder (VAS) simulation experiment for a severe storm environment
Radiance fields were simulated for prethunderstorm environments in Oklahoma to demonstrate three points: (1) significant moisture gradients can be seen directly in images of the VISSIR Atmospheric Sounder (VAS) channels; (2) temperature and moisture profiles can be retrieved from VAS radiances with sufficient accuracy to be useful for mesoscale analysis of a severe storm environment; and (3) the quality of VAS mesoscale soundings improves with conditioning by local weather statistics. The results represent the optimum retrievability of mesoscale information from VAS radiance without the use of ancillary data. The simulations suggest that VAS data will yield the best soundings when a human being classifies the scene, picks relatively clear areas for retrieval, and applies a "local" statistical data base to resolve the ambiguities of satellite observations in favor of the most probable atmospheric structure.
Chesters, D.↗
Continuation of studies in statistical decision theory in large scale biological experiments Final report, 1 May 1965 - 31 Jul. 1966
Statistical decision theory applied to Martian atmosphere analysis, life detection experiments, and gas chromatogram measurements of n-alkane distributions in materials
ALKANE↗
Analysis of extreme wind shear
New methods utilizing extreme value statistical theory are applied in the analysis of the largest wind component shear in a wind profile as a function of shear layer thickness and season. Seasonal variability of extreme shear decreases as the shear layer thickness decreases. Wind profile measurement system smoothing and its effect upon extreme wind shear statistics is simulated by application of digital low-pass filters to Jimsphere wind profiles.
Adelfang, Stanley I.↗
A statistical rain attenuation prediction model with application to the advanced communication technology satellite project. 1: Theoretical development and application to yearly predictions for selected cities in the United States
A rain attenuation prediction model is described for use in calculating satellite communication link availability for any specific location in the world that is characterized by an extended record of rainfall. Such a formalism is necessary for the accurate assessment of such availability predictions in the case of the small user-terminal concept of the Advanced Communication Technology Satellite (ACTS) Project. The model employs the theory of extreme value statistics to generate the necessary statistical rainrate parameters from rain data in the form compiled by the National Weather Service. These location dependent rain statistics are then applied to a rain attenuation model to obtain a yearly prediction of the occurrence of attenuation on any satellite link at that location. The predictions of this model are compared to those of the Crane Two-Component Rain Model and some empirical data and found to be very good. The model is then used to calculate rain attenuation statistics at 59 locations in the United States (including Alaska and Hawaii) for the 20 GHz downlinks and 30 GHz uplinks of the proposed ACTS system. The flexibility of this modeling formalism is such that it allows a complete and unified treatment of the temporal aspects of rain attenuation that leads to the design of an optimum stochastic power control algorithm, the purpose of which is to efficiently counter such rain fades on a satellite link.
Manning, Robert M.↗
The rotation of small asteroids
The Binzel and Mulholland (1983) sample of photoelectrically determined rotational parameters for 17 main belt asteroids with diameters less than 30 km are compared with previous observations of asteroids of that size range. Rigorous statistical tests are applied to investigate bias effects and quantify results on asteroid rotation. The samples are described and compared for rotational frequency, rotational amplitude, frequency distribution, and diameter and frequency dependence. It is concluded that the observed rotational frequency distribution can be acceptably fit by two Maxwellian distributions, which is consistent with the hypothesis that there are separate populations of slow and fast rotating asteroids. The frequency distributions of main belt asteroids less than 15 km in diameter and earth and Mars crossers do not differ significantly, but the larger mean lightcurve amplitude of these crossers is statistically significant. No significant diameter dependence on rotational frequency is found among the sample asteroids.
Binzel, R. P.↗
Separating the Chemical and Dynamical Contributions to the Ozone Change
Statistical analysis is used to extract the sensitivity of ozone to changes in stratospheric chlorine due to emissions of chlorofluorcarbons from the observed ozone record. The statistical analysis relies on a model that accounts for natural variations in ozone including the seasonal cycle, the solar cycle, variations in aerosols due to volcanic eruption, and the quasi- biennial oscillation, A noise term includes contributions to ozone variability due to inter-annual variability in the stratospheric circulation not due to the quasi-biennial oscillation, The residual circulation varies due to variability in planetary wave forcing, and studies using meteorological analyses show that the build-up of ozone over the winter is correlated with the planetary wave Eliassen-Palm flux. This variability in the residual circulation is not included in the statistical model, and contributes to the apparent ozone sensitivity to chlorine derived from observations for 1979 - 2000. We have investigated these relationships using multi-decadal simulations of our off-line chemistry and transport model (CTM). Our simulations use meteorological fields output from a 50 year simulation of a general circulation model (GCM). A 50 climatology specifies the sea surface temperatures to produce the GCM simulation. The CTM was used with these winds to produce two simulations, one in which the boundary conditions for chlorofluorcarbons and other source gases vary as specified for 1973-2022 by the Scenario A2 of the World Meteorological Organization ozone assessment, and the second with source gases fixed to their 1979 values. The same statistical analysis used to derive trends from observations is applied to the CTM output. When applied to the difference between the two simulations the statistical analysis provides a more precise measure of the ozone sensitivity to chlorine change. We are testing ways of including the interannual variability in the residual circulation in the statistical model so that we can derive the same result from the Scenario A2 simulation as is obtained when the statistical analysis is applied to the difference between the two simulations. This should provide direction as to how to account for the changes in ozone due to interannual variability in the residual circulation in the statistical model that is applied to the observed data record.
Douglass, Anne R.↗
Components of interannual ozone change based on Nimbus 7 TOMS data
A multiple regression statistical model is applied to estimate the latitude and seasonal dependences of the solar cycle, quasi-biennial oscillation (QBO), and anthropogenic trend components of stratospheric total ozone change using 13.2 years of Nimbus 7 TOMS data. The characteristics of the linear trend component are in agreement with earlier studies. The QBO regression coefficient is significantly different from zero at high southern latitudes in the Austral spring supporting earlier evidence that the Antarctic ozone depletion is modulated by the QBO. The existence of a solar cycle component is indicated by empirical studies of model residuals and by the approximate agreement of the derived global mean solar coefficient amplitude with photochemical calculations. Initial estimates for the latitude dependence of the solar coefficient suggest higher amplitudes with increasing latitude, especially in the Southern Hemisphere in spring. The statistical model predicts a return to more rapid ozone depletions during the next 4 years as solar minimum is approached.
Hood, Lon L.↗
Inverse problems: Fuzzy representation of uncertainty generates a regularization
In many applied problems (geophysics, medicine, and astronomy) we cannot directly measure the values x(t) of the desired physical quantity x in different moments of time, so we measure some related quantity y(t), and then we try to reconstruct the desired values x(t). This problem is often ill-posed in the sense that two essentially different functions x(t) are consistent with the same measurement results. So, in order to get a reasonable reconstruction, we must have some additional prior information about the desired function x(t). Methods that use this information to choose x(t) from the set of all possible solutions are called regularization methods. In some cases, we know the statistical characteristics both of x(t) and of the measurement errors, so we can apply statistical filtering methods (well-developed since the invention of a Wiener filter). In some situations, we know the properties of the desired process, e.g., we know that the derivative of x(t) is limited by some number delta, etc. In this case, we can apply standard regularization techniques (e.g., Tikhonov's regularization). In many cases, however, we have only uncertain knowledge about the values of x(t), about the rate with which the values of x(t) can change, and about the measurement errors. In these cases, usually one of the existing regularization methods is applied. There exist several heuristics that choose such a method. The problem with these heuristics is that they often lead to choosing different methods, and these methods lead to different functions x(t). Therefore, the results x(t) of applying these heuristic methods are often unreliable. We show that if we use fuzzy logic to describe this uncertainty, then we automatically arrive at a unique regularization method, whose parameters are uniquely determined by the experts knowledge. Although we start with the fuzzy description, but the resulting regularization turns out to be quite crisp.
Kreinovich, V.↗
Quantum detection theory
Statistical estimation theory applied to quantum mechanics and signal detection with optical instruments
Helstrom, C. W.↗