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NASA NTRS1976

Characterizations of linear sufficient statistics

A necessary and sufficient condition is developed such that there exists a continous linear sufficient statistic T for a dominated collection of totally finite measures defined on the Borel field generated by the open sets of a Banach space X. In particular, corollary necessary and sufficient conditions are given so that there exists a rank K linear sufficient statistic T for any finite collection of probability measures having n-variate normal densities. In this case a simple calculation, involving only the population means and covariances, determines the smallest integer K for which there exists a rank K linear sufficient statistic T (as well as an associated statistic T itself).

Peters, B. C., Jr.↗
NASA NTRS1977

Characterizations of linear sufficient statistics

A surjective bounded linear operator T from a Banach space X to a Banach space Y must be a sufficient statistic for a dominated family of probability measures defined on the Borel sets of X. These results were applied, so that they characterize linear sufficient statistics for families of the exponential type, including as special cases the Wishart and multivariate normal distributions. The latter result was used to establish precisely which procedures for sampling from a normal population had the property that the sample mean was a sufficient statistic.

Peters, B. C., Jr.↗
NASA NTRS1973

Sufficient Statistics: an Example

The feature selection problem is considered resulting from the transformation x = Bz where B is a k by n matrix of rank k and k is or = to n. Such a transformation can be considered to reduce the dimension of each observation vector z, and in general, such a transformation results in a loss of information. In terms of the divergence, this information loss is expressed by the fact that the average divergence D sub B computed using variable x is less than or equal to the average divergence D computed using variable z. If D sub B = D, then B is said to be a sufficient statistic for the average divergence D. If B is a sufficient statistic for the average divergence, then it can be shown that the probability of misclassification computed using variable x (of dimension k is or = to n) is equal to the probability of misclassification computed using variable z. Also included is what is believed to be a new proof of the well known fact that D is or = to D sub B. Using the techniques necessary to prove the above fact, it is shown that the Brattacharyya distance as measured by variable x is less than or equal to the Brattacharyya distance as measured by variable z.

Quirein, J.↗
NASA NTRS1972

Sufficient Statistics for Divergence and the Probability of Misclassification

One particular aspect is considered of the feature selection problem which results from the transformation x=Bz, where B is a k by n matrix of rank k and k is or = to n. It is shown that in general, such a transformation results in a loss of information. In terms of the divergence, this is equivalent to the fact that the average divergence computed using the variable x is less than or equal to the average divergence computed using the variable z. A loss of information in terms of the probability of misclassification is shown to be equivalent to the fact that the probability of misclassification computed using variable x is greater than or equal to the probability of misclassification computed using variable z. First, the necessary facts relating k-dimensional and n-dimensional integrals are derived. Then the mentioned results about the divergence and probability of misclassification are derived. Finally it is shown that if no information is lost (in x = Bz) as measured by the divergence, then no information is lost as measured by the probability of misclassification.

Quirein, J.↗
NASA NTRS2015

Free-Energy Calculations. A Mathematical Perspective

Ion channels are pore-forming assemblies of transmembrane proteins that mediate and regulate ion transport through cell walls. They are ubiquitous to all life forms. In humans and other higher organisms they play the central role in conducting nerve impulses. They are also essential to cardiac processes, muscle contraction and epithelial transport. Ion channels from lower organisms can act as toxins or antimicrobial agents, and in a number of cases are involved in infectious diseases. Because of their important and diverse biological functions they are frequent targets of drug action. Also, simple natural or synthetic channels find numerous applications in biotechnology. For these reasons, studies of ion channels are at the forefront of biophysics, structural biology and cellular biology. In the last decade, the increased availability of X-ray structures has greatly advanced our understanding of ion channels. However, their mechanism of action remains elusive. This is because, in order to assist controlled ion transport, ion channels are dynamic by nature, but X-ray crystallography captures the channel in a single, sometimes non-native state. To explain how ion channels work, X-ray structures have to be supplemented with dynamic information. In principle, molecular dynamics (MD) simulations can aid in providing this information, as this is precisely what MD has been designed to do. However, MD simulations suffer from their own problems, such as inability to access sufficiently long time scales or limited accuracy of force fields. To assess the reliability of MD simulations it is only natural to turn to the main function of channels - conducting ions - and compare calculated ionic conductance with electrophysiological data, mainly single channel recordings, obtained under similar conditions. If this comparison is satisfactory it would greatly increase our confidence that both the structures and our computational methodologies are sufficiently accurate. Channel conductance, defined as the ratio of ionic current through the channel to applied voltage, can be calculated in MD simulations by way of applying an external electric field to the system and counting the number of ions that traverse the channel per unit time. If the current is small, a voltage significantly higher than the experimental one needs to be applied to collect sufficient statistics of ion crossing events. Then, the calculated conductance has to be extrapolated to the experimental voltage using procedures of unknown accuracy. Instead, we propose an alternative approach that applies if ion transport through channels can be described with sufficient accuracy by the one-dimensional diffusion equation in the potential given by the free energy profile and applied voltage. Then, it is possible to test the assumptions of the equation, recover the full voltage/current dependence, determine the reliability of the calculated conductance and reconstruct the underlying (equilibrium) free energy profile, all from MD simulations at a single voltage. We will present the underlying theory, model calculations that test this theory and simulations on ion conductance through a channel that has been extensively studied experimentally. To our knowledge this is the first case in which the complete, experimentally measured dependence of the current on applied voltage has been reconstructed from MD simulations.

free energy↗
NASA NTRS2010

Weighting Statistical Inputs for Data Used to Support Effective Decision Making During Severe Emergency Weather and Environmental Events

National Aeronautical and Space Administration (NASA) weather and atmospheric environmental organizations are insatiable consumers of geophysical, hydrometeorological and solar weather statistics. The expanding array of internet-worked sensors producing targeted physical measurements has generated an almost factorial explosion of near real-time inputs to topical statistical datasets. Normalizing and value-based parsing of such statistical datasets in support of time-constrained weather and environmental alerts and warnings is essential, even with dedicated high-performance computational capabilities. What are the optimal indicators for advanced decision making? How do we recognize the line between sufficient statistical sampling and excessive, mission destructive sampling ? How do we assure that the normalization and parsing process, when interpolated through numerical models, yields accurate and actionable alerts and warnings? This presentation will address the integrated means and methods to achieve desired outputs for NASA and consumers of its data.

Gardner, Adrian↗
NASA NTRS2009

A Methodology for Determining Statistical Performance Compliance for Airborne Doppler Radar with Forward-Looking Turbulence Detection Capability

The objective of the research developed and presented in this document was to statistically assess turbulence hazard detection performance employing airborne pulse Doppler radar systems. The FAA certification methodology for forward looking airborne turbulence radars will require estimating the probabilities of missed and false hazard indications under operational conditions. Analytical approaches must be used due to the near impossibility of obtaining sufficient statistics experimentally. This report describes an end-to-end analytical technique for estimating these probabilities for Enhanced Turbulence (E-Turb) Radar systems under noise-limited conditions, for a variety of aircraft types, as defined in FAA TSO-C134. This technique provides for one means, but not the only means, by which an applicant can demonstrate compliance to the FAA directed ATDS Working Group performance requirements. Turbulence hazard algorithms were developed that derived predictive estimates of aircraft hazards from basic radar observables. These algorithms were designed to prevent false turbulence indications while accurately predicting areas of elevated turbulence risks to aircraft, passengers, and crew; and were successfully flight tested on a NASA B757-200 and a Delta Air Lines B737-800. Application of this defined methodology for calculating the probability of missed and false hazard indications taking into account the effect of the various algorithms used, is demonstrated for representative transport aircraft and radar performance characteristics.

Bowles, Roland L.↗
NASA NTRS1972

A study of 2-20 KeV X-rays from the Cygnus region

Two rocket-borne proportional counters, each with 650 sq c, met area and 1.8 x 7.1 deg FWHM rectangular mechanical collimation, surveyed the Cygnus region in the 2 to 20 keV energy range on two occasions. X-ray spectral data gathered on 21 September 1970 from discrete sources in Cygnus are presented. The data from Cyg X-1, Cyg X-2, and Cyg X-3 have sufficient statistical significance to indicate mutually exclusive spectral forms for the three. Upper limits are presented for X-ray intensities above 2 keV for Cyg X-4 and Cyg X-5 (Cygnus loop). A search was made on 9 August 1971 for a diffuse component of X-rays 1.5 keV associated with an interarm region of the galaxy at galactic longitudes in the vicinity of 60 degrees. A statistically significant excess associated with a narrow disk component was detected. Several possible emission models are discussed, with the most likely candidate being a population of unresolvable low luminosity discrete sources.

Bleach, R. D.↗
NASA NTRS1971

On the minimax feedback control of uncertain dynamic systems.

In this paper the problem of optimal feedback control of uncertain discrete-time dynamic systems is considered where the uncertain quantities do not have a stochastic description but instead are known to belong to given sets. The problem is converted to a sequential minimax problem and dynamic programming is suggested as a general method for its solution. The notion of a sufficiently informative function, which parallels the notion of a sufficient statistic of stochastic optimal control, is introduced, and conditions under which the optimal controller decomposes into an estimator and an actuator are identified.

Bertsekas, D. P.↗
NASA NTRS1973

Sufficiently informative functions and the minimax feedback control of uncertain dynamic systems.

The problem of optimal feedback control of uncertain discrete-time dynamic systems is considered where the uncertain quantities do not have a stochastic description but instead are known to belong to given sets. The problem is converted to a sequential minimax problem and dynamic programming is suggested as a general method for its solution. The notion of a sufficiently informative function, which parallels the notion of a sufficient statistic of stochastic optimal control, is introduced, and conditions under which the optimal controller decomposes into an estimator and an actuator are identified.

Bertsekas, D. P.↗
NASA NTRS1972

An Adaptive Technique for a Redundant-Sensor Navigation System

An on-line adaptive technique is developed to provide a self-contained redundant-sensor navigation system with a capability to utilize its full potentiality in reliability and performance. The gyro navigation system is modeled as a Gauss-Markov process, with degradation modes defined as changes in characteristics specified by parameters associated with the model. The adaptive system is formulated as a multistage stochastic process: (1) a detection system, (2) an identification system and (3) a compensation system. It is shown that the sufficient statistics for the partially observable process in the detection and identification system is the posterior measure of the state of degradation, conditioned on the measurement history.

Chien, T. T.↗
NASA NTRS1974

Determination of the radial gradient in the region 0.81-1.0 AU using both high- and low-energy /more than 10-GeV and more than 52-MeV/ detectors for the 1-AU monitor

A determination of the radial gradient for alpha particles (31-46 MeV/nuc) and protons with energies above 7.5 MeV and 44-77 MeV in the region 1.0-0.81 AU is presented for the solar-quiet year 1966. The determinations are based on data from the Pioneer 6 space probe. Two different detectors are used: the Deep River neutron monitor and measurements of low energy protons made on the IMP-C satellite. The average energy response of the Deep River monitor is 16 GeV, whereas the IMP-C data is for protons with energies above 50 MeV. The resulting radial gradient is found to be nearly zero for the alpha particles and slightly negative for the protons. The same qualitative results were found using the IMP-C data and the Deep River neutron monitor to measure the temporal variation in the cosmic ray intensity. The present analysis indicates that detectors over a wide range of energies are suitable for measuring the radial gradient, providing sufficient statistical precision is obtained to evaluate short-term modulation and the azimuthal separation of the detectors is not great.

Sheldon, W. R.↗
NASA NTRS1976

Effective defect density for MOS breakdown - Dependence on oxide thickness

A new procedure for measuring effective defect density takes time-dependent primary dielectric breakdown in MOS devices into account. A time-varying breakdown probability is obtained by applying a constant field stress to a statistically sufficient number of MOS capacitors. Effective defects are assumed distributed randomly in two dimensions, hence indistinguishable. The effective defect density is found to vary with oxide thickness; tentative explanations are ventured to account for this (interfacial tensile stress, ion patching enhanced by local trapping, breakdown in the form of filamentary discharges with release of stored electrostatic energy).

Li, S. P.↗
NASA NTRS1977

Feature discrimination and detection probability in synthetic aperture radar imaging system

Images obtained using synthetic aperture radar (SAR) systems can only represent the intensities of resolution cells in the scene of interest probabilistically since radar receiver noise and Rayleigh scattering of the transmitted radiation are always present. Consequently, when features to be identified differ only by their contribution to the mean power of the radar return, discrimination can be treated by detection theory. In this paper, we develop a 'sufficient statistic' for discriminating between competing features and compare it with some suboptimal methods frequently used. Discrimination is measured by probability of detection error and depends on number of samples or 'looks', signal-to-noise ratio (SNR), and ratio of mean power returns from the competing features. Our results show discrimination and image quality rapidly saturate with SNR (very small improvement for SNR not less than 10 dB) but continue to improve with increasing number of looks.

Lipes, R. G.↗
NASA NTRS1982

Improved Model for MOS Breakdown

With an improved model, accelerated high-field tests can be used to predict gate-oxide breakdown in metal-oxide-semi-conductor (MOS) structures. Principal mechanism in MOS breakdown is mobile-ion emission from metal/oxide interface, which occurs during application of positive gate-bias field. Breakdown is related to clustering of emitted ions at localized defect sites in oxide/silicon interface. Using new model to interpret data, tests that normally take several weeks at low fields to accumulate sufficient statistics can be completed in only a few hours at high fields.

Li, S. P.↗
NASA NTRS1981

A model of the human observer and decision maker

The decision process is described in terms of classical sequential decision theory by considering the hypothesis that an abnormal condition has occurred by means of a generalized likelihood ratio test. For this, a sufficient statistic is provided by the innovation sequence which is the result of the perception an information processing submodel of the human observer. On the basis of only two model parameters, the model predicts the decision speed/accuracy trade-off and various attentional characteristics. A preliminary test of the model for single variable failure detection tasks resulted in a very good fit of the experimental data. In a formal validation program, a variety of multivariable failure detection tasks was investigated and the predictive capability of the model was demonstrated.

Wewerinke, P. H.↗