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Statistical significance test for transition matrices of atmospheric Markov chains

Low-frequency variability of large-scale atmospheric dynamics can be represented schematically by a Markov chain of multiple flow regimes. This Markov chain contains useful information for the long-range forecaster, provided that the statistical significance of the associated transition matrix can be reliably tested. Monte Carlo simulation yields a very reliable significance test for the elements of this matrix. The results of this test agree with previously used empirical formulae when each cluster of maps identified as a distinct flow regime is sufficiently large and when they all contain a comparable number of maps. Monte Carlo simulation provides a more reliable way to test the statistical significance of transitions to and from small clusters. It can determine the most likely transitions, as well as the most unlikely ones, with a prescribed level of statistical significance.

Vautard, Robert↗

Cycle life test

Statistical information concerning cell performance characteristics and limitations of secondary spacecraft cells is presented. Weaknesses in cell design as well as battery weaknesses encountered in various satellite programs are reported. Emphasis is placed on improving the reliability of space batteries.

Harkness, J. D.↗

Validation Testing and Statistical Analysis of the Rotary Tumbler Fabric Abrasion Method

The Artemis space suit glove environmental protection garment (EPG) will be the first line of protection used to shield the crewmember’s hands from the environments encountered during extravehicular activity (EVA). As the Artemis missions will include more extreme environments than those experienced on the International Space Station, development, verification, and validation of gloves requires the development of new test methods. A previous paper focused on the development of a test procedure to characterize lunar EVA glove fabrics using ASTM standardized test methods and the design and validation of a new standardized test procedure for comparing abrasion resistance between fabrics using a dust and rock filled rotary tumbler. Preliminary results of testing were presented in that paper. This paper reports on the validation testing and statistical analysis of the newly developed tumbler abrasion test method.

Robert J Jones↗

Eclipse timings of the low-mass X-ray binary EXO 0748-676: Statistical arguments against orbital period changes

EXO 0748-676, an eclipsing low-mass X-ray binary, is one of only about four or five low-mass X-ray binaries for which orbital period evolution has been reported. We observed a single eclipse egress with ROSAT . The time of this egress is consistent with the apparent increase in P(sub orb) previously reported on the basis of EXOSAT and Ginga observations. Standard analysis, in which O-C (observed minus calculated) timing residuals are examined for deviations from a constant period, implicitly assume that the only uncertainty in each residual is measurement error and that these errors are independent. We argue that the variable eclipse durations and profiles observed in EXO 0748-676 imply that there is an additional source of uncertainty in timing measurements, that this uncertainty is intrinsic to the binary system, and that it is correlated from observation to observation with a variance which increases as a function of the number of binary cycles between observations. This intrinsic variability gives rise to spurious trends in O-C residuals which are misinterpreted as changes in the orbital period. We describe several statistics tests which can be used to test for the presence of intrinsic variability. We apply those statistical tests which are suitable to the EXO 0748-676 observations. The apparent changes in the orbital period of EXO 0748-676 can be completely accounted for by intrinsic variability with an rms variability of approximately 0.35 s per orbital cycle. The variability appears to be correlated from cycle-to-cycle on timescales of less than 1 yr. We suggest that the intrinsic variability is related to slow changes in either the source's X-ray luminosity or the structure of the companion star's atmosphere. We note that several other X-ray binaries and cataclysmic variables have previously reported orbital period changes which may also be due to intrinsic variability rather than orbital period evolution.

Hertz, Paul↗

Earth Observing System Covariance Realism

The purpose of covariance realism is to properly size a primary object's covariance in order to add validity to the calculation of the probability of collision. The covariance realism technique in this paper consists of three parts: collection/calculation of definitive state estimates through orbit determination, calculation of covariance realism test statistics at each covariance propagation point, and proper assessment of those test statistics. An empirical cumulative distribution function (ECDF) Goodness-of-Fit (GOF) method is employed to determine if a covariance is properly sized by comparing the empirical distribution of Mahalanobis distance calculations to the hypothesized parent 3-DoF chi-squared distribution. To realistically size a covariance for collision probability calculations, this study uses a state noise compensation algorithm that adds process noise to the definitive epoch covariance to account for uncertainty in the force model. Process noise is added until the GOF tests pass a group significance level threshold. The results of this study indicate that when outliers attributed to persistently high or extreme levels of solar activity are removed, the aforementioned covariance realism compensation method produces a tuned covariance with up to 80 to 90% of the covariance propagation timespan passing (against a 60% minimum passing threshold) the GOF tests-a quite satisfactory and useful result.

Realism↗

Earth Observation System Flight Dynamics System Covariance Realism

This presentation applies a covariance realism technique to the National Aeronautics and Space Administration (NASA) Earth Observation System (EOS) Aqua and Aura spacecraft based on inferential statistics. The technique consists of three parts: collection calculation of definitive state estimates through orbit determination, calculation of covariance realism test statistics at each covariance propagation point, and proper assessment of those test statistics.

A-Train↗

Test of statistical models for gases with and without internal energy states.

The problem of nonlinear rarefied Couette flow with heat transfer has been studied for both monatomic and diatomic gases using the Boltzmann equation with the Bhatnagar-Gross-Krook type models as the governing equation and the method of discrete ordinates as a tool. The calculated results have been compared with the existing experimental data in order to test the accuracy and the applicability of the statistical models for this one-dimensional problem. The calculated density results are found to be in good agreement with available experimental data; the calculated heat flux solution for the linear case is found to always be lower than the experimental data of Teagan and Springer. The comparisons made here indicate that the statistical models are indeed reasonably accurate so that their use is justified in the type of problems investigated.

Huang, A. B.↗

A bootstrap approach to bump hunting

An important question in cluster analysis and pattern recognition is the determination of the number of clusters into which a given population should be divided. Frequently, particularly when certain specific clustering methods are being used, the number of clusters is taken to be equal to the number of modes, or local maxima, in the probability density function underlying the given data set. The use of kernal density estimates in mode estimation is discussed. The test statistic to be used is defined and a bootstrap technique for assessing significance is given. An illustrative application is followed by an examination of the asymptotic behavior of the test statistic.

Silverman, B. W.↗

A coronagraphic search for brown dwarfs around nearby stars

Brown dwarf companions have been searched for around stars within 10 pc of the Sun using the Johns-Hopkins University Adaptive Optics Coronagraph (AOC), a stellar coronagraph with an image stabilizer. The AOC covers the field around the target star with a minimum search radius of 1 sec .5 and a field of view of 1 arcmin sq. We have reached an unprecedented dynamic range of Delta m = 13 in our search for faint companions at I band. Comparison of our survey with other brown dwarf searches shows that the AOC technique is unique in its dynamic range while at the same time just as sensitive to brown dwarfs as the recent brown dwarf surveys. The present survey covered 24 target stars selected from the Gliese catalog. A total of 94 stars were detected in 16 fields. The low-latitude fields are completely dominated by background star contamination. Kolmogorov-Smirnov tests were carried out for a sample restricted to high latitudes and a sample with small angular separations. The high-latitude sample (b greater than or equal to 44 deg) appears to show spatial concentration toward target stars. The small separation sample (Delta Theta less than 20 sec) shows weaker dependence on Galactic coordinates than field stars. These statistical tests suggest that both the high-latitude sample and the small separation sample can include a substantial fraction of true companions. However, the nature of these putative companions is mysterious. They are too faint to be white dwarfs and too blue for brown dwarfs. Ignoring the signif icance of the statistical tests, we can reconcile most of the detections with distant main-sequence stars or white dwarfs except for a candidate next to GL 475. Given the small size of our sample, we conclude that considerably more targets need to be surveyed before a firm conclusion on the possibility of a new class of companions can be made.

Nakajima, T.↗

The distribution of galaxies in Abell 1975

The distribution of galaxies in the field of Abell 1795 is studied, based on a red photograph obtained with the Palomar 1.2 m Schmidt telescope. A battery of statistical tests has been applied to the positional data of galaxies in A 1795, in order to assess the significance of asymmetry and subclustering. The large-scale distribution of galaxies is asymmetric, with an elongation to the north. Although there appear to be two, or possibly three, clumps of galaxies in the cluster core, various statistical tests provide no convincing evidence for subclustering. This may be due to the small number of galaxies in the core. These results are discussed in light of the recent observations by Hill et al. (1988) that the cD galaxy in A 1795 has a large peculiar velocity with respect to the cluster mean.

Oegerle, William R.↗

On the Relationship Between Transit Velocity of Interplanetary Shocks and Solar Active Processes

Recently, it was reported that preferential relationships exist between the transit velocity V(sub T) of earthward-directed interplanetary shocks and solar active processes, in particular, eruptive filaments outside active regions (the size of the erupting filament L(sub f)) and solar flares (the value of the X-ray characteristic J). Unfortunately, statistical testing of the proposed associations was not accomplished, nor was the 'geo-effectiveness' of the events adequately described. Reported here are the results of a re-examination of the 21 eruptive filaments (SSC-EF events) and 26 X-ray flares (SSC-F events) that have been associated with storm sudden commencements (SSCs) at Earth. Simple statistical testing refutes the claim that a preferential relationship exists between V(sub T) and L(sub F), while it supports the claim that one exists between V(sub T) and J. More importantly, the inferred relationship between V(sub T) and J is found to be more complicated than previously thought. In particular, it now appears that SSC-F events may be separable into two groups, based on the value of J: a low-J group (J less than 56), in which V(sub T) varies directly with J, and a high-J group (J greater than 56), in which V(sub T) varies inversely with J. As a whole, high-J events are associated with shocks of higher average transit velocity than those of low-J events, and SSC-F events with shocks of higher average transit velocity than those of SSC-EF events. Further, high-J events tend to be of greater X-ray class ( greater than M3), longer duration (greater then 80 min), and are more likely to be associated with type II/IV radio emission (9 of 12) than low-J events. They also tend to occur in magnetically complex (gamma/delta configuration) active regions (10 of 12) that are large in area extent (area greater than 445 millionths of a solar hemisphere) on the day of flaring (9 of 12). Of the 9 solar proton events that affected the Earth's environment that were found to be associated with SSC-F events, six were high-J events. Concerning 'geo-effectiveness', there appears to be no preferential relationship between the value of the J-parameter and the most negative value of the Dst geomagnetic index Dst(min) following the SSC, which is found to usually occur at 6-14 h after SSC onset (18 of 26) and which ranged in value from -1 to -249 (having a median value of about -75). Of the 26 SSC-F events, only 14 can be associated with a Dst(min) less than or equal to -75, and of these only 7 were high-J events. Of the 14 storm-related events (i.e. Dst(min) less than or equal to -75), three have previously been identified as being either 'magnetic clouds' or 'bidirectional flows', both manifestations of earthward-directed coronal mass ejections (CMEs). Superposed epoch analyses of selected solar wind parameters and Dst during the interval of storm-related SSC-F events demonstrate that geoeffective SSC-F events tend to be associated with solar wind flows that are faster, greater in magnetic field strength, and have a rotating field which has a strong southward component shortly after SSC onset, in comparison to SSC-F events that do not have Dst(min) less than or equal to 75. Therefore, it is inferred that geoeffective SSC-F events are probably fast earthward-directed CMEs. Although no single parameter is found that can serve as a predictor of high-skill level for determining the geoeffectiveness of an SSC-F event prior to its occurrence at Earth, one finds that knowledge of the flare's hemispheric location and appearance or lack of appearance of a two-ribbon structure is sufficient to correctly predict the geoeffectiveness of 20 out of 25 of the SSC-F events (80%). Surprisingly, the association or lack of association of metric type II/IV radio emission as a characteristic for determining the geoeffectiveness of the SSC-F events proved unfruitful, as did, to a lesser extent, the duration of the X-ray emission.

Wilson, Robert M.↗

Can we identify lensed gamma-ray bursts?

A gravitationally lensed gamma-ray burst (GRB) would appear as multiple bursts with identical light curves, separated in time and differing only by the scaling of their amplitudes. In reality, the detected bursts will be noisy, and therefore they may be difficult to identify as lensed images. Furthermore, faint, intrinsically similar, yet distinct light curves may be falsely identified as lensing events. In this paper we develop two statistical tests to distinguish noisy burst light curves. We use Fourier analysis techniques to analyze the signals for both intrinsic variability and variability due to noise. We are able to determine the noise level, and we compare the bursts only at frequency channels that are signal dominated. Utilizing these methods, we are able to make quantitative statements about whether two bursts are distinct. We apply these statistics to scaled versions of two subbursts of GRB 910503 -- subbursts previously investigated by Wambsganss using a different statistical test. We find that our methods are able to distinguish these bursts at slightly smaller amplitudes than those at which Wambsganss's method succeeds. We then apply our techniques to 'candidate' lensing events taken from the Burst and Transient Source Experiment (BATSE) catalog, and we find that nearly all of them, except for the very shortest ones (durations approx. less than 3 sec), are distinguishable. We therefore expect that a majority of bursts will be distinguishable from one another.

Nowak, Michael A.↗

Quantitative Validation of the Integrated Medical Model (IMM) for ISS Missions

Lifetime Surveillance of Astronaut Health (LSAH) provided observed medical event data on 33 ISS and 111 STS person-missions for use in further improving and validating the Integrated Medical Model (IMM). Using only the crew characteristics from these observed missions, the newest development version, IMM v4.0, will simulate these missions to predict medical events and outcomes. Comparing IMM predictions to the actual observed medical event counts will provide external validation and identify areas of possible improvement. In an effort to improve the power of detecting differences in this validation study, the total over each program ISS and STS will serve as the main quantitative comparison objective, specifically the following parameters: total medical events (TME), probability of loss of crew life (LOCL), and probability of evacuation (EVAC). Scatter plots of observed versus median predicted TMEs (with error bars reflecting the simulation intervals) will graphically display comparisons while linear regression will serve as the statistical test of agreement. Two scatter plots will be analyzed 1) where each point reflects a mission and 2) where each point reflects a condition-specific total number of occurrences. The coefficient of determination (R2) resulting from a linear regression with no intercept bias (intercept fixed at zero) will serve as an overall metric of agreement between IMM and the real world system (RWS). In an effort to identify as many possible discrepancies as possible for further inspection, the -level for all statistical tests comparing IMM predictions to observed data will be set to 0.1. This less stringent criterion, along with the multiple testing being conducted, should detect all perceived differences including many false positive signals resulting from random variation. The results of these analyses will reveal areas of the model requiring adjustment to improve overall IMM output, which will thereby provide better decision support for mission critical applications.

validation↗

Statistical Aspects of North Atlantic Basin Tropical Cyclones During the Weather Satellite Era, 1960-2013

This Technical Publication (TP) is part 2 of a two-part study of the North Atlantic basin tropical cyclones that occurred during the weather satellite era, 1960-2013. In particular, this TP examines the inferred statistical relationships between 25 tropical cyclone parameters and 9 specific climate-related factors, including the (1) Oceanic Niño Index (ONI), (2) Southern Oscillation Index (SOI), (3) Atlantic Multidecadal Oscillation (AMO) index, (4) Quasi-Biennial Oscillation (QBO) index, (5) North Atlantic Oscillation (NAO) index of the Climate Prediction Center (CPC), (6) NAO index of the Climate Research Unit (CRU), (7) Armagh surface air temperature (ASAT), (8) Global Land-Ocean Temperature Index (GLOTI), and (9) Mauna Loa carbon dioxide (CO2) (MLCO2) index. Part 1 of this two-part study examined the statistical aspects of the 25 tropical cyclone parameters (e.g., frequencies, peak wind speed (PWS), accumulated cyclone energy (ACE), etc.) and provided the results of statistical testing (i.e., runs-testing, the t-statistic for independent samples, and Poisson distributions). Also, the study gave predictions for the frequencies of the number of tropical cyclones (NTC), number of hurricanes (NH), number of major hurricanes (NMH), and number of United States land-falling hurricanes (NUSLFH) expected for the 2014 season, based on the statistics of the overall interval 1960-2013, the subinterval 1995-2013, and whether the year 2014 would be either an El Niño year (ENY) or a non-El Niño year (NENY).

Wilson, Robert M.↗

Testing for periodicity of extinction

The statistical techniques used by Raup and Sepkoski (1984 and 1986) to identify a 26-Myr periodicity in the biological extinction record for the past 250 Myr are reexamined, responding in detail to the criticisms of Stigler and Wagner (1987). It is argued that evaluation of a much larger set of extinction data using a time scale with 51 sampling intervals supports the finding of periodicity. In a reply by Sigler and Wagner, the preference for a 26-Myr period is attributed to a numerical quirk in the Harland et al. (1982) time scale, in which the subinterval boundaries are not linear interpolations between the stage boundaries but have 25-Myr periodicity. It is stressed that the results of the stringent statistical tests imposed do not disprove periodicity but rather indicate that the evidence and analyses presented so far are inadequate.

Raup, David M.↗

Detection of large-scale alignment of Lick counts around Abell clusters

The possible tendency of galaxies to be distributed in an aligned fashion, on sheets or filaments, on scales greater than the Abell radius, has been tested by a variety of statistics. The subject remains controversial because the statistical tests have either not been sensitive to the alignment or capable of unambiguously signalling alignment in a general, clumpy distribution of galaxies. The present approach combines ideas of Bingelli (1982) and Fry and Peebles (1980) in an examination of the cross correlation of Lick counts relative to the preferred direction defined by the cluster. This can substantially reduce the noise, and it is suggested on this basis that alignment has been found on large scales for Lick galaxy counts and Abell cluster positions and their angles.

Argyres, P. C.↗