Search NASA⌕ Search

SEARCH · Search NASA

Results for “Markov Chain”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
NASA NTRS2005

Cosmological Constraints from Sunyaev-Zeldovich Effect and X-ray data for 37 Galaxy Clusters

We present a sample of 37 clusters of galaxies (0.14<=z<=0.89) for which we have Sunyaev-Zeldovich Effect data and Chandra X-ray imaging and spectroscopy. We use a Markov chain Monte Carlo technique to determine the spatial properties and surface brightness of the X-ray emitting gas, the X-ray temperature and abundance, and the SZE decrement for each cluster. From these observables, we infer each cluster's total mass, gas mass fraction, and angular diameter distance. The sample properties are used to constrain the Hubble parameter and Omega Matter, and scaling relations between integrated SZE flux and cluster mass and temperature are constructed. We also investigate the cosmological constraints that could be obtained if the X-ray/SZE sample were extended to a redshift of z approximately 2.

Bonamente, Massimiliano↗
NASA NTRS2006

Determination of the Cosmic Distance Scale from Sunyaev-Zel'dovich Effect and Chandra X-ray Measurements of High Redshift Galaxy Clusters

We determine the distance to 38 clusters of galaxies in the redshift range 0.14 less than or equal to z less than or equal to 0.89 using X-ray data from Chandra and Sunyaev-Zeldovich Effect data from the Owens Valley Radio Observatory and the Berkeley-Illinois-Maryland Association interferometric arrays. The cluster plasma and dark matter distributions are analyzed using a hydrostatic equilibrium model that accounts for radial variations in density, temperature and abundance, and, the statistical and systematic errors of this method are quantified. The analysis is performed via a Markov chain Monte Carlo technique that provides simultaneous estimation of all model parameters. W

Bonamente, Massimiliano↗
NASA NTRS2006

Markovian Statistical Data Analysis of Single-Event Upsets Triggered by High Intensity Neutrons

This paper analyzes data from a single-event upset experiment conducted at the Los Alamos National Laboratory. Statistical tools, based on well-known x(sup 2) hypothesis testing theory, are used to determine if sequences of upsets can be modeled as a homogeneous Markov chain of a specific order. The experiment consisted of radiating a new experimental flight control computer (FCC) with a high intensity neutron beam while the FCC controlled a simulation of a Boeing 737. The analyzed data is a sequence of states that indicates when the FCC is under an upset condition.

Lakdawala, Anushka V.↗
NASA NTRS2006

An Ensemble-Based Smoother with Retrospectively Updated Weights for Highly Nonlinear Systems

Monte Carlo computational methods have been introduced into data assimilation for nonlinear systems in order to alleviate the computational burden of updating and propagating the full probability distribution. By propagating an ensemble of representative states, algorithms like the ensemble Kalman filter (EnKF) and the resampled particle filter (RPF) rely on the existing modeling infrastructure to approximate the distribution based on the evolution of this ensemble. This work presents an ensemble-based smoother that is applicable to the Monte Carlo filtering schemes like EnKF and RPF. At the minor cost of retrospectively updating a set of weights for ensemble members, this smoother has demonstrated superior capabilities in state tracking for two highly nonlinear problems: the double-well potential and trivariate Lorenz systems. The algorithm does not require retrospective adaptation of the ensemble members themselves, and it is thus suited to a streaming operational mode. The accuracy of the proposed backward-update scheme in estimating non-Gaussian distributions is evaluated by comparison to the more accurate estimates provided by a Markov chain Monte Carlo algorithm.

Monte Carlo↗
NASA NTRS2008

Five-Year Wilkinson Microwave Anisotropy Probe (WMAP1) Observations: Galactic Foreground Emission

We present a new estimate of foreground emission in the WMAP data, using a Markov chain Monte Carlo (MCMC) method. The new technique delivers maps of each foreground component for a variety of foreground models, error estimates of the uncertainty of each foreground component, and provides an overall goodness-of-fit measurement. The resulting foreground maps are in broad agreement with those from previous techniques used both within the collaboration and by other authors. We find that for WMAP data, a simple model with power-law synchrotron, free-free, and thermal dust components fits 90% of the sky with a reduced X(sup 2) (sub v) of 1.14. However, the model does not work well inside the Galactic plane. The addition of either synchrotron steepening or a modified spinning dust model improves the fit. This component may account for up to 14% of the total flux at Ka-band (33 GHz). We find no evidence for foreground contamination of the CMB temperature map in the 85% of the sky used for cosmological analysis.

Gold, B.↗
NASA NTRS2008

Black Hole Mergers as Probes of Structure Formation

Intense structure formation and reionization occur at high redshift, yet there is currently little observational information about this very important epoch. Observations of gravitational waves from massive black hole (MBH) mergers can provide us with important clues about the formation of structures in the early universe. Past efforts have been limited to calculating merger rates using different models in which many assumptions are made about the specific values of physical parameters of the mergers, resulting in merger rate estimates that span a very wide range (0.1 - 104 mergers/year). Here we develop a semi-analytical, phenomenological model of MBH mergers that includes plausible combinations of several physical parameters, which we then turn around to determine how well observations with the Laser Interferometer Space Antenna (LISA) will be able to enhance our understanding of the universe during the critical z 5 - 30 structure formation era. We do this by generating synthetic LISA observable data (total BH mass, BH mass ratio, redshift, merger rates), which are then analyzed using a Markov Chain Monte Carlo method. This allows us to constrain the physical parameters of the mergers. We find that our methodology works well at estimating merger parameters, consistently giving results within 1- of the input parameter values. We also discover that the number of merger events is a key discriminant among models. This helps our method be robust against observational uncertainties. Our approach, which at this stage constitutes a proof of principle, can be readily extended to physical models and to more general problems in cosmology and gravitational wave astrophysics.

Alicea-Munoz, E.↗
NASA NTRS2008

Using Black Hole Mergers to Explore Structure Formation

Observations of gravitational waves from massive black hole mergers will open a new window into the era of structure formation in the early universe. Past efforts have concentrated on calculating merger rates using different physical assumptions, resulting in merger rate estimates that span a wide range (0.1 - 1 0A4 mergers/year). We develop a semi-analytical, phenomenological model of massive black hole mergers that includes plausible combinations of several physical parameters, which we then turn around to determine how well observations with the Laser Interferometer Space Antenna (LISA) will be able to enhance our understanding of the universe during the critical z approx. 5 - 30 epoch. Our approach involves generating synthetic LISA observable data (total BH masses, BH mass ratios, redshifts, merger rates), which are then analyzed using a Markov Chain Monte Carlo method, thus finding constraints for the physical parameters of the mergers. We find that our method works well at estimating merger parameters and that the number of merger events is a key discriminant among models, therefore making our method robust against observational uncertainties. Our approach can also be extended to more physically-driven models and more general problems in cosmology.

Alicea-Munoz, E.↗
NASA NTRS2009

Using Black Hole Mergers to Explore Structure Formation

Observations of gravitational waves from massive black hole mergers will open a new window into the era of structure formation in the early universe. Past efforts have concentrated on calculating merger rates using different physical assumptions, resulting in merger rate estimates that span a wide range (0.1 - 10(exp 4) mergers/year). We develop a semi-analytical, phenomenological model of massive black hole mergers that includes plausible combinations of several physical parameters, which we then turn around to determine how well observations with the Laser Interferometer Space Antenna (LISA) will be able to enhance our understanding of the universe during the critical z approximately equal to 5-30 epoch. Our approach involves generating synthetic LISA observable data (total BH masses, BH mass ratios, redshifts, merger rates), which are then analyzed using a Markov Chain Monte Carlo method, thus finding constraints for the physical parameters of the mergers. We find that our method works well at estimating merger parameters and that the number of merger events is a key discriminant among models, therefore making our method robust against observational uncertainties. Our approach can also be extended to more physically-driven models and more general problems in cosmology. This work is supported in part by the Cooperative Education Program at NASA/GSFC.

Alicea-Munoz, E.↗
NASA NTRS2008

Black Hole Mergers as Probes of Structure Formation

Observations of gravitational waves from massive black hole (MBH) mergers can provide us with important clues about the era of structure formation in the early universe. Previous research in this field has been limited to calculating merger rates of MBHs using different models where many assumptions are made about the specific values of physical parameters of the mergers, resulting in merger rate estimates that span 5 to 6 orders of magnitude. We develop a semi-analytical, phenomenological model that includes plausible combinations of several physical parameters involved in the mergers. which we then turn around to determine how well LISA observations will be able to enhance our understanding of the universe during the critical z approximately equal to 5-30 structure formation era. We do this by generating synthetic LISA observable data (masses, redshifts, merger rates), which are then analyzed using a Markov Chain Monte Carlo (MCMC) method. This allows us to constrain the physical parameters of the mergers.

Alicea-Munoz, Emily↗
NASA NTRS2006

An Efficient Approach for the Reliability Analysis of Phased-Mission Systems with Dependent Failures

We consider the reliability analysis of phased-mission systems with common-cause failures in this paper. Phased-mission systems (PMS) are systems supporting missions characterized by multiple, consecutive, and nonoverlapping phases of operation. System components may be subject to different stresses as well as different reliability requirements throughout the course of the mission. As a result, component behavior and relationships may need to be modeled differently from phase to phase when performing a system-level reliability analysis. This consideration poses unique challenges to existing analysis methods. The challenges increase when common-cause failures (CCF) are incorporated in the model. CCF are multiple dependent component failures within a system that are a direct result of a shared root cause, such as sabotage, flood, earthquake, power outage, or human errors. It has been shown by many reliability studies that CCF tend to increase a system's joint failure probabilities and thus contribute significantly to the overall unreliability of systems subject to CCF.We propose a separable phase-modular approach to the reliability analysis of phased-mission systems with dependent common-cause failures as one way to meet the above challenges in an efficient and elegant manner. Our methodology is twofold: first, we separate the effects of CCF from the PMS analysis using the total probability theorem and the common-cause event space developed based on the elementary common-causes; next, we apply an efficient phase-modular approach to analyze the reliability of the PMS. The phase-modular approach employs both combinatorial binary decision diagram and Markov-chain solution methods as appropriate. We provide an example of a reliability analysis of a PMS with both static and dynamic phases as well as CCF as an illustration of our proposed approach. The example is based on information extracted from a Mars orbiter project. The reliability model for this orbiter considers the various phases of Launch, Cruise, Mars Orbit Insertion, and Orbit. Some of the CCF for the orbiter in this mission include environmental effects, such as micrometeoroids, human operator errors, and software errors.

reliability analysis↗
NASA NTRS2008

Precision Measurement of Black Hole Binary Dynamics: Analyzing the LISA Data Stream

One of the richest potential sources of insight into fundamental physics that LISA will be capable of observing is the inspiral of supermassive black hole binaries (BHBs). However, the data analysis challenge presented by the LISA data stream is quite unlike the situation for present day gravitational wave detectors. In order to make the precision measurements necessary to achieve LISA's science goals, the BHB signal must be distinguished from a data stream that not only contains instrumental noise, but potentially thousands of other signals as well, so that the "background" we wish to separate out to focus on the BHB signal is likely to be highly nonstationary and nongaussian, as well as being of scientific interest in its own right. In addition, whereas the theoretical templates that we calculate in order to ultimately estimate the parameters can afford to be somewhat inaccurate and still be effective for present day and near future detectors, this is not the case for LISA, and extremely high fidelity of the theoretical templates for high signal-to-noise signals will be required to prevent theoretical errors from dominating the parameter estimates. NVe, will describe efforts in the community of LISA data analysts to address the challenges regarding the specific issue of BHB signals. These efforts include using a Markov Chain Monte Carlo approach with the freedom to model the BHB and the other signals present in the data stream simultaneously, rather than trying to remove other signals and risk biasing the remaining data. The Mock LISA Data Challenge is a community of LISA scientists who generate rounds of simulated LISA noise with increasingly difficult signal content, and invite the LISA data analysis community to exercise their methods, or develop new methods, in an attempt to extract the parameters for the signals embedded in the mock data. In addition to practical approaches such ,is this to assess the level of parameter accuracy, one can apply the Fisher matrix formalism to assess both the statistical errors from noise and the theoretical errors

McWilliams, Sean T.↗
NASA NTRS2010

Separating Gravitational Wave Signals from Instrument Artifacts

Central to the gravitational wave detection problem is the challenge of separating features in the data produced by astrophysical sources from features produced by the detector. Matched filtering provides an optimal solution for Gaussian noise, but in practice, transient noise excursions or "glitches" complicate the analysis. Detector diagnostics and coincidence tests can be used to veto many glitches which may otherwise be misinterpreted as gravitational wave signals. The glitches that remain can lead to long tails in the matched filter search statistics and drive up the detection threshold. Here we describe a Bayesian approach that incorporates a more realistic model for the instrument noise allowing for fluctuating noise levels that vary independently across frequency bands, and deterministic "glitch fitting" using wavelets as "glitch templates", the number of which is determined by a trans-dimensional Markov chain Monte Carlo algorithm. We demonstrate the method's effectiveness on simulated data containing low amplitude gravitational wave signals from inspiraling binary black hole systems, and simulated non-stationary and non-Gaussian noise comprised of a Gaussian component with the standard LIGO/Virgo spectrum, and injected glitches of various amplitude, prevalence, and variety. Glitch fitting allows us to detect significantly weaker signals than standard techniques.

Littenberg, Tyson B.↗
NASA NTRS2010

Utilizing In Situ Directional Hyperspectral Measurements to Validate Bio-Indicator Simulations for a Corn Crop Canopy

Two radiative transfer canopy models, SAIL and the two-layer Markov-Chain Canopy Reflectance Model (MCRM), were coupled with in situ leaf optical properties to simulate canopy-level spectral band ratio vegetation indices with the focus on the photochemical reflectance index in a cornfield. In situ hyperspectral measurements were made at both leaf and canopy levels. Leaf optical properties were obtained from both sunlit and shaded leaves. Canopy reflectance was acquired for eight different relative azimuth angles (psi) at three different view zenith angles (Theta (sub v)), and later used to validate model outputs. Field observations of photochemical reflectance index (PRI) for sunlit leaves exhibited lower values than shaded leaves, indicating higher light stress. Canopy PRI expressed obvious sensitivity to viewing geometry, as a function of both Theta (sub v) and psi . Overall, simulations from MCRM exhibited better agreements with in situ values than SAIL. When using only sunlit leaves as input, the MCRM-simulated PRI values showed satisfactory correlation and RMSE, as compared to in situ values. However, the performance of the MCRM model was significantly improved after defining a lower canopy layer comprised of shaded leaves beneath the upper sunlit leaf layer. Four other widely used band ratio vegetation indices were also studied and compared with the PRI results. MCRM simulations were able to generate satisfactory simulations for these other four indices when using only sunlit leaves as input; but unlike PRI, adding shaded leaves did not improve the performance of MCRM. These results support the hypothesis that the PRI is sensitive to physiological dynamics while the others detect static factors related to canopy structure. Sensitivity analysis was performed on MCRM in order to better understand the effects of structure related parameters on the PRI simulations. Leaf area index (LAI) showed the most significant impact on MCRM-simulated PRI among the parameters studied. This research shows the importance of hyperspectral and narrow band sensor studies, and especially the necessity of including the green wavelengths (e.g., 531 nm) on satellites proposing to monitor carbon dynamics of terrestrial ecosystems.

Cheng, Yen-Ben↗
NASA NTRS2012

Modeling Phase-Aligned Gamma-Ray and Radio Millisecond Pulsar Light Curves

Since the discovery of the first eight gamma-ray millisecond pulsars (MSPs) by the Fermi Large Area Telescope, this population has been steadily expanding. Four of the more recent detections, PSR J00340534, PSR J1939+2134 (B1937+21; the first MSP ever discovered), PSR J1959+2048 (B1957+20; the first discovery of a black widow system), and PSR J2214+3000, exhibit a phenomenon not present in the original discoveries: nearly phase-aligned radio and gamma-ray light curves (LCs). To account for the phase alignment, we explore models where both the radio and gamma-ray emission originate either in the outer magnetosphere near the light cylinder or near the polar caps. Using a Markov Chain Monte Carlo technique to search for best-fit model parameters, we obtain reasonable LC fits for the first three of these MSPs in the context of altitude-limited outer gap (alOG) and two-pole caustic (alTPC) geometries (for both gamma-ray and radio emission). These models differ from the standard outer gap (OG)/two-pole caustic (TPC) models in two respects: the radio emission originates in caustics at relatively high altitudes compared to the usual conal radio beams, and we allow both the minimum and maximum altitudes of the gamma-ray and radio emission regions to vary within a limited range (excluding the minimum gamma-ray altitude of the alTPC model, which is kept constant at the stellar radius, and that of the alOG model, which is set to the position-dependent null charge surface altitude). Alternatively, phase-aligned solutions also exist for emission originating near the stellar surface in a slot gap scenario (low-altitude slot gap (laSG) models). We find that the alTPC models provide slightly better LC fits than the alOG models, and both of these give better fits than the laSG models (for the limited range of parameters considered in the case of the laSG models). Thus, our fits imply that the phase-aligned LCs are likely of caustic origin, produced in the outer magnetosphere, and that the radio emission for these pulsars may come from close to the light cylinder. In addition, we were able to constrain the minimum and maximum emission altitudes with typical uncertainties of 30% of the light cylinder radius. Our results therefore describe a third gamma-ray MSP subclass, in addition to the two previously found by Venter et al.: those with LCs fit by standard OG/TPC models and those with LCs fit by pair-starved polar cap models.

Venter, C.↗
NASA NTRS2012

Pulsar Emission Geometry and Accelerating Field Strength

The high-quality Fermi LAT observations of gamma-ray pulsars have opened a new window to understanding the generation mechanisms of high-energy emission from these systems, The high statistics allow for careful modeling of the light curve features as well as for phase resolved spectral modeling. We modeled the LAT light curves of the Vela and CTA I pulsars with simulated high-energy light curves generated from geometrical representations of the outer gap and slot gap emission models. within the vacuum retarded dipole and force-free fields. A Markov Chain Monte Carlo maximum likelihood method was used to explore the phase space of the magnetic inclination angle, viewing angle. maximum emission radius, and gap width. We also used the measured spectral cutoff energies to estimate the accelerating parallel electric field dependence on radius. under the assumptions that the high-energy emission is dominated by curvature radiation and the geometry (radius of emission and minimum radius of curvature of the magnetic field lines) is determined by the best fitting light curves for each model. We find that light curves from the vacuum field more closely match the observed light curves and multiwavelength constraints, and that the calculated parallel electric field can place additional constraints on the emission geometry

DeCesar, Megan E.↗
NASA NTRS2012

Modeling and Maximum Likelihood Fitting of Gamma-Ray and Radio Light Curves of Millisecond Pulsars Detected with Fermi

Pulsed gamma rays have been detected with the Fermi Large Area Telescope (LAT) from more than 20 millisecond pulsars (MSPs), some of which were discovered in radio observations of bright, unassociated LAT sources. We have fit the radio and gamma-ray light curves of 19 LAT-detected MSPs in the context of geometric, outermagnetospheric emission models assuming the retarded vacuum dipole magnetic field using a Markov chain Monte Carlo maximum likelihood technique. We find that, in many cases, the models are able to reproduce the observed light curves well and provide constraints on the viewing geometries that are in agreement with those from radio polarization measurements. Additionally, for some MSPs we constrain the altitudes of both the gamma-ray and radio emission regions. The best-fit magnetic inclination angles are found to cover a broader range than those of non-recycled gamma-ray pulsars.

Johnson, T. J.↗
NASA NTRS2012

A Bayesian Framework for Reliability Analysis of Spacecraft Deployments

Deployable subsystems are essential to mission success of most spacecraft. These subsystems enable critical functions including power, communications and thermal control. The loss of any of these functions will generally result in loss of the mission. These subsystems and their components often consist of unique designs and applications for which various standardized data sources are not applicable for estimating reliability and for assessing risks. In this study, a two stage sequential Bayesian framework for reliability estimation of spacecraft deployment was developed for this purpose. This process was then applied to the James Webb Space Telescope (JWST) Sunshield subsystem, a unique design intended for thermal control of the Optical Telescope Element. Initially, detailed studies of NASA deployment history, "heritage information", were conducted, extending over 45 years of spacecraft launches. This information was then coupled to a non-informative prior and a binomial likelihood function to create a posterior distribution for deployments of various subsystems uSing Monte Carlo Markov Chain sampling. Select distributions were then coupled to a subsequent analysis, using test data and anomaly occurrences on successive ground test deployments of scale model test articles of JWST hardware, to update the NASA heritage data. This allowed for a realistic prediction for the reliability of the complex Sunshield deployment, with credibility limits, within this two stage Bayesian framework.

Evans, John W.↗
NASA NTRS2012

The Photochemical Reflectance Index from Directional Cornfield Reflectances: Observations and Simulations

The two-layer Markov chain Analytical Canopy Reflectance Model (ACRM) was linked with in situ hyperspectral leaf optical properties to simulate the Photochemical Reflectance Index (PRI) for a corn crop canopy at three different growth stages. This is an extended study after a successful demonstration of PRI simulations for a cornfield previously conducted at an early vegetative growth stage. Consistent with previous in situ studies, sunlit leaves exhibited lower PRI values than shaded leaves. Since sunlit (shaded) foliage dominates the canopy in the reflectance hotspot (coldspot), the canopy PRI derived from field hyperspectral observations displayed sensitivity to both view zenith angle and relative azimuth angle at all growth stages. Consequently, sunlit and shaded canopy sectors were most differentiated when viewed along the azimuth matching the solar principal plane. These directional PRI responses associated with sunlit/shaded foliage were successfully reproduced by the ACRM. As before, the simulated PRI values from the current study were closer to in situ values when both sunlit and shaded leaves were utilized as model input data in a two-layer mode, instead of a one-layer mode with sunlit leaves only. Model performance as judged by correlation between in situ and simulated values was strongest for the mature corn crop (r = 0.87, RMSE = 0.0048), followed by the early vegetative stage (r = 0.78; RMSE = 0.0051) and the early senescent stage (r = 0.65; RMSE = 0.0104). Since the benefit of including shaded leaves in the scheme varied across different growth stages, a further analysis was conducted to investigate how variable fractions of sunlit/shaded leaves affect the canopy PRI values expected for a cornfield, with implications for 20 remote sensing monitoring options. Simulations of the sunlit to shaded canopy ratio near 50/50 +/- 10 (e.g., 60/40) matching field observations at all growth stages were examined. Our results suggest in the importance of the sunlit/shaded fraction and canopy structure in understanding and interpreting PRI.

Cheng, Yen-Ben↗