Results for “Bayesian method” — Page 4

NASA NTRS2011

Tests of the Grobner Basis Solution for Lightning Ground Flash Fraction Retrieval

Satellite lightning imagers such as the NASA Tropical Rainfall Measuring Mission Lightning Imaging Sensor (TRMM/LIS) and the future GOES-R Geostationary Lightning Mapper (GLM) are designed to detect total lightning (ground flashes + cloud flashes). However, there is a desire to discriminate ground flashes from cloud flashes from the vantage point of space since this would enhance the overall information content of the satellite lightning data and likely improve its operational and scientific applications (e.g., in severe weather warning, lightning nitrogen oxides studies, and global electric circuit analyses). A Bayesian inversion method was previously introduced for retrieving the fraction of ground flashes in a set of flashes observed from a satellite lightning imager. The method employed a constrained mixed exponential distribution model to describe the lightning optical measurements. To obtain the optimum model parameters (one of which is the ground flash fraction), a scalar function was minimized by a numerical method. In order to improve this optimization, a Grobner basis solution was introduced to obtain analytic representations of the model parameters that serve as a refined initialization scheme to the numerical optimization. In this study, we test the efficacy of the Grobner basis initialization using actual lightning imager measurements and ground flash truth derived from the national lightning network.

Koshak, William↗

NASA NTRS2012

The Ground Flash Fraction Retrieval Algorithm Employing Differential Evolution: Simulations and Applications

The ability to estimate the fraction of ground flashes in a set of flashes observed by a satellite lightning imager, such as the future GOES-R Geostationary Lightning Mapper (GLM), would likely improve operational and scientific applications (e.g., severe weather warnings, lightning nitrogen oxides studies, and global electric circuit analyses). A Bayesian inversion method, called the Ground Flash Fraction Retrieval Algorithm (GoFFRA), was recently developed for estimating the ground flash fraction. The method uses a constrained mixed exponential distribution model to describe a particular lightning optical measurement called the Maximum Group Area (MGA). To obtain the optimum model parameters (one of which is the desired ground flash fraction), a scalar function must be minimized. This minimization is difficult because of two problems: (1) Label Switching (LS), and (2) Parameter Identity Theft (PIT). The LS problem is well known in the literature on mixed exponential distributions, and the PIT problem was discovered in this study. Each problem occurs when one allows the numerical minimizer to freely roam through the parameter search space; this allows certain solution parameters to interchange roles which leads to fundamental ambiguities, and solution error. A major accomplishment of this study is that we have employed a state-of-the-art genetic-based global optimization algorithm called Differential Evolution (DE) that constrains the parameter search in such a way as to remove both the LS and PIT problems. To test the performance of the GoFFRA when DE is employed, we applied it to analyze simulated MGA datasets that we generated from known mixed exponential distributions. Moreover, we evaluated the GoFFRA/DE method by applying it to analyze actual MGAs derived from low-Earth orbiting lightning imaging sensor data; the actual MGA data were classified as either ground or cloud flash MGAs using National Lightning Detection Network[TM] (NLDN) data. Solution error plots are provided for both the simulations and actual data analyses.

Koshak, William↗

NASA NTRS2017

A Method for Snow Reanalysis: The Sierra Nevada (USA) Example

This work presents a state-of-the art methodology for constructing snow water equivalent (SWE) reanalysis. The method is comprised of two main components: (1) a coupled land surface model and snow depletion curve model, which is used to generate an ensemble of predictions of SWE and snow cover area for a given set of (uncertain) inputs, and (2) a reanalysis step, which updates estimation variables to be consistent with the satellite observed depletion of the fractional snow cover time series. This method was applied over the Sierra Nevada (USA) based on the assimilation of remotely sensed fractional snow covered area data from the Landsat 5-8 record (1985-2016). The verified dataset (based on a comparison with over 9000 station years of in situ data) exhibited mean and root-mean-square errors less than 3 and 13 cm, respectively, and correlation greater than 0.95 compared with in situ SWE observations. The method (fully Bayesian), resolution (daily, 90-meter), temporal extent (31 years), and accuracy provide a unique dataset for investigating snow processes. This presentation illustrates how the reanalysis dataset was used to provide a basic accounting of the stored snowpack water in the Sierra Nevada over the last 31 years and ultimately improve real-time streamflow predictions.

Bayesian↗

NASA NTRS2018

Estimation of Seasonal Snow Water Equivalent Using Landsat Observations

This work presents a methodology for estimating seasonal snow water equivalent (SWE) from the use of remotely sensed Visible and Near Infrared observations from the Landsat mission. The method is comprised of two main components: (1) a coupled land surface model and snow depletion curve model, which is used to generate an ensemble of predictions of SWE and snow cover area for a given set of (uncertain) inputs, and (2) a reanalysis step, which updates estimation variables to be consistent with the satellite observed depletion of the fractional snow cover time series. This method was applied over the Sierra Nevada (USA) based on the assimilation of remotely sensed fractional snow covered area data over the Landsat 5-8 record (1985-2016). The verified dataset (based on a comparison with over 9000 station years of in situ data) exhibited mean and root-mean-square errors less than 3 and 13 cm, respectively, and correlations with in situ SWE observations of greater than 0.95. The method (fully Bayesian), resolution (daily, 90-meter), temporal extent (32 years), and accuracy provide a unique dataset for investigating snow processes. In particular, this presentation illustrates how the reanalysis dataset was used to provide climatology of the seasonal snowfall accumulation rates, distributions, and variability over the last three decades.

SWE↗

NASA NTRS2020

An assessment of Earth's climate sensitivity using multiple lines of evidence

We assess evidence relevant to Earth's equilibrium climate sensitivity per doubling of atmospheric CO2, characterized by an effective sensitivity S . This evidence includes feedback process understanding, the historical climate record, and the paleoclimate record. An S value lower than 2 K is difficult to reconcile with any of the three lines of evidence. The amount of cooling during the Last Glacial Maximum provides strong evidence against values of S greater than 4.5 K. Other lines of evidence in combination also show that this is relatively unlikely. We use a Bayesian approach to produce a probability density (PDF) for S given all the evidence, including tests of robustness to difficult‐to‐quantify uncertainties and different priors. The 66% range is 2.6‐3.9 K for our Baseline calculation, and remains within 2.3‐4.5 K under the robustness tests; corresponding 5‐95% ranges are 2.3‐4.7 K, bounded by 2.0‐5.7 K (although such high‐confidence ranges should be regarded more cautiously). This indicates a stronger constraint on S than reported in past assessments, by lifting the low end of the range. This narrowing occurs because the three lines of evidence agree and are judged to be largely independent, and because of greater confidence in understanding feedback processes and in combining evidence. We identify promising avenues for further narrowing the range in S , in particular using comprehensive models and process understanding to address limitations in the traditional forcing‐feedback paradigm for interpreting past changes.

Climate↗

NASA NTRS2018

Variability Timescale and Spectral Index of Sgr A* in the Near Infrared: Approximate Bayesian Computation Analysis of the Variability of the Closest Supermassive Black Hole

Sagittarius A* (Sgr A* ) is the variable radio, near-infrared (NIR), and X-ray source associated with accretion onto the Galactic center black hole. We present an analysis of the most comprehensive NIR variability data set of Sgr A* to date: eight 24 hr epochs of continuous monitoring of Sgr A* at 4.5 μm with the IRAC instrument on the Spitzer Space Telescope, 93 epochs of 2.18 μm data from Naos Conica at the Very Large Telescope, and 30 epochs of 2.12 μm data from the NIRC2 camera at the Keck Observatory, in total 94,929 measurements. A new approximate Bayesian computation method for fitting the first-order structure function extracts information beyond current fast Fourier transformation (FFT) methods of power spectral density (PSD) estimation. With a combined fit of the data of all three observatories, the characteristic coherence timescale of Sgr A* is b 243 57 82 t = - + minutes (90% credible interval). The PSD has no detectable features on timescales down to 8.5 minutes (95% credible level), which is the ISCO orbital frequency for a dimensionless spin parameter a = 0.92. One light curve measured simultaneously at 2.12 and 4.5 μm during a low flux-density phase gave a spectral index αs = 1.6 ± 0.1 (F µ n s n -a ). This value implies that the Sgr A* NIR color becomes bluer during higher flux-density phases. The probability densities of flux densities of the combined data sets are best fit by log-normal distributions. Based on these distributions, the Sgr A* spectral energy distribution is consistent with synchrotron radiation from a nonthermal electron population from below 20 GHz through the NIR.

accretion↗

NASA NTRSDate not supplied

Effects of Dose Error and Sample Size on Sonic Boom Dose-response Curves

NASA will soon be collecting noise-annoyance community survey data as the X-59 aircraft flies supersonically over several communities in the USA. Sparse measurements of the X-59 sonic thumps will be used together with physics-based simulations to estimate noise doses at survey participant locations. These dose estimates have associated error that affects the accuracy of modeled dose-response curves, which can result in misestimation of annoyance. The precision in dose-response curves is also a consideration in selecting the number of survey participants. To enable pretest studies of dose error and precision, simulated dose-response data were generated based on NASA’s Quiet Supersonic Flights 2018 test. The data included various degrees of dose error and sample size. Frequentist multilevel logistic regression models were fit to the true and perturbed dose-response data. Simple proportional relationships were identified between the model parameters and the perturbation standard deviation. The summary dose-response curves illustrate the impact on accuracy if dose error is not accounted for in the model. The precision in the dose-response curves is also shown as the number of participants and degree of participation is varied. Finally, sampling variability is illustrated by showing the dose-response curves for several replicates with random draws of participants and errors.

X-59↗

NASA NTRSDate not supplied

Effects of Dose Error and Sample Size on Sonic Boom Dose-Response Curves

NASA will soon be collecting noise-annoyance community survey data as the X-59 aircraft flies supersonically over several communities in the USA. Sparse measurements of the X-59 sonic thumps will be used together with physics-based simulations to estimate noise doses at survey participant locations. These dose estimates have associated error that affects the accuracy of modeled dose-response curves, which can result in misestimation of annoyance. The precision in dose-response curves is also a consideration in selecting the number of survey participants. To enable pretest studies of dose error and precision, simulated dose-response data were generated based on NASA’s Quiet Supersonic Flights 2018 test. The data included various degrees of dose error and sample size. Frequentist multilevel logistic regression models were fit to the true and perturbed dose-response data. Simple proportional relationships were identified between the model parameters and the perturbation standard deviation. The summary dose-response curves illustrate the impact on accuracy if dose error is not accounted for in the model. The precision in the dose-response curves is also shown as the number of participants and degree of participation is varied. Finally, sampling variability is illustrated by showing the dose-response curves for several replicates with random draws of participants and errors.

X-59↗

NASA NTRS2024

XLSSC 122 Caught in the Act of Growing Up: Spatially Resolved SZ Observations of a z=1.98 Galaxy Cluster

Context. How protoclusters evolved from sparse galaxy overdensities to mature galaxy clusters is still not well understood. In this context, detecting and characterizing the hot intracluster medium (ICM) at high redshifts (z ∼ 2) is key to understanding how the continuous accretion from the filamentary large-scale structure and the mergers along it impact the first phases of cluster formation. Aims. We study the dynamical state and morphology of the z = 1:98 galaxy cluster XLSSC 122 with high-resolution observations (≈5″) of the ICM through the Sunyaev–Zeldovich (SZ) effect. XLSSC 122 is the highest redshift optically confirmed galaxy cluster found in an unbiased, widefield survey. Methods. Via Bayesian forward modeling, we mapped the ICM on scales from the virial radius down to the core of the cluster. To constrain such a broad range of spatial scales, we employed a new technique that jointly forward-models parametric descriptions of the pressure distribution to interferometric ACA and ALMA observations and multiband imaging data from ACT. Results. We detect the SZ effect with 11σ significance in the ALMA+ACA observations and find a flattened inner pressure profile that is consistent with a noncool core classification with a significance of ≥3σ. In contrast to the previous works, we find better agreement between the SZ effect signal and the X-ray emission as well as the cluster member distribution. Further, XLSSC 122 exhibits an excess of SZ flux in the south of the cluster where no X-ray emission is detected. By reconstructing the interferometric observations and modeling in the uv-plane, we obtain a tentative detection of an infalling group or filamentary-like structure in the southeast that is believed to boost and heat up the ICM while the density of the gas is still low. In addition to characterizing the dynamical state of the cluster, we provide an improved SZ mass estimate M500,c = 1.66−0.20+0.23 × 1014 M⊙ . Conclusions. Altogether, the observations indicate that we see XLSSC 122 in a dynamic phase of cluster formation while a large reservoir of gas is already thermalized.

large-scale structure of Universe↗

NASA NTRS2024

Summary and Annotated Bibliography of Measurement Error Corrections with Potential Application in Future Quesst Mission Community Noise Studies

This document is motivated by likely needs of the Quesst mission community response tests, which will culminate in data collection and estimation of dose-response regression relationships for consideration by domestic and international aviation regulators. Furthermore, basic research questions evaluating interactions between rates of community annoyance, dose levels, and indicators of the presence of rattle, vibration, and startle hinge on hypothesis testing in the context of regression models. For a variety of reasons, noise doses may be known only imprecisely and may not reflect the actual level experienced by responding subjects. These differences between true dose and estimated dose, be they systematic or random, constitute covariate measurement error. Available statistics literature speaks to the impacts of measurement error on regression models, both in terms of bias in estimated coefficients and predicted values, and in terms of the loss of statistical power for hypothesis testing. Given the particulars of a categorical annoyance response variable and a continuous noise dose predictor variable subject to measurement error during testing, the emphasis of this report is on findings and methods pertinent to generalized linear (and mixed) models likely to be employed during the Quesst mission community tests. We reach the following conclusions: 1. Of four reviewed methods, structural Bayesian measurement error models and simulation extrapolation (SIMEX) may be the most readily applicable to Quesst mission community noise study objectives. 2. If warranted, a linear measurement model can help model systematic sources of measurement error that the classical measurement error does not. 3. For its ready implementation and small additional input requirements, simulation extrapolation may be ideally suited for addressing secondary research questions involving interactions between annoyance, noise dose, and other factors through hypothesis testing. 4. For their flexibility and ability to propagate uncertainty, structural Bayesian hierarchical models have great appeal for mission purposes; some care may be needed in developing appropriate probability models describing actual noise exposure during testing. An annotated bibliography logs additional papers and resources that may be of value to analysts in other projects and disciplines.

Dose-Response Model↗

NASA NTRS2001

Portfolios in Stochastic Local Search: Efficiently Computing Most Probable Explanations in Bayesian Networks

Portfolio methods support the combination of different algorithms and heuristics, including stochastic local search (SLS) heuristics, and have been identified as a promising approach to solve computationally hard problems. While successful in experiments, theoretical foundations and analytical results for portfolio-based SLS heuristics are less developed. This article aims to improve the understanding of the role of portfolios of heuristics in SLS. We emphasize the problem of computing most probable explanations (MPEs) in Bayesian networks (BNs). Algorithmically, we discuss a portfolio-based SLS algorithm for MPE computation, Stochastic Greedy Search (SGS). SGS supports the integration of different initialization operators (or initialization heuristics) and different search operators (greedy and noisy heuristics), thereby enabling new analytical and experimental results. Analytically, we introduce a novel Markov chain model tailored to portfolio-based SLS algorithms including SGS, thereby enabling us to analytically form expected hitting time results that explain empirical run time results. For a specific BN, we show the benefit of using a homogenous initialization portfolio. To further illustrate the portfolio approach, we consider novel additive search heuristics for handling determinism in the form of zero entries in conditional probability tables in BNs. Our additive approach adds rather than multiplies probabilities when computing the utility of an explanation. We motivate the additive measure by studying the dramatic impact of zero entries in conditional probability tables on the number of zero-probability explanations, which again complicates the search process. We consider the relationship between MAXSAT and MPE, and show that additive utility (or gain) is a generalization, to the probabilistic setting, of MAXSAT utility (or gain) used in the celebrated GSAT and WalkSAT algorithms and their descendants. Utilizing our Markov chain framework, we show that expected hitting time is a rational function - i.e. a ratio of two polynomials - of the probability of applying an additive search operator. Experimentally, we report on synthetically generated BNs as well as BNs from applications, and compare SGSs performance to that of Hugin, which performs BN inference by compilation to and propagation in clique trees. On synthetic networks, SGS speeds up computation by approximately two orders of magnitude compared to Hugin. In application networks, our approach is highly competitive in Bayesian networks with a high degree of determinism. In addition to showing that stochastic local search can be competitive with clique tree clustering, our empirical results provide an improved understanding of the circumstances under which portfolio-based SLS outperforms clique tree clustering and vice versa.

Mengshoel, Ole J.↗

NASA NTRS2012

Model-Based Method for Sensor Validation

Fault detection, diagnosis, and prognosis are essential tasks in the operation of autonomous spacecraft, instruments, and in situ platforms. One of NASA s key mission requirements is robust state estimation. Sensing, using a wide range of sensors and sensor fusion approaches, plays a central role in robust state estimation, and there is a need to diagnose sensor failure as well as component failure. Sensor validation can be considered to be part of the larger effort of improving reliability and safety. The standard methods for solving the sensor validation problem are based on probabilistic analysis of the system, from which the method based on Bayesian networks is most popular. Therefore, these methods can only predict the most probable faulty sensors, which are subject to the initial probabilities defined for the failures. The method developed in this work is based on a model-based approach and provides the faulty sensors (if any), which can be logically inferred from the model of the system and the sensor readings (observations). The method is also more suitable for the systems when it is hard, or even impossible, to find the probability functions of the system. The method starts by a new mathematical description of the problem and develops a very efficient and systematic algorithm for its solution. The method builds on the concepts of analytical redundant relations (ARRs).

Vatan, Farrokh↗

NASA NTRS1974

A Bayesian analysis of two probability models describing thunderstorm activity at Cape Kennedy, Florida

A Bayesian analysis of the two discrete probability models, the negative binomial and the modified negative binomial distributions, which have been used to describe thunderstorm activity at Cape Kennedy, Florida, is presented. The Bayesian approach with beta prior distributions is compared to the classical approach which uses a moment method of estimation or a maximum-likelihood method. The accuracy and simplicity of the Bayesian method is demonstrated.

Williford, W. O.↗

NASA NTRS2022

Advanced Statistical Methods in Spacecraft Flight Software Cost Estimation: Bayesian Regression and Nonlinear Principal Components Analysis to Support System Engineering in the Early Project Lifecycle

This paper provides an overview of the new features and model updates in the upcoming release of the NASA Analogy Software Cost Tool (ASCoT). ASCoT, hosted within the Online NASA Space Estimation Tools (ONSET) on the One NASA Cost Engineering (ONCE) Database, is a web-based tool that provides a suite of estimation tools to support early lifecycle NASA flight software cost analysis. In addition to the traditional parametric flight software costing method COCOMO II, ASCoT contains a Bayesian linear regression to predict total flight software development cost as a function of total spacecraft cost, as well as four analogic methods: k-Nearest Neighbors (kNN) and Clustering models to predict Effort (in work-months) and total source lines of code (SLOC). These methods are designed to work primarily with system-level inputs such as mission type (orbiter, lander, etc.), mission destination (Earth, Inner Planetary, etc.), and the number of instruments and deployables. Nonlinear principal components analysis (NLPCA) is performed to find the principal features of the data composed of both categorical and numerical variables and is necessary prior to defining our analogic methods. Sensitivity analyses and in- and out-of-sample model performance results are presented for the Bayesian CER and the analogic models.

Johnson, James K.↗

NASA NTRS2020

Using Bayesian Estimation to Quantify the Risks of Spaceflight

Complex PRA is the best method and current gold standard, as it allows us to reflect changes (improvements) in individual spacecraft system risks over time. Yet, Bayesian methods – using simple inputs – allowed us to get estimates that are in line with high-complexity PRA. Here Bayesian estimation acts as a “gut check” on PRA (supposing a “reasonable” prior is used). Frequentist calculations can overestimate P(failure), especially when total number of trials are few (e.g., after Challenger). In general, Bayesian probability estimation can be used in any risk assessment situation to integrate what we think we know ahead of time with what we observe over time.

Reynolds, Robert J.↗

NASA NTRS2012

Parametric 3D Atmospheric Reconstruction in Highly Variable Terrain with Recycled Monte Carlo Paths and an Adapted Bayesian Inference Engine

We describe a method for accelerating a 3D Monte Carlo forward radiative transfer model to the point where it can be used in a new kind of Bayesian retrieval framework. The remote sensing challenge is to detect and quantify a chemical effluent of a known absorbing gas produced by an industrial facility in a deep valley. The available data is a single low resolution noisy image of the scene in the near IR at an absorbing wavelength for the gas of interest. The detected sunlight has been multiply reflected by the variable terrain and/or scattered by an aerosol that is assumed partially known and partially unknown. We thus introduce a new class of remote sensing algorithms best described as "multi-pixel" techniques that call necessarily for a 3D radaitive transfer model (but demonstrated here in 2D); they can be added to conventional ones that exploit typically multi- or hyper-spectral data, sometimes with multi-angle capability, with or without information about polarization. The novel Bayesian inference methodology uses adaptively, with efficiency in mind, the fact that a Monte Carlo forward model has a known and controllable uncertainty depending on the number of sun-to-detector paths used.

Monte Carlo↗

NASA NTRSDate not supplied

Uncertainty Quantification of Inducer Natural Frequency using Conditional Assessment of Modeling and Modal Testing of Simpler Systems

The low pressure fuel pump inducer of the new Space Launch System RS25 core stage engine operates in a highly complex environment that substantially affects its modal characteristics. Some of the more important effects are fluid-added mass resulting from operation within a light liquid (Hydrogen), and the magnification of this effect due to tight tip clearance. Since higher order cavitation has been identified as a significant harmonic driver, knowledge of the natural frequency of potentially excitable modes is critical for safe operation, but this frequency cannot be measured during the severe operational environment. A comprehensive testing and analysis program has therefore been performed over the last four years to identify the nominal value and uncertainty of the frequency by modeling and testing four simpler structures which share some of the characteristics of the operational inducer. This testing was used to assess and adjust modeling techniques and excellent correlation was achieved. Identification of the uncertainty in the inducer frequency itself was still problematic, however. This difficulty led to an investigation of Bayesian uncertainty quantification techniques, and to the application of the relatively simple technique of Multi-Variate Normal conditional distributions to calculate the inducer natural frequency uncertainty. Assumptions on prior distributions of uncertainty of the fluid-added mass and tip clearance effect are initially applied to models of each of the simple structures and the inducer itself, and these uncertainties are propagated to generate natural frequencies using design of experiments. Simple response surfaces are then created from this data in order to calculate a Covariance Matrix relating all of these natural frequencies. Finally, the results from modal test of the simple structures are considered to be observations and used to calculate the conditional variance of the desired inducer frequencies. As this method is less rigorous than more complicated Bayesian methods reported in the literature, a conservative factor is applied to the result, but the resulting uncertainty is still significantly less than originally estimated and will greatly assist certification of the inducer for use in the engine.

Uncertainty Quantification↗

NASA NTRSDate not supplied

Uncertainty Quantification of Inducer Eigenvalues using Conditional Assessment of Models and Modal Test of Simpler Systems

The low pressure fuel pump inducer of the new Space Launch System RS25 core stage engine operates in a highly complex environment that substantially affects its modal characteristics. Some of the more important effects are fluid-added mass resulting from operation within a light liquid (Hydrogen), and the magnification of this effect due to tight tip clearance. Since higher order cavitation has been identified as a significant harmonic driver, knowledge of the natural frequency of potentially excitable modes is critical for safe operation, but this frequency cannot be measured during the severe operational environment. A comprehensive testing and analysis program has therefore been performed over the last four years to identify the nominal value and uncertainty of the frequency by modeling and testing four simpler structures which share some of the characteristics of the operational inducer. This testing was used to assess and adjust modeling techniques and excellent correlation was achieved. Identification of the uncertainty in the inducer frequency itself was still problematic, however. This difficulty led to an investigation of Bayesian uncertainty quantification techniques, and to the application of the relatively simple technique of Multi-Variate Normal conditional distributions to calculate the inducer natural frequency uncertainty. Assumptions on prior distributions of uncertainty of the fluid-added mass and tip clearance effect are initially applied to models of each of the simple structures and the inducer itself, and these uncertainties are propagated to generate natural frequencies using design of experiments. Simple response surfaces are then created from this data in order to calculate a Covariance Matrix relating all of these natural frequencies. Finally, the results from modal test of the simple structures are considered to be observations and used to calculate the conditional variance of the desired inducer frequencies. As this method is less rigorous than more complicated Bayesian methods reported in the literature, a conservative factor is applied to the result, but the resulting uncertainty is still significantly less than originally estimated and will greatly assist certification of the inducer for use in the engine.

Uncertainty Quantification↗