SEARCH · Search NASA

Results for “Prior Distribution”

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.

SourceResearch connectionFrom yearThrough year

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

At least 19 records

All sources NASA NTRS DOE OSTI

NASA NTRS1975

Bayesian estimation - A sensitivity analysis

The robustness of the assigned prior distribution in a Bayesian estimation problem is examined. A Bayesian analysis for a stochastic intensity parameter of a Poisson distribution is summarized in which the natural conjugate is assigned as the prior distribution of the random parameter. The sensitivity analysis is carried out by assuming the existence of a true prior which is different in form from that of the assigned prior distribution. By using mean-squared error as a measure of performance, the ensuing Bayes decision function is compared to the corresponding minimum variance unbiased estimator. Results indicate that the Bayes estimator is largely robust to deviations from the assigned prior and remains squared-error superior to the MVU type within a broad region.

Canavos, G. C.↗

NASA NTRS1974

On the robustness of a Bayes estimate

This paper examines the robustness of a Bayes estimator with respect to the assigned prior distribution. A Bayesian analysis for a stochastic scale parameter of a Weibull failure model is summarized in which the natural conjugate is assigned as the prior distribution of the random parameter. The sensitivity analysis is carried out by the Monte Carlo method in which, although an inverted gamma is the assigned prior, realizations are generated using distribution functions of varying shape. For several distributional forms and even for some fixed values of the parameter, simulated mean squared errors of Bayes and minimum variance unbiased estimators are determined and compared. Results indicate that the Bayes estimator remains squared-error superior and appears to be largely robust to the form of the assigned prior distribution.

Canavos, G. C.↗

NASA NTRS2015

Data Applicability of Heritage and New Hardware For Launch Vehicle Reliability Models

Bayesian reliability requires the development of a prior distribution to represent degree of belief about the value of a parameter (such as a component's failure rate) before system specific data become available from testing or operations. Generic failure data are often provided in reliability databases as point estimates (mean or median). A component's failure rate is considered a random variable where all possible values are represented by a probability distribution. The applicability of the generic data source is a significant source of uncertainty that affects the spread of the distribution. This presentation discusses heuristic guidelines for quantifying uncertainty due to generic data applicability when developing prior distributions mainly from reliability predictions.

Al Hassan, Mohammad↗

NASA NTRS2022

Optimal Estimation Framework for Ocean Color Atmospheric Correction and Pixel-level Uncertainty Quantification

Ocean color remote sensing requires compensation for atmospheric scattering and absorption (aerosol, Rayleigh, and trace gases), referred to as atmospheric correction (AC). AC allows inference of parameters such as spectrally resolved remote sensing reflectance ( R rs )(λ) ; sr 1 ) at the ocean surface from the top-of-atmosphere reflectance. Often, the uncertainty of this process is not fully explored. Bayesian inference techniques provide a simultaneous AC and uncertainty assessment via a full posterior distribution of the relevant variables, given the prior distribution of those variables and the radiative transfer (RT) likelihood function. Given uncertainties in the algorithm inputs, the Bayesian framework enables better constraints on the AC process by using the complete spectral information compared to traditional approaches that use only a subset of bands for AC. This paper investigates a Bayesian inference research method (Optimal Estimation, OE) for ocean color AC by simultaneously retrieving atmospheric and ocean properties using all visible and near-infrared spectral bands. The OE algorithm analytically approximates the posterior distribution of parameters based on normality assumptions and provides a potentially viable operational algorithm with a reduced computational expense. We developed a Neural Network (NN) RT forward model look-up-table-based emulator to increase algorithm efficiency further and thus speed up the likelihood computations. We then applied the OE algorithm to synthetic data and observations from the MODerate resolution Imaging Spectroradiometer (MODIS) on NASA’s Aqua spacecraft. We compared the R rs )(λ) retrieval and its uncertainty estimates from the OE method with in-situ validation data from the SeaWiFS Bio-optical Archive and Storage System (SeaBASS) and Aerosol Robotic Network Ocean Color (AERONET-OC) datasets. The OE algorithm improved R rs )(λ) estimates relative to the NASA standard operational algorithm by improving all statistical metrics at 443, 555, and 667 nm. Unphysical negative R rs )(λ) , which often appear in complex water conditions, was reduced by a factor of 3. The OE-derived pixel-level R rs )(λ) uncertainty estimates were also assessed relative to in-situ data and were shown to have skill.

Atmospheric correction↗

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

Uncertainty Quantification↗

NASA NTRS2011

Markov Chain Monte Carlo Bayesian Learning for Neural Networks

Conventional training methods for neural networks involve starting al a random location in the solution space of the network weights, navigating an error hyper surface to reach a minimum, and sometime stochastic based techniques (e.g., genetic algorithms) to avoid entrapment in a local minimum. It is further typically necessary to preprocess the data (e.g., normalization) to keep the training algorithm on course. Conversely, Bayesian based learning is an epistemological approach concerned with formally updating the plausibility of competing candidate hypotheses thereby obtaining a posterior distribution for the network weights conditioned on the available data and a prior distribution. In this paper, we developed a powerful methodology for estimating the full residual uncertainty in network weights and therefore network predictions by using a modified Jeffery's prior combined with a Metropolis Markov Chain Monte Carlo method.

Goodrich, Michael S.↗

NASA NTRSDate not supplied

Image-to-Image Wildfire Detection via Quantum-Compatible Variational Segmentation from Remotely-sensed Data

Over the last decade, the incidence of wildfires has surged, causing widespread destruction globally. To better comprehend and manage these incidents, remote sensing and aerial missions have been implemented in recent efforts. However, this has resulted in an exponential rise in the amount of remote sensing data utilization, leading to a need for intelligent automation of data extraction in wildfire studies. Machine learning provides an accurate automated approach for detecting these natural anomalies and facilitates decision-makers to take prompt actions. To make insightful decisions in wildfire management, it is imperative to move beyond simple detection and explore the potential of probabilistic generative machine learning for creating "what-if" scenarios for various wildfire conditions. Such models offer improved representation of the stochastic nature of wildfire events. However, the optimization of these models can be computationally expensive, especially when using classical computers. Quantum computers have recently emerged as a promising solution to reduce the computational cost of training such models and improve their performance. In this study, we aim to utilize quantum-compatible machine learning techniques to implement our probabilistic generative approach. To that end, we propose a supervised probabilistic variational model consisting of a U-NET-based image-to-image component along with encoder and decoder networks which work as a variational autoencoder (VAE) component. Additionally, we explore the type of latent distribution type in the VAE component and implement different means for modeling the prior distribution. We further investigate the quantum-compatible versions of the model compared to the classical counterpart and benchmark potential benefits of quantum compatibility over the classical model.

quantum machine learning↗

NASA NTRS1972

A Bayesian approach to parameter and reliability estimation in the Poisson distribution.

For life testing procedures, a Bayesian analysis is developed with respect to a random intensity parameter in the Poisson distribution. Bayes estimators are derived for the Poisson parameter and the reliability function based on uniform and gamma prior distributions of that parameter. A Monte Carlo procedure is implemented to make possible an empirical mean-squared error comparison between Bayes and existing minimum variance unbiased, as well as maximum likelihood, estimators. As expected, the Bayes estimators have mean-squared errors that are appreciably smaller than those of the other two.

Canavos, G. C.↗

NASA NTRS2018

A Singular Value Decomposition Framework for Retrievals with Vertical Distribution Information from Greenhouse Gas Column Absorption Spectroscopy Measurements

We describe a variation of the Optimal Estimation (OE) method for greenhouse gas remote sensing retrievals using a singular value decomposition (SVD) and an uninformative prior. The SVD method is capable of discerning vertical information in column integrated absorption measurements. While traditional Bayesian optimal estimation (OE) assumes a prior distribution in order to regularize the inversion problem, the SVD approach identifies principal components that can be retrieved from the measurement without explicitly specifying a prior mean and prior covariance matrix. We discuss the method, illustrate its use on an integrated path differential absorption CO2 lidar measurement model, and compare it to traditional optimal estimation using numerical simulations. In the absence of forward model error, the mathematics behind the SVD method guarantee it to be bias-free, which is confirmed by the numerical simulations. In contrast, traditional OE retrievals exhibit bias when the prior mean used in the retrieval differs from the true mean. While the SVD approach can be used for most trace gas retrievals, it is particularly useful for situations where prior knowledge of the trace gas profile is poor. The SVD analysis is also useful in illustrating how vertical information is treated by the traditional OE approach.

Ramanathan, Anand K.↗

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 NTRS1977

Bayesian estimation of crack initiation times from service data

Lockheed C-130 Hercules aircraft have during their service life been periodically inspected and growing cracks around rivet holes were recorded. This record has recently been used to determine the statistical distributions of crack initiation times and the distribution of initial crack sizes. When crack initiation times are calculated from such cracks, by backward extrapolation of the growth relation, the resulting distribution of crack initiation times will indicate a preponderance of short times to crack initiation. If however, such distributions are combined with the reliability of the inspection procedure, the statistical distribution of missed initiation times can be estimated. The method used is based on Bayes theorem which permits the calculation of the 'prior' distribution (initiation times before inspection) from a knowledge of the 'posterior' distribution (initiation times obtained from the inspection) and a 'likelihood function' (reliability of the inspection) procedure. The results indicate that during an early inspection a large percentage of initiation times will be missed and that the fraction of located initiation times increases during later inspections.

Heller, R. A.↗

NASA NTRS2018

A Singular Value Decomposition Framework for Retrievals with Vertical Distribution Information from Greenhouse Gas Column Absorption Spectroscopy Measurements

We review the singular value decomposition (SVD) framework and use it for quantifying and discerning vertical information in greenhouse gas retrievals from column integrated absorption measurements. While the commonly used traditional Bayesian optimal estimation (OE) assumes a prior distribution in order to regularize the inversion problem, the SVD approach identifies principal components that can be retrieved from the measurement without explicitly specifying a prior mean and prior covariance matrix. We review the SVD method, explicitly recognize the use of an uninformative prior and show it to incur no bias from the choice of the prior. We also make the connection between the SVD method and the pseudo-inverse, which makes it more intuitive and easy to understand. We illustrate the use of the SVD method on an integrated path differential absorption CO2 lidar measurement model and verify our derivations and bias-free properties versus optimal estimation using numerical simulations. In contrast, traditional OE retrievals exhibit bias when the prior mean used in the retrieval differs from the true mean. Hence, the SVD method is particularly useful for situations in which knowledge of the prior mean and prior covariance of the true state (e.g., greenhouse gas profiles) is inadequate.

Ramanathan, Anand K.↗

NASA NTRS2013

An Ensemble Recentering Kalman Filter with an Application to Argo Temperature Data Assimilation into the NASA GEOS-5 Coupled Model

A two-step ensemble recentering Kalman filter (ERKF) analysis scheme is introduced. The algorithm consists of a recentering step followed by an ensemble Kalman filter (EnKF) analysis step. The recentering step is formulated such as to adjust the prior distribution of an ensemble of model states so that the deviations of individual samples from the sample mean are unchanged but the original sample mean is shifted to the prior position of the most likely particle, where the likelihood of each particle is measured in terms of closeness to a chosen subset of the observations. The computational cost of the ERKF is essentially the same as that of a same size EnKF. The ERKF is applied to the assimilation of Argo temperature profiles into the OGCM component of an ensemble of NASA GEOS-5 coupled models. Unassimilated Argo salt data are used for validation. A surprisingly small number (16) of model trajectories is sufficient to significantly improve model estimates of salinity over estimates from an ensemble run without assimilation. The two-step algorithm also performs better than the EnKF although its performance is degraded in poorly observed regions.

Particle Filter↗

NASA NTRS2013

Bayesian Approach for Reliability Assessment of Sunshield Deployment on JWST

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 Bayesian approach for reliability estimation of spacecraft deployment was developed for this purpose. This approach was then applied to the James Webb Space Telescope (JWST) Sunshield subsystem, a unique design intended for thermal control of the observatory's telescope and science instruments. In order to collect the prior information on deployable systems, detailed studies of "heritage information", were conducted extending over 45 years of spacecraft launches. The NASA Goddard Space Flight Center (GSFC) Spacecraft Operational Anomaly and Reporting System (SOARS) data were then used to estimate the parameters of the conjugative beta prior distribution for anomaly and failure occurrence, as the most consistent set of available data and that could be matched to launch histories. This allows for an emperical Bayesian prediction for the risk of an anomaly occurrence of the complex Sunshield deployment, with credibility limits, using prior deployment data and test information.

Kaminskiy, Mark P.↗

NASA NTRS1975

Reliability-based optimum inspection and maintenance procedures

The development of reliability-based optimum inspection and maintenance schedules for engines needs an understanding of the fatigue behavior of the engines. Critical areas of the engine structure prone to fatigue damage are usually identified beforehand or after the fleet has been put into operation. In these areas, fatigue cracks initiate after several flight hours, and these cracks grow in length until failure takes place when these cracks attain the critical lengths. Crack initiation time and its growth rate are considered to be random variables. Usually, the inspection (fatigue) or test data from similar engines are used as prior distributions. The existing state-of-the-art is to ignore the different lengths of cracks obserbed at various inspections and to consider only the fact that a crack existed (or did not exist) at the time of inspection. In this paper, a procedure has been developed to obtain the probability of finding a crack of a given size at a certain time if the probability distributions for crack initiation and rates of growth are known. Application of the developed stochastic models to devise optimum procedures for inspection and maintenance are also discussed.

Nanagud, S.↗

NASA NTRS1980

Proportion estimation using prior cluster purities

The prior distribution of CLASSY component purities is studied, and this information incorporated into maximum likelihood crop proportion estimators. The method is tested on Transition Year spring small grain segments.

Terrell, G. R.↗

NASA NTRS1980

The multicategory case of the sequential Bayesian pixel selection and estimation procedure

A Bayesian technique for stratified proportion estimation and a sampling based on minimizing the mean squared error of this estimator were developed and tested on LANDSAT multispectral scanner data using the beta density function to model the prior distribution in the two-class case. An extention of this procedure to the k-class case is considered. A generalization of the beta function is shown to be a density function for the general case which allows the procedure to be extended.

Pore, M. D.↗