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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 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 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 NTRS2020

A Second Look at 12 Candidate Dual AGNs Using BAYMAX

We present an analysis of 12 optically selected dual active galactic nucleus (AGN) candidates at z < 0.34. Each candidate was originally identified via double-peaked [O III] λ5007 emission lines and received follow-up Chandra and Hubble Space Telescope (HST) observations. Because the X-ray data are low-count (<100 counts) with small separations (<1''), a robust analysis is necessary for classifying each source. Pairing long-slit [O III] observations with existing Chandra observations, we re-analyze the X-ray observations with Bayesian AnalYsis of AGNs in X-rays to determine whether the X-ray emission from each system is more likely a single or dual point source. We find that 4 of the 12 sources are likely dual X-ray point-source systems. We examine each point source's spectra via a Monte Carlo method that probabilistically identifies the likely origin of each photon. When doing so, we find that (i) the secondary X-ray point sources in two of the systems have L(X)< 10(exp 40) erg/s, such that we cannot rule out a non-AGN origin, (ii) one source has a secondary with L(X)> 10(exp 40) erg/s but a spectrum that is too soft to definitively preclude being X-ray emitting diffuse gas that was photoionized by the primary AGN, and (iii) one system (SDSS J1126+2944) is a dual AGN. Additionally, using complementary HST observations, we analyze a subsample of systems that are visually identified as merging. Our results suggest that dual AGNs may preferentially reside in mergers with small separations, consistent with both simulations and observations.

Adi Foord↗
NASA NTRS2013

Uncertainty Quantification of GEOS-5 L-band Radiative Transfer Model Parameters Using Bayesian Inference and SMOS Observations

Uncertainties in L-band (1.4 GHz) radiative transfer modeling (RTM) affect the simulation of brightness temperatures (Tb) over land and the inversion of satellite-observed Tb into soil moisture retrievals. In particular, accurate estimates of the microwave soil roughness, vegetation opacity and scattering albedo for large-scale applications are difficult to obtain from field studies and often lack an uncertainty estimate. Here, a Markov Chain Monte Carlo (MCMC) simulation method is used to determine satellite-scale estimates of RTM parameters and their posterior uncertainty by minimizing the misfit between long-term averages and standard deviations of simulated and observed Tb at a range of incidence angles, at horizontal and vertical polarization, and for morning and evening overpasses. Tb simulations are generated with the Goddard Earth Observing System (GEOS-5) and confronted with Tb observations from the Soil Moisture Ocean Salinity (SMOS) mission. The MCMC algorithm suggests that the relative uncertainty of the RTM parameter estimates is typically less than 25 of the maximum a posteriori density (MAP) parameter value. Furthermore, the actual root-mean-square-differences in long-term Tb averages and standard deviations are found consistent with the respective estimated total simulation and observation error standard deviations of m3.1K and s2.4K. It is also shown that the MAP parameter values estimated through MCMC simulation are in close agreement with those obtained with Particle Swarm Optimization (PSO).

MCMC↗
NASA NTRS2006

Exploring the Connection Between Sampling Problems in Bayesian Inference and Statistical Mechanics

The Bayesian and statistical mechanical communities often share the same objective in their work - estimating and integrating probability distribution functions (pdfs) describing stochastic systems, models or processes. Frequently, these pdfs are complex functions of random variables exhibiting multiple, well separated local minima. Conventional strategies for sampling such pdfs are inefficient, sometimes leading to an apparent non-ergodic behavior. Several recently developed techniques for handling this problem have been successfully applied in statistical mechanics. In the multicanonical and Wang-Landau Monte Carlo (MC) methods, the correct pdfs are recovered from uniform sampling of the parameter space by iteratively establishing proper weighting factors connecting these distributions. Trivial generalizations allow for sampling from any chosen pdf. The closely related transition matrix method relies on estimating transition probabilities between different states. All these methods proved to generate estimates of pdfs with high statistical accuracy. In another MC technique, parallel tempering, several random walks, each corresponding to a different value of a parameter (e.g. "temperature"), are generated and occasionally exchanged using the Metropolis criterion. This method can be considered as a statistically correct version of simulated annealing. An alternative approach is to represent the set of independent variables as a Hamiltonian system. Considerab!e progress has been made in understanding how to ensure that the system obeys the equipartition theorem or, equivalently, that coupling between the variables is correctly described. Then a host of techniques developed for dynamical systems can be used. Among them, probably the most powerful is the Adaptive Biasing Force method, in which thermodynamic integration and biased sampling are combined to yield very efficient estimates of pdfs. The third class of methods deals with transitions between states described by rate constants. These problems are isomorphic with chemical kinetics problems. Recently, several efficient techniques for this purpose have been developed based on the approach originally proposed by Gillespie. Although the utility of the techniques mentioned above for Bayesian problems has not been determined, further research along these lines is warranted

Pohorille, Andrew↗
NASA NTRS2008

Tool Support for Parametric Analysis of Large Software Simulation Systems

The analysis of large and complex parameterized software systems, e.g., systems simulation in aerospace, is very complicated and time-consuming due to the large parameter space, and the complex, highly coupled nonlinear nature of the different system components. Thus, such systems are generally validated only in regions local to anticipated operating points rather than through characterization of the entire feasible operational envelope of the system. We have addressed the factors deterring such an analysis with a tool to support envelope assessment: we utilize a combination of advanced Monte Carlo generation with n-factor combinatorial parameter variations to limit the number of cases, but still explore important interactions in the parameter space in a systematic fashion. Additional test-cases, automatically generated from models (e.g., UML, Simulink, Stateflow) improve the coverage. The distributed test runs of the software system produce vast amounts of data, making manual analysis impossible. Our tool automatically analyzes the generated data through a combination of unsupervised Bayesian clustering techniques (AutoBayes) and supervised learning of critical parameter ranges using the treatment learner TAR3. The tool has been developed around the Trick simulation environment, which is widely used within NASA. We will present this tool with a GN&C (Guidance, Navigation and Control) simulation of a small satellite system.

Schumann, Johann↗
NASA NTRS2000

Filtering in Hybrid Dynamic Bayesian Networks

We implement a 2-time slice dynamic Bayesian network (2T-DBN) framework and make a 1-D state estimation simulation, an extension of the experiment in (v.d. Merwe et al., 2000) and compare different filtering techniques. Furthermore, we demonstrate experimentally that inference in a complex hybrid DBN is possible by simulating fault detection in a watertank system, an extension of the experiment in (Koller & Lerner, 2000) using a hybrid 2T-DBN. In both experiments, we perform approximate inference using standard filtering techniques, Monte Carlo methods and combinations of these. In the watertank simulation, we also demonstrate the use of 'non-strict' Rao-Blackwellisation. We show that the unscented Kalman filter (UKF) and UKF in a particle filtering framework outperform the generic particle filter, the extended Kalman filter (EKF) and EKF in a particle filtering framework with respect to accuracy in terms of estimation RMSE and sensitivity with respect to choice of network structure. Especially we demonstrate the superiority of UKF in a PF framework when our beliefs of how data was generated are wrong. Furthermore, we investigate the influence of data noise in the watertank simulation using UKF and PFUKD and show that the algorithms are more sensitive to changes in the measurement noise level that the process noise level. Theory and implementation is based on (v.d. Merwe et al., 2000).

Andersen, Morten Nonboe↗
NASA NTRS2019

Computational Bayesian Methods Applied to Complex Problems in Bio and Astro Statistics

In this dissertation we apply computational Bayesian methods to three distinct problems. In the first chapter, we address the issue of unrealistic covariance matrices used to estimate collision probabilities. We model covariance matrices with a Bayesian Normal-Inverse-Wishart model, which we fit with Gibbs sampling. In the second chapter, we are interested in determining the sample sizes necessary to achieve a particular interval width and establish non-inferiority in the analysis of prevalences using two fallible tests. To this end, we use a third order asymptotic approximation. In the third chapter, we wish to synthesize evidence across multiple domains in measurements taken longitudinally across time, featuring a substantial amount of structurally missing data, and fit the model with Hamiltonian Monte Carlo in a simulation to analyze how estimates of a parameter of interest change across sample sizes.

Elrod, Chris↗
NASA NTRSDate not supplied

Assimilation of microwave satellite observations over the rainbands of tropical cyclones

The potential of microwave observations in improving the weather forecasts is limited by the accuracy of all-sky radiative transfer calculations. We introduce a novel Bayesian MonteCarlo technique to improve the assimilation of microwave observations over the rainbands of tropical cyclones. The BMCI technique eliminates the need for a forward model in the data assimilation system. The technique includes three steps, (i) generating a comprehensive dataset using in-situ cloud measurements and atmospheric profiles, (ii) generating synthetic ATMS observations from the training dataset, and (iii) using real observations to estimate the geophysical variables over the rainbands of tropical cyclones. The retrieved profiles of temperature, relative humidity, and cloud water content as well assurface information such as SST were then assimilated into the model. The results show that assimilating the BMCI retrievals can influence the dynamical features of the cyclone, including a stronger warm core, a symmetric eye, and vertically aligned wind columns.

Monte Carlo↗
NASA NTRS2004

Neural network uncertainty assessment using Bayesian statistics: a remote sensing application

Neural network (NN) techniques have proved successful for many regression problems, in particular for remote sensing; however, uncertainty estimates are rarely provided. In this article, a Bayesian technique to evaluate uncertainties of the NN parameters (i.e., synaptic weights) is first presented. In contrast to more traditional approaches based on point estimation of the NN weights, we assess uncertainties on such estimates to monitor the robustness of the NN model. These theoretical developments are illustrated by applying them to the problem of retrieving surface skin temperature, microwave surface emissivities, and integrated water vapor content from a combined analysis of satellite microwave and infrared observations over land. The weight uncertainty estimates are then used to compute analytically the uncertainties in the network outputs (i.e., error bars and correlation structure of these errors). Such quantities are very important for evaluating any application of an NN model. The uncertainties on the NN Jacobians are then considered in the third part of this article. Used for regression fitting, NN models can be used effectively to represent highly nonlinear, multivariate functions. In this situation, most emphasis is put on estimating the output errors, but almost no attention has been given to errors associated with the internal structure of the regression model. The complex structure of dependency inside the NN is the essence of the model, and assessing its quality, coherency, and physical character makes all the difference between a blackbox model with small output errors and a reliable, robust, and physically coherent model. Such dependency structures are described to the first order by the NN Jacobians: they indicate the sensitivity of one output with respect to the inputs of the model for given input data. We use a Monte Carlo integration procedure to estimate the robustness of the NN Jacobians. A regularization strategy based on principal component analysis is proposed to suppress the multicollinearities in order to make these Jacobians robust and physically meaningful.

Neural Networks (Computer)↗
NASA NTRS2002

The footprints of visual attention in the Posner cueing paradigm revealed by classification images

In the Posner cueing paradigm, observers' performance in detecting a target is typically better in trials in which the target is present at the cued location than in trials in which the target appears at the uncued location. This effect can be explained in terms of a Bayesian observer where visual attention simply weights the information differently at the cued (attended) and uncued (unattended) locations without a change in the quality of processing at each location. Alternatively, it could also be explained in terms of visual attention changing the shape of the perceptual filter at the cued location. In this study, we use the classification image technique to compare the human perceptual filters at the cued and uncued locations in a contrast discrimination task. We did not find statistically significant differences between the shapes of the inferred perceptual filters across the two locations, nor did the observed differences account for the measured cueing effects in human observers. Instead, we found a difference in the magnitude of the classification images, supporting the idea that visual attention changes the weighting of information at the cued and uncued location, but does not change the quality of processing at each individual location.

Non-NASA Center↗