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All sourcesNASA NTRSDOE OSTI
NASA NTRS1995

Inferring the spatial and energy distribution of gamma-ray burst sources. 1: Methodology

We describe Bayesian methods for analyzing the distribution of gamma-ray burst peak photon fluxes and directions. These methods fit the differential distribution, and have the following advantages over rival methods: (1) they do not destroy information by binning or averaging the data (as do, say, chi squared, the averaged value of V/V(sub max), and angular moment analyses); (2) they straightforwardly handle uncertainties in the measured quantities; (3) they analyze the strength and direction information jointly; (4) they use information available about nondetections; and (5) they automatically identify and account for biases and selection effects given a precise description of the experiment. In these methods, the most important information needed about the instrument threshold is not its value at the times of burst triggers, as is used in the average value of V/V(sub max) analyses, but rather the value of the threshold at times when no trigger occurred. We show that this information can be summarized as an average detection efficiency that is similar to the product of the exposure and efficiency reported in the First Burst and Transient Source Experiment (BATSE) Burst (1B) Catalog, but significantly different from it at low fluxes. We also quantify an important bias that results from estimating the peak flux by scanning the burst to find the peak number of counts in a window of specified duration, as was done for the 1B Catalog. When the duration of the peak of the light curve is longer than the window duration, a simple flux estimate based on the peak counts significantly overestimates the peak flux in a nonlinear fashion that distorts the shape of the log(N)-log(P) distribution. This distortion also corrupts analyses of the V/V(sub max) distribution that use ratios of counts above background to estimate V/V(sub max). The Bayesian calculation specifies how to account for this bias. Implementation of the Bayesian approach requires some changes in the way burst data are reported that we describe in detail. Subsequent papers will report analyses of the 1B Catalog data using the methods described here.

Loredo, Thomas J.↗
NASA NTRS2018

Exoplanet Biosignatures: Future Directions

We introduce a Bayesian method for guiding future directions for detection of life on exoplanets. We describe empirical and theoretical work necessary to place constraints on the relevant likelihoods, including those emerging from better understanding stellar environment, planetary climate and geophysics, geochemical cycling, the universalities of physics and chemistry, the contingencies of evolutionary history, the properties of life as an emergent complex system, and the mechanisms driving the emergence of life. We provide examples for how the Bayesian formalism could guide future search strategies, including determining observations to prioritize or deciding between targeted searches or larger lower resolution surveys to generate ensemble statistics and address how a Bayesian methodology could constrain the prior probability of life with or without a positive detection.

Bayesian analysis↗
NASA NTRS2022

Gaussian Process Regression Method for Costing SmallSat Bus Capabilities

NASA is responding to the growing interest in, andcapabilities of, small satellites for science applications with an increasingnumber and frequency of Announcements of Opportunityfor small satellite space missions. Estimating the probabilitythat these mission concepts will fit within the small cost capsof these opportunities is largely driven by the probability thatone of the burgeoning number of small satellite providers will beable to meet the payload’s accommodation requirements withinthe budget for the spacecraft. JPL has collected a databasecontaining technical specifications and cost of commerciallyavailable Smallsat buses across various vendors. The primarypurpose of the database is for use in JPL’s Team X architecturestudies to inform cost estimates of a spacecraft bus which fitsthe customer’s technical requirements for their payload andmission. Customer needs are often unique and don’t alignperfectly with an off-the-shelf commercial spacecraft bus, whichmotivates the need to develop a cost model across the continuoustechnical parameter space.Al’s Bus Cost Distribution Estimator (ABCDE) uses Gaussianprocess regression (GPR) to predict commercial Smallsat spacecraftbus cost based on a subset of a customer’s technicalrequirements (payload mass, payload power, delta V, pointingcontrol, and downlink rate). GPR is implemented in ABCDE asa Bayesian method which fits an implied multivariate regressionon the technical parameters and uses kriging to intentionally“overfit” the residuals. Overfitting the residuals allows costestimates to collapse in uncertainty closer to the data pointswhile maintaining larger uncertainty intervals in regions of parameterspace with fewer data records. The data used to fit thismodel is sensitive and represents cost estimates for off-the-shelfcommercial buses. GPR simultaneously protects the sensitivityof the database and uses the sparse nature of the database toaccount for uncertainty in cost in a useful way. For a givenset of customer technical requirements, the tool provides a costestimate distribution, the percentiles of which can be interpretedas a confidence level of finding a commercial bus under a specifiedcost cap. ABCDE dramatically pushes the boundaries ofspacecraft cost estimation models due to its Bayesian methodology(accounting for the maximum uncertainty in the underlyingregression), the mathematically advanced kriging methodology,and the novelty of its application in Team X architecture tradestudies.

Austin, Alex↗
NASA NTRS2013

Monte Carlo Bayesian Inference on a Statistical Model of Sub-gridcolumn Moisture Variability Using High-resolution Cloud Observations : Sensitivity Tests and Results - Part II

Part I presented a Monte Carlo Bayesian method for constraining a complex statistical model of GCM sub-gridcolumn moisture variability using high-resolution MODIS cloud data, thereby permitting large-scale model parameter estimation and cloud data assimilation. This part performs some basic testing of this new approach, verifying that it does indeed significantly reduce mean and standard deviation biases with respect to the assimilated MODIS cloud optical depth, brightness temperature and cloud top pressure, and that it also improves the simulated rotational-Ramman scattering cloud optical centroid pressure (OCP) against independent (non-assimilated) retrievals from the OMI instrument. Of particular interest, the Monte Carlo method does show skill in the especially difficult case where the background state is clear but cloudy observations exist. In traditional linearized data assimilation methods, a subsaturated background cannot produce clouds via any infinitesimal equilibrium perturbation, but the Monte Carlo approach allows finite jumps into regions of non-zero cloud probability. In the example provided, the method is able to restore marine stratocumulus near the Californian coast where the background state has a clear swath. This paper also examines a number of algorithmic and physical sensitivities of the new method and provides guidance for its cost-effective implementation. One obvious difficulty for the method, and other cloud data assimilation methods as well, is the lack of information content in the cloud observables on cloud vertical structure, beyond cloud top pressure and optical thickness, thus necessitating strong dependence on the background vertical moisture structure. It is found that a simple flow-dependent correlation modification due to Riishojgaard (1998) provides some help in this respect, by better honoring inversion structures in the background state.

Monte Carlo Bayesian inference↗
NASA NTRS2005

Gesture Based Control and EMG Decomposition

This paper presents two probabilistic developments for use with Electromyograms (EMG). First described is a new-electric interface for virtual device control based on gesture recognition. The second development is a Bayesian method for decomposing EMG into individual motor unit action potentials. This more complex technique will then allow for higher resolution in separating muscle groups for gesture recognition. All examples presented rely upon sampling EMG data from a subject's forearm. The gesture based recognition uses pattern recognition software that has been trained to identify gestures from among a given set of gestures. The pattern recognition software consists of hidden Markov models which are used to recognize the gestures as they are being performed in real-time from moving averages of EMG. Two experiments were conducted to examine the feasibility of this interface technology. The first replicated a virtual joystick interface, and the second replicated a keyboard. Moving averages of EMG do not provide easy distinction between fine muscle groups. To better distinguish between different fine motor skill muscle groups we present a Bayesian algorithm to separate surface EMG into representative motor unit action potentials. The algorithm is based upon differential Variable Component Analysis (dVCA) [l], [2] which was originally developed for Electroencephalograms. The algorithm uses a simple forward model representing a mixture of motor unit action potentials as seen across multiple channels. The parameters of this model are iteratively optimized for each component. Results are presented on both synthetic and experimental EMG data. The synthetic case has additive white noise and is compared with known components. The experimental EMG data was obtained using a custom linear electrode array designed for this study.

Wheeler, Kevin R.↗
NASA NTRS2019

Bayesian Estimation of Earth’s Undiscovered Mineralogical Diversity Using Noninformative Priors

Recently, statistical distributions have been explored to provide estimates of the mineralogical diversity of Earth, and Earth-like planets. In this paper, a Bayesian approach is introduced to estimate Earth’s undiscovered mineralogical diversity. Samples are generated from a posterior distribution of the model parameters using Markov chain Monte Carlo simulations such that estimates and inference are directly obtained. It was previously shown that the mineral species frequency distribution conforms to a generalized inverse Gauss–Poisson (GIGP) large number of rare events model. Even though the model fit was good, the population size estimate obtained by using this model was found to be unreasonably low by mineralogists. In this paper, several zero-truncated, mixed Poisson distributions are fitted and compared, where the Poisson-lognormal distribution is found to provide the best fit. Subsequently, the population size estimates obtained by Bayesian methods are compared to the empirical Bayes estimates. Species accumulation curves are constructed and employed to estimate the population size as a function of sampling size. Finally, the relative abundances, and hence the occurrence probabilities of species in a random sample, are calculated numerically for all mineral species in Earth’s crust using the Poisson-lognormal distribution. These calculations are connected and compared to the calculations obtained in a previous paper using the GIGP model for which mineralogical criteria of an Earth-like planet were given.

Bayesian statistics↗
NASA NTRS1984

An automated land-use mapping comparison of the Bayesian maximum likelihood and linear discriminant analysis algorithms

The Bayesian maximum likelihood parametric classifier has been tested against the data-based formulation designated 'linear discrimination analysis', using the 'GLIKE' decision and "CLASSIFY' classification algorithms in the Landsat Mapping System. Identical supervised training sets, USGS land use/land cover classes, and various combinations of Landsat image and ancilliary geodata variables, were used to compare the algorithms' thematic mapping accuracy on a single-date summer subscene, with a cellularized USGS land use map of the same time frame furnishing the ground truth reference. CLASSIFY, which accepts a priori class probabilities, is found to be more accurate than GLIKE, which assumes equal class occurrences, for all three mapping variable sets and both levels of detail. These results may be generalized to direct accuracy, time, cost, and flexibility advantages of linear discriminant analysis over Bayesian methods.

Tom, C. H.↗
NASA NTRS1991

Two papers on feed-forward networks

Connectionist feed-forward networks, trained with back-propagation, can be used both for nonlinear regression and for (discrete one-of-C) classification, depending on the form of training. This report contains two papers on feed-forward networks. The papers can be read independently. They are intended for the theoretically-aware practitioner or algorithm-designer; however, they also contain a review and comparison of several learning theories so they provide a perspective for the theoretician. The first paper works through Bayesian methods to complement back-propagation in the training of feed-forward networks. The second paper addresses a problem raised by the first: how to efficiently calculate second derivatives on feed-forward networks.

Buntine, Wray L.↗
NASA NTRS1991

Computational problems and signal processing in SETI

The Search for Extraterrestrial Intelligence (SETI), currently being planned at NASA, will require that an enormous amount of data (on the order of 10 exp 11 distinct signal paths for a typical observation) be analyzed in real time by special-purpose hardware. Even though the SETI system design is not based on maximum entropy and Bayesian methods (partly due to the real-time processing constraint), it is expected that enough data will be saved to be able to apply these and other methods off line where computational complexity is not an overriding issue. Interesting computational problems that relate directly to the system design for processing such an enormous amount of data have emerged. Some of these problems are discussed, along with the current status on their solution.

Deans, Stanley R.↗
NASA NTRS1996

Software For Multivariate Bayesian Classification

PHD general-purpose classifier computer program. Uses Bayesian methods to classify vectors of real numbers, based on combination of statistical techniques that include multivariate density estimation, Parzen density kernels, and EM (Expectation Maximization) algorithm. By means of simple graphical interface, user trains classifier to recognize two or more classes of data and then use it to identify new data. Written in ANSI C for Unix systems and optimized for online classification applications. Embedded in another program, or runs by itself using simple graphical-user-interface. Online help files makes program easy to use.

Saul, Ronald↗
NASA NTRS1998

A Conceptual Approach to Assimilating Remote Sensing Data to Improve Soil Moisture Profile Estimates in a Surface Flux/Hydrology Model: Disaggregation - 3

This is a followup on the preceding presentation by Crosson and Schamschula. The grid size for remote microwave measurements is much coarser than the hydrological model computational grids. To validate the hydrological models with measurements we propose mechanisms to disaggregate the microwave measurements to allow comparison with outputs from the hydrological models. Weighted interpolation and Bayesian methods are proposed to facilitate the comparison. While remote measurements occur at a large scale, they reflect underlying small-scale features. We can give continuing estimates of the small scale features by correcting the simple 0th-order, starting with each small-scale model with each large-scale measurement using a straightforward method based on Kalman filtering.

Caulfield, John↗
NASA NTRS1999

Direct Measurement of the Supernova Rate in Starburst Galaxies

Supernovae play a key role in the dynamics, structure, and chemical evolution of galaxies. The massive stars that end their lives as supernovae live for short times. Many are still associated with dusty star formation regions when they explode, making them difficult to observe at visible wavelengths. In active star forming regions (galactic nuclei and starburst regions), dust extintion is especially severe. Thus, determining the supernova rate in the active star forming regions of galaxies, where the supernova rate can be one or two orders of magnitude higher than the average, has proven to be difficult. From observations of SN1987A, we know that the [NiII] 6.63 micron emission line was the strongest line in the infrared spectrum for a period of a year and a half after the explosion. Since dust extintion is much less at 6.63 pm than at visible wavelengths (A(sub 6.63)/A(sub V) = 0.025), the NiII line can be used as a sensitive probe for the detection of recent supernovae. We have observed a sample of starburst galaxies at 6.63 micron using ISOCAM to search for the NiII emission line characteristic of recent supernovae. We did not detect any NiII line emission brighter than a 5sigma limit of 5 mJy. We can set upper limits to the supernova rate in our sample, scaled to the rate in M82, of less than 0.3 per year at the 90% confidence level using Bayesian methods. Assuming that a supernova would have a NiII with the same luminosity as observed in SN1987A, we find less than 0.09 and 0.15 per year at the 50% and 67% confidence levels. These rates are somewhat less if a more normal type II supernovae has a NiII line luminosity greater than the line in SN1987A.

Bregman, Jesse D.↗
NASA NTRS2000

Direct Measurement of the Supernova Rate in Starburst Galaxies

Supernovae play a key role in the dynamics, structure, and chemical evolution of galaxies. The massive stars that end their lives as supernovae live for short enough times that many are still associated with dusty star formation regions when they explode, making them difficult to observe at visible wavelengths. In active star forming regions (galactic nuclei and starburst regions), dust extinction is especially severe. Thus, determining the supernova rate in active star forming regions of galaxies, where the supernova rate can be one or two orders of magnitude higher than the average, has proven to be difficult. From observations of SN1987A, we know that the [NiII] 6.63 micrometer emission line was the strongest line in the infrared spectrum for a period of a year and half after th explosion. Since dust extinction is much less at 6.63 micrometers than at visible wavelengths (A(sub 6.63)/A(sub V) = 0.025), the [NiII] line can be used as a sensitive probe for the detection of recent supernovae. We have observed a sample of starburst galaxies at 6.63 micrometers using ISOCAM to search for the [NiII] emission line characteristic of recent supernovae. We did not detect any [NiII] line emission brighter than a 5-sigma limit of 5 mJy. We can set upper limits to the supernova rate in our sample, scaled ot the rate in M82, of less than 0.3 per year at the 90% confidence level using Bayesian methods. Assuming that a supernova would have a [NiII] line with the same luminosity as observed in SN1987A, we find less than 0.09 and 0.15 per year at the 50% and 67% confidence levels. These rates are somewhat less if a more normal type II supernovae has a [NiII] line luminosity greater than the line in SN1987A.

Bregman, J. D.↗
NASA NTRS2008

Bayesian Inference in the Modern Design of Experiments

This paper provides an elementary tutorial overview of Bayesian inference and its potential for application in aerospace experimentation in general and wind tunnel testing in particular. Bayes Theorem is reviewed and examples are provided to illustrate how it can be applied to objectively revise prior knowledge by incorporating insights subsequently obtained from additional observations, resulting in new (posterior) knowledge that combines information from both sources. A logical merger of Bayesian methods and certain aspects of Response Surface Modeling is explored. Specific applications to wind tunnel testing, computational code validation, and instrumentation calibration are discussed.

DeLoach, Richard↗
NASA NTRS2015

Detection and Modeling of High-Dimensional Thresholds for Fault Detection and Diagnosis

Many Fault Detection and Diagnosis (FDD) systems use discrete models for detection and reasoning. To obtain categorical values like oil pressure too high, analog sensor values need to be discretized using a suitablethreshold. Time series of analog and discrete sensor readings are processed and discretized as they come in. This task isusually performed by the wrapper code'' of the FDD system, together with signal preprocessing and filtering. In practice,selecting the right threshold is very difficult, because it heavily influences the quality of diagnosis. If a threshold causesthe alarm trigger even in nominal situations, false alarms will be the consequence. On the other hand, if threshold settingdoes not trigger in case of an off-nominal condition, important alarms might be missed, potentially causing hazardoussituations. In this paper, we will in detail describe the underlying statistical modeling techniques and algorithm as well as the Bayesian method for selecting the most likely shape and its parameters. Our approach will be illustrated by several examples from the Aerospace domain.

Computer Systems↗
NASA NTRS2018

3D Mapping of the Neutral X-Ray Absorption in the Local Interstellar Medium: The Gaia and XMM-Newton Synergy

We present a three-dimensional map of the hydrogen density distribution in the Galactic interstellar medium. The hydrogen-equivalent column densities were obtained from the Exploring the X-ray Transient and variable Sky project (EXTRAS) which provides equivalent NH values from X-ray spectral fits of observations within the XMM-Newton Data Release. EXTRAS include multiple fits for each source, allowing an accurate determination of the equivalent column densities, which depends on the continuum modelling of the spectra. A cross-correlation between the EXTRAS catalogue and the first Gaia Data Release was performed in order to obtain accurate parallax and distance measurements. We use a Bayesian method explained in Rezaei Kh. et al. (2017) in order to predict the most probable distribution of the density at any arbitrary point, even for lines of sight along which there are no initial observation. The resulting map shows small-scale density structures which could not have been modelled by using analytic density profiles. In this paper, we present a proof of concept of the kind of science possible with the synergy of these catalogues. However, given the systematic uncertainties connected to the source identification and to the dependence of NH on the spectral model, the present maps should be considered qualitatively at this point.

Gatuzz, Efrain↗
NASA NTRS2022

Trends in Europe Storm Surge Extremes Match the Rate of Sea-level Rise

Coastal communities across the world are already feeling the disastrous impacts of climate change through variations in extreme sea levels1. These variations reflect the combined effect of sea-level rise and changes in storm surge activity. Understanding the relative importance of these two factors in altering the likelihood of extreme events is crucial to the success of coastal adaptation measures. Existing analyses of tide gauge records agree that sea-level rise has been a considerable driver of trends in sea-level extremes since at least 1960. However, the contribution from changes in storminess remains unclear, owing to the difficulty of inferring this contribution from sparse data and the consequent inconclusive results that have accumulated in the literature. Here we analyse tide gauge observations using spatial Bayesian methods to show that, contrary to current thought, trends in surge extremes and sea-level rise both made comparable contributions to the overall change in extreme sea levels in Europe since 1960 . We determine that the trend pattern of surge extremes reflects the contributions from a dominant north–south dipole associated with internal climate variability and a single-sign positive pattern related to anthropogenic forcing. Our results demonstrate that both external and internal influences can considerably affect the likelihood of surge extremes over periods as long as 60 years, suggesting that the current coastal planning practice of assuming stationary surge extremes might be inadequate.

Francisco M Calafat↗
NASA NTRS1983

QUEST - A Bayesian adaptive psychometric method

An adaptive psychometric procedure that places each trial at the current most probable Bayesian estimate of threshold is described. The procedure takes advantage of the common finding that the human psychometric function is invariant in form when expressed as a function of log intensity. The procedure is simple, fast, and efficient, and may be easily implemented on any computer.

Watson, A. B.↗