Monte Carlo Bayesian inference on a statistical model of sub‐gridcolumn moisture variability using high‐resolution cloud observations. Part 1: Method
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Peter M. Norris↗
SEARCH · Engineering Papers
Results for “Bayesian method”
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On Bayesian Inductive Inference & Predictive Estimation
We investigate Bayesian inference and the Principle of Maximum Entropy (PME) as methods for doing inference under uncertainty. This investigation is primarily through concrete examples that have been previously investigated in the literature. We find that it is possible to do Bayesian inference and PME inference using the same information, despite claims to the contrary, but that the results are not directly comparable. This is because Bayesian inference yields a probability density function (pdf) over the unknown model parameters, whereas PME yields point estimates. If mean estimates are extracted from the Bayesian pdfs, the resulting parameter estimates can differ radically from the PME values and also from the Maximum Likelihood values. We conclude that these differences are due to the Bayesian inference not assuming anything beyond the given prior probabilities and the data, whereas PME implicitly assumes that the given constraints are the only constraints that are operating. Since this assumption can be wrong, PME values may have to be revised when subsequent data shows evidence for more constraints. The entropy concentration previously "proved" by E. T. Jaynes is shown to be in error. Further, we show that PME is a generalized form of independence assumption, and so can be a very powerful method of inference when the variables being investigated are largely independent of each other.
Cheeseman, Peter↗
Statistical methods and subjective probability Status report
Bibliography of subjective probability and Bayesian procedures - regression analyses
BIBLIOGRAPHY↗
Evaluation of the procedure 1A component of the 1980 US/Canada wheat and barley exploratory experiment
Several techniques which use clusters generated by a new clustering algorithm, CLASSY, are proposed as alternatives to random sampling to obtain greater precision in crop proportion estimation: (1) Proportional Allocation/relative count estimator (PA/RCE) uses proportional allocation of dots to clusters on the basis of cluster size and a relative count cluster level estimate; (2) Proportional Allocation/Bayes Estimator (PA/BE) uses proportional allocation of dots to clusters and a Bayesian cluster-level estimate; and (3) Bayes Sequential Allocation/Bayesian Estimator (BSA/BE) uses sequential allocation of dots to clusters and a Bayesian cluster level estimate. Clustering in an effective method in making proportion estimates. It is estimated that, to obtain the same precision with random sampling as obtained by the proportional sampling of 50 dots with an unbiased estimator, samples of 85 or 166 would need to be taken if dot sets with AI labels (integrated procedure) or ground truth labels, respectively were input. Dot reallocation provides dot sets that are unbiased. It is recommended that these proportion estimation techniques are maintained, particularly the PA/BE because it provides the greatest precision.
Chapman, G. M.↗
An overview of the essential differences and similarities of system identification techniques
Information is given in the form of outlines, graphs, tables and charts. Topics include system identification, Bayesian statistical decision theory, Maximum Likelihood Estimation, identification methods, structural mode identification using a stochastic realization algorithm, and identification results regarding membrane simulations and X-29 flutter flight test data.
Mehra, Raman K.↗
Studies of asteroids, comets, and Jupiter's outer satellites
Observational, theoretical, and computational research was performed, mainly on asteroids. Two principal areas of research, centering on astrometry and photometry, are interrelated in their aim to study the overall structure of the asteroid belt and the physical and orbital properties of individual asteroids. Two highlights are: detection of CN emission from Chiron; and realization that 1990 MB is the first known Trojan type asteroid of a planet other than Jupiter. A new method of asteroid orbital error analysis, based on Bayesian theory, was developed.
Bowell, Edward↗
Chemical Compositions and Abundance Anomalies in Stellar Coronae ADP99
We have been investigating different statistical methods for analysing the metal abundances of sources with low S/N. A Bayesian technique has been developed that determines the most probable line-to-continuum ratio in the source, thereby leading to the metallicity. This method is a promising approach with which to mine the ASCA archive. Some of this work has now been published in conference proceedings. The flavour of the project has changed very slightly in the last year owing to the increasing availability of several good quality Chandra HETG and LETG spectra for stars for which we had reduced and analysed ASCA data. The Chandra grating spectra in principle provide a means of calibrating the results from the low resolution ASCA spectra and we have started some work toward that goal. One paper concerning abundance ratios in active stars is appearing shortly in conference proceedings and is being readied for publication in a main-stream astrophysical journal. This paper demonstrates for the first time that abundance anomalies cannot be categorized simply in terms of First Ionization Potential (FIP) or inverse-FIP based effects. Different Ne enhancements are found in different star types but a link between enhancement factors and stellar properties is not obvious. The publication noted as in preparation in an earlier report, finding strong Ne enhancements in active stars, is now published. These results will again be used to "calibrate" low resolution results for which line ratio techniques cannot be employed.
Drake, Jeremy↗
Astrophysical Model Selection in Gravitational Wave Astronomy
Theoretical studies in gravitational wave astronomy have mostly focused on the information that can be extracted from individual detections, such as the mass of a binary system and its location in space. Here we consider how the information from multiple detections can be used to constrain astrophysical population models. This seemingly simple problem is made challenging by the high dimensionality and high degree of correlation in the parameter spaces that describe the signals, and by the complexity of the astrophysical models, which can also depend on a large number of parameters, some of which might not be directly constrained by the observations. We present a method for constraining population models using a hierarchical Bayesian modeling approach which simultaneously infers the source parameters and population model and provides the joint probability distributions for both. We illustrate this approach by considering the constraints that can be placed on population models for galactic white dwarf binaries using a future space-based gravitational wave detector. We find that a mission that is able to resolve approximately 5000 of the shortest period binaries will be able to constrain the population model parameters, including the chirp mass distribution and a characteristic galaxy disk radius to within a few percent. This compares favorably to existing bounds, where electromagnetic observations of stars in the galaxy constrain disk radii to within 20%.
hierarchical↗
A Framework for Assessment of Aviation Safety Technology Portfolios
The programs within NASA's Aeronautics Research Mission Directorate (ARMD) conduct research and development to improve the national air transportation system so that Americans can travel as safely as possible. NASA aviation safety systems analysis personnel support various levels of ARMD management in their fulfillment of system analysis and technology prioritization as defined in the agency's program and project requirements. This paper provides a framework for the assessment of aviation safety research and technology portfolios that includes metrics such as projected impact on current and future safety, technical development risk and implementation risk. The paper also contains methods for presenting portfolio analysis and aviation safety Bayesian Belief Network (BBN) output results to management using bubble charts and quantitative decision analysis techniques.
Jones, Sharon M.↗
Fermi-GBM GRBs with Characteristics Similar to GRB 170817A
We present a search for gamma-ray bursts in the Fermi-GBM (Gamma Burst Monitor) 10-year catalog that show similar characteristics to GRB170817A, the first electromagnetic counterpart to a GRB (Gamma-Ray Burst) identified as a binary neutron star (BNS) merger via gravitational wave observations. Our search is focused on a nonthermal pulse, followed by a thermal component,as observed for GRB 170817A. We employ search methods based on the measured catalog parameters and Bayesian Block analysis. Our multipronged approach, which includes examination of the localization and spectral properties of the thermal component, yields a total of 13 candidates, including GRB170817A and the previously reported similar burst, GRB 150101B. The similarity of the candidates is likely caused by the same processes that shaped the gamma-ray signal of GRB170817A, thus providing evidence of a nearby sample of short GRBs resulting from BNS merger events. Some of the newly identified counterparts were observed by other space telescopes and ground observatories, but none of them have a measured redshift. We present an analysis of this subsample, and we discuss two models. From uncovering 13 candidates during a time period of 10 years we predict that Fermi-GBM will trigger on-board on about one burst similar to GRB170817A per year.
von Kienlin, A.↗
The effect of modeling dose uncertainty on low-boom community noise dose-response curves
In logistic dose-response modeling, failing to account for uncertainty in estimated doses can cause an artificial flattening or attenuation of the slope of the summary curve. In Lee et al. [J. Acoust. Soc. Am. 147(4), pp. 2222-2234 (2020)], data from two NASA low-amplitude sonic boom community noise survey tests were modeled using a Bayesian multilevel logistic regression (MLR) statistical model that assumed there was no uncertainty in the noise dose estimates. However, in these community tests, the noise dose uncertainty was estimated by Page et al. [NASA/CR-2014-218180 and NASA/CR-2020-220589/Volume I] using a leave-one-out method. In the current work, a term was added to extend the Bayesian MLR model to account for the estimated noise dose uncertainty quantified in the Page et al. analyses. This uncertainty term was included in two ways, either as classical or as Berkson uncertainty, and yield similar results. When the uncertainty is accounted for in the Bayesian MLR model, the dose-response curves become 5-10% steeper, but the difference in the noise dose that elicits a 5% highly annoyed response is small (less than 1 dB). This result is encouraging for future X-59 community tests whose survey area will be sparsely populated with noise monitors.
X-59↗
3D Surface Reconstruction and Automatic Camera Calibration
Illustrations in this view-graph presentation are presented on a Bayesian approach to 3D surface reconstruction and camera calibration.Existing methods, surface analysis and modeling,preliminary surface reconstruction results, and potential applications are addressed.
Jalobeanu, Andre↗
System identification computational considerations.
System identification methods may be accurately characterized as inverse computational problems. Three approaches to the computational problem are considered. Equation error methods are based on regression analysis techniques. Attention is given to the maximum conditional likelihood estimate and the maximum unconditional likelihood (Bayesian) estimate. Gradient dependent algorithms for solving the minimization problems are discussed, taking into account Gaussian methods, quadratic model methods, and the homogeneous function model method of Jacobson and Oksman. Some advanced methods are also examined.
Bowles, R. L.↗
Application of a Bayesian Framework for Plasticity Model Selection
Interpretable Machine Learning (IML) has performed well when tasked with deriving constitutive material models. However, IML has been shown to prefer models that overfit noise in data, which tends to lead to bloat and a decrease in interpretability. Due to these issues, the ability of IML to reliably derive models that fit the data and are both interpretable and generalizable is limited. A method developed recently has shown promise to improve upon traditional IML by using a Bayesian fitness definition for the evolution of free-form models with non-deterministic parameters. This framework was developed for genetic-programming-based symbolic regression(GPSR) and involves model parameter estimation using Sequential Monte Carlo sampling (SMC).The method has demonstrated a reduction in bloat when dealing with noisy data in comparison to conventional GPSR. The results of this framework applied to stress-strain data for copper show models that more effectively predict the experimental data better than was previously shown with GPSR.
plasticity↗
Results of GEOS 3/ATS 6 satellite-to-satellite tracking orbit determination experiment
The purpose of the Geos 3/ATS 6 satellite-to-satellite tracking experiment was to develop, test, and evaluate methods of deriving orbit estimates from satellite-to-satellite tracking data. The results of the form of conventional orbit overlap tests, and a comparison of a Geos 3 orbit estimate obtained from satellite-to-satellite (SST) tracking data with an orbit estimate derived form C-band data. The method recommeded for estimating orbits from SST data is a Bayesian least squares procedure utilizing independent ranging to the relay satellite.
Argentiero, P.↗
Software models: A Bayesian approach to parameter estimation in the Jelenski-Moranda software reliability model
Maximum likelihood estimation procedures for the Jelinski-Moranda software reliability model often give misleading answers. A reparameterization and a Bayesian analysis eliminate some of the problems incurred by MLE methods and often give better predictions on sets of real and simulated data. Practical difficulties in estimating the initial number of errors N and the failure rate of each error phi by the method of maximum likelihood are: N, the MLE of N, is occasionally infinite (i.e., the routines for calculating N and phi do not converge). It is shown that N is finite sub i only if the regression line of the interevent times t sub i vs. i has positive slope. A serious problem is that often N approximates n, the sample size, and sometimes N = n. Thus the MLE predicts that the program is perfect even when it is far from being so. Only when almost all failures have been removed can N and phi be trusted near the end of debugging.
Littlewood, B.↗
Monte Carlo Algorithms for a Bayesian Analysis of the Cosmic Microwave Background
A viewgraph presentation on the review of Bayesian approach to Cosmic Microwave Background (CMB) analysis, numerical implementation with Gibbs sampling, a summary of application to WMAP I and work in progress with generalizations to polarization, foregrounds, asymmetric beams, and 1/f noise is given.
Bayesian inference↗
Bayesian Analysis of the Power Spectrum of the Cosmic Microwave Background
There is a wealth of cosmological information encoded in the spatial power spectrum of temperature anisotropies of the cosmic microwave background. The sky, when viewed in the microwave, is very uniform, with a nearly perfect blackbody spectrum at 2.7 degrees. Very small amplitude brightness fluctuations (to one part in a million!!) trace small density perturbations in the early universe (roughly 300,000 years after the Big Bang), which later grow through gravitational instability to the large-scale structure seen in redshift surveys... In this talk, I will discuss a Bayesian formulation of this problem; discuss a Gibbs sampling approach to numerically sampling from the Bayesian posterior, and the application of this approach to the first-year data from the Wilkinson Microwave Anisotropy Probe. I will also comment on recent algorithmic developments for this approach to be tractable for the even more massive data set to be returned from the Planck satellite.
Bayesian inference↗