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Results for “Bayesian error estimator”

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.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS2004

Precipitation and Latent Heating Distributions from Satellite Passive Microwave Radiometry: Method and Uncertainties - Part 1

A revised Bayesian algorithm for estimating surface rain rate, convective rain proportion, and latent heating/drying profiles from satellite-borne passive microwave radiometer observations over ocean backgrounds is described. The algorithm searches a large database of cloud-radiative model simulations to find cloud profiles that are radiatively consistent with a given set of microwave radiance measurements. The properties of these radiatively consistent profiles are then composited to obtain best estimates of the observed properties. The revised algorithm is supported by an expanded and more physically consistent database of cloud-radiative model simulations. The algorithm also features a better quantification of the convective and non-convective contributions to total rainfall, a new geographic database, and an improved representation of background radiances in rain-free regions. Bias and random error estimates are derived from applications of the algorithm to synthetic radiance data, based upon a subset of cloud resolving model simulations, and from the Bayesian formulation itself. Synthetic rain rate and latent heating estimates exhibit a trend of high (low) bias for low (high) retrieved values. The Bayesian estimates of random error are propagated to represent errors at coarser time and space resolutions, based upon applications of the algorithm to TRMM Microwave Imager (TMI) data. Errors in instantaneous rain rate estimates at 0.5 deg resolution range from approximately 50% at 1 mm/h to 20% at 14 mm/h. These errors represent about 70-90% of the mean random deviation between collocated passive microwave and spaceborne radar rain rate estimates. The cumulative algorithm error in TMI estimates at monthly, 2.5 deg resolution is relatively small (less than 6% at 5 mm/day) compared to the random error due to infrequent satellite temporal sampling (8-35% at the same rain rate).

Olson, William S.↗
NASA NTRS2006

Precipitation and Latent Heating Distributions from Satellite Passive Microwave Radiometry: Improved Method and Uncertainties - Part 1

A revised Bayesian algorithm for estimating surface rain rate, convective rain proportion, and latent heating profiles from satellite-borne passive microwave radiometer observations over ocean backgrounds is described. The algorithm searches a large database of cloud-radiative model simulations to find cloud profiles that are radiatively consistent with a given set of microwave radiance measurements. The properties of these radiatively consistent profiles are then composited to obtain best estimates of the observed properties. The revised algorithm is supported by an expanded and more physically consistent database of cloud-radiative model simulations. The algorithm also features a better quantification of the convective and nonconvective contributions to total rainfall, a new geographic database, and an improved representation of background radiances in rain-free regions. Bias and random error estimates are derived from applications of the algorithm to synthetic radiance data, based upon a subset of cloud-resolving model simulations, and from the Bayesian formulation itself. Synthetic rain-rate and latent heating estimates exhibit a trend of high (low) bias for low (high) retrieved values. The Bayesian estimates of random error are propagated to represent errors at coarser time and space resolutions, based upon applications of the algorithm to TRMM Microwave Imager (TMI) data. Errors in TMI instantaneous rain-rate estimates at 0.5 -resolution range from approximately 50% at 1 mm/h to 20% at 14 mm/h. Errors in collocated spaceborne radar rain-rate estimates are roughly 50%-80% of the TMI errors at this resolution. The estimated algorithm random error in TMI rain rates at monthly, 2.5deg resolution is relatively small (less than 6% at 5 mm day.1) in comparison with the random error resulting from infrequent satellite temporal sampling (8%-35% at the same rain rate). Percentage errors resulting from sampling decrease with increasing rain rate, and sampling errors in latent heating rates follow the same trend. Averaging over 3 months reduces sampling errors in rain rates to 6%-15% at 5 mm day.1, with proportionate reductions in latent heating sampling errors.

Olson, William S.↗
NASA NTRS1975

Methods Studies on System Identification from Transient Rotor Tests

Some of the more important methods are discussed that have been used or proposed for aircraft parameter identification. The methods are classified into two groups: Equation error or regression estimates and Bayesian estimates and their derivatives that are based on probabilistic concepts. In both of these two groups the cost function can be optimized either globally over the entire time span of the transient, or sequentially, leading to the formulation of optimum filters. Identifiability problems and the validation of the estimates are briefly outlined, and applications to lifting rotors are discussed.

Hohenemser, K. H.↗
NASA NTRS1992

Asteroid orbital error analysis: Theory and application

We present a rigorous Bayesian theory for asteroid orbital error estimation in which the probability density of the orbital elements is derived from the noise statistics of the observations. For Gaussian noise in a linearized approximation the probability density is also Gaussian, and the errors of the orbital elements at a given epoch are fully described by the covariance matrix. The law of error propagation can then be applied to calculate past and future positional uncertainty ellipsoids (Cappellari et al. 1976, Yeomans et al. 1987, Whipple et al. 1991). To our knowledge, this is the first time a Bayesian approach has been formulated for orbital element estimation. In contrast to the classical Fisherian school of statistics, the Bayesian school allows a priori information to be formally present in the final estimation. However, Bayesian estimation does give the same results as Fisherian estimation when no priori information is assumed (Lehtinen 1988, and reference therein).

Muinonen, K.↗
NASA NTRS1983

Trajectory-Estimation Error Analysis

Orbital and Geodetic Parameter Estimation Error Analysis Program (ORAN) is Bayesian least-squares simulation program for orbital trajectories. ORAN does not process data; rather, computes accuracy of results of data reduction if measurements are processed by minimum-variance data-reduction program. Actual data used to provide time when given measurement was available and estimated noise on that measurement.

Putney, B.↗
NASA NTRS2016

Probabilistic Damage Characterization Using the Computationally-Efficient Bayesian Approach

This work presents a computationally-ecient approach for damage determination that quanti es uncertainty in the provided diagnosis. Given strain sensor data that are polluted with measurement errors, Bayesian inference is used to estimate the location, size, and orientation of damage. This approach uses Bayes' Theorem to combine any prior knowledge an analyst may have about the nature of the damage with information provided implicitly by the strain sensor data to form a posterior probability distribution over possible damage states. The unknown damage parameters are then estimated based on samples drawn numerically from this distribution using a Markov Chain Monte Carlo (MCMC) sampling algorithm. Several modi cations are made to the traditional Bayesian inference approach to provide signi cant computational speedup. First, an ecient surrogate model is constructed using sparse grid interpolation to replace a costly nite element model that must otherwise be evaluated for each sample drawn with MCMC. Next, the standard Bayesian posterior distribution is modi ed using a weighted likelihood formulation, which is shown to improve the convergence of the sampling process. Finally, a robust MCMC algorithm, Delayed Rejection Adaptive Metropolis (DRAM), is adopted to sample the probability distribution more eciently. Numerical examples demonstrate that the proposed framework e ectively provides damage estimates with uncertainty quanti cation and can yield orders of magnitude speedup over standard Bayesian approaches.

Warner, James E.↗
NASA NTRS1972

Evaluation of errors in prior mean and variance in the estimation of integrated circuit failure rates using Bayesian methods

The critical point of any Bayesian analysis concerns the choice and quantification of the prior information. The effects of prior data on a Bayesian analysis are studied. Comparisons of the maximum likelihood estimator, the Bayesian estimator, and the known failure rate are presented. The results of the many simulated trails are then analyzed to show the region of criticality for prior information being supplied to the Bayesian estimator. In particular, effects of prior mean and variance are determined as a function of the amount of test data available.

Fletcher, B. C.↗
NASA NTRS1980

As-built design specification for proportion estimate software subsystem

The Proportion Estimate Processor evaluates four estimation techniques in order to get an improved estimate of the proportion of a scene that is planted in a selected crop. The four techniques to be evaluated were provided by the techniques development section and are: (1) random sampling; (2) proportional allocation, relative count estimate; (3) proportional allocation, Bayesian estimate; and (4) sequential Bayesian allocation. The user is given two options for computation of the estimated mean square error. These are referred to as the cluster calculation option and the segment calculation option. The software for the Proportion Estimate Processor is operational on the IBM 3031 computer.

Obrien, S.↗
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.↗
NASA NTRS1988

Effects of model deficiencies on parameter estimation

Reliable structural dynamic models will be required as a basis for deriving the reduced-order plant models used in control systems for large space structures. Ground vibration testing and model verification will play an important role in the development of these models; however, fundamental differences between the space environment and earth environment, as well as variations in structural properties due to as-built conditions, will make on-orbit identification essential. The efficiency, and perhaps even the success, of on-orbit identification will depend on having a valid model of the structure. It is envisioned that the identification process will primarily involve parametric methods. Given a correct model, a variety of estimation algorithms may be used to estimate parameter values. This paper explores the effects of modeling errors and model deficiencies on parameter estimation by reviewing previous case histories. The effects depend at least to some extent on the estimation algorithm being used. Bayesian estimation was used in the case histories presented here. It is therefore conceivable that the behavior of an estimation algorithm might be useful in detecting and possibly even diagnosing deficiencies. In practice, the task is complicated by the presence of systematic errors in experimental procedures and data processing and in the use of the estimation procedures themselves.

Hasselman, T. K.↗
NASA NTRS1976

Data acquisition and path selection decision making for an autonomous roving vehicle

Problems related to the guidance of an autonomous rover for unmanned planetary exploration were investigated. Topics included in these studies were: simulation on an interactive graphics computer system of the Rapid Estimation Technique for detection of discrete obstacles; incorporation of a simultaneous Bayesian estimate of states and inputs in the Rapid Estimation Scheme; development of methods for estimating actual laser rangefinder errors and their application to date provided by Jet Propulsion Laboratory; and modification of a path selection system simulation computer code for evaluation of a hazard detection system based on laser rangefinder data.

Frederick, D. K.↗
NASA NTRS1992

Quantifying parameters for Bayesian prior assumptions when estimating the probability of failure of software

Software reliability has become increasingly important, especially in life-critical situations. The ability to measure the results of testing and to quantify software reliability is needed. If this is accomplished, a certain minimum amount of reliability for a piece of software can be specified, and testing and/or other analysis may be done until that minimum number has been attained. There are many models for estimating software reliability. The accuracy of these models has been challenged and many revisions for the models and recalibration techniques have been devised. Of particular interest is the method of estimating the probability of failure of software when no failures have yet occurred in its current version as described by Miller. This model uses black box testing with formulae based on Bayesian estimation. The focus is on three interrelated issues: estimating the probability of failure when testing has revealed no errors; modifying this estimation when the input use distribution does not match the test distribution; and combining the results from random testing with other relevant information to obtain a possibly more accurate estimate of the probability of failure. Obtaining relevant information about the software and combining the results for a better estimate for the Miller model are discussed.

Long, Jacquelyn E.↗
NASA NTRS1997

A mathematical model of diurnal variations in human plasma melatonin levels

Studies in animals and humans suggest that the diurnal pattern in plasma melatonin levels is due to the hormone's rates of synthesis, circulatory infusion and clearance, circadian control of synthesis onset and offset, environmental lighting conditions, and error in the melatonin immunoassay. A two-dimensional linear differential equation model of the hormone is formulated and is used to analyze plasma melatonin levels in 18 normal healthy male subjects during a constant routine. Recently developed Bayesian statistical procedures are used to incorporate correctly the magnitude of the immunoassay error into the analysis. The estimated parameters [median (range)] were clearance half-life of 23.67 (14.79-59.93) min, synthesis onset time of 2206 (1940-0029), synthesis offset time of 0621 (0246-0817), and maximum N-acetyltransferase activity of 7.17(2.34-17.93) pmol x l(-1) x min(-1). All were in good agreement with values from previous reports. The difference between synthesis offset time and the phase of the core temperature minimum was 1 h 15 min (-4 h 38 min-2 h 43 min). The correlation between synthesis onset and the dim light melatonin onset was 0.93. Our model provides a more physiologically plausible estimate of the melatonin synthesis onset time than that given by the dim light melatonin onset and the first reliable means of estimating the phase of synthesis offset. Our analysis shows that the circadian and pharmacokinetics parameters of melatonin can be reliably estimated from a single model.

NASA Discipline Number 70-10↗
NASA NTRS1972

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.↗
NASA NTRS1986

Application of physical parameter identification to finite element models

A time domain technique for matching response predictions of a structural dynamic model to test measurements is developed. Significance is attached to prior estimates of physical model parameters and to experimental data. The Bayesian estimation procedure allows confidence levels in predicted physical and modal parameters to be obtained. Structural optimization procedures are employed to minimize an error functional with physical model parameters describing the finite element model as design variables. The number of complete FEM analyses are reduced using approximation concepts, including the recently developed convoluted Taylor series approach. The error function is represented in closed form by converting free decay test data to a time series model using Prony' method. The technique is demonstrated on simulated response of a simple truss structure.

Bronowicki, Allen J.↗