Bayesian identification of system parameters
Bayesian identification of system parameters for observable and nonobservable input signals
Kerr, R. B.↗
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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.↗
A Bayesian model for visual space perception
A model for visual space perception is proposed that contains desirable features in the theories of Gibson and Brunswik. This model is a Bayesian processor of proximal stimuli which contains three important elements: an internal model of the Markov process describing the knowledge of the distal world, the a priori distribution of the state of the Markov process, and an internal model relating state to proximal stimuli. The universality of the model is discussed and it is compared with signal detection theory models. Experimental results of Kinchla are used as a special case.
Curry, R. E.↗
Application of Bayesian decision theory to airborne gamma snow measurement
Measured values of several variables are incorporated into the calculation of snow water equivalent as measured from an aircraft by snow attenuation of terrestrial gamma radiation. Bayesian decision theory provides a snow water equivalent measurement by taking into account the uncertainties in the individual measurement variables and filtering information about the measurement variables through prior notions of what the calculated variable (water equivalent) should be.
Bissell, V. C.↗
Bayesian classification in a time-varying environment
The problem of classifying a pattern based on multiple observation made in a time-varying environment is analyzed. The identity of the pattern may itself change. A Bayesian solution is derived, after which the conditions of the physical situation are invoked to produce a cascade classifier model. Experimental results based on remote sensing data demonstrate the effectiveness of the classifier.
Swain, P. H.↗
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.↗
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.↗
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.↗
Bayesian design of decision rules for failure detection
The formulation of the decision making process of a failure detection algorithm as a Bayes sequential decision problem provides a simple conceptualization of the decision rule design problem. As the optimal Bayes rule is not computable, a methodology that is based on the Bayesian approach and aimed at a reduced computational requirement is developed for designing suboptimal rules. A numerical algorithm is constructed to facilitate the design and performance evaluation of these suboptimal rules. The result of applying this design methodology to an example shows that this approach is potentially a useful one.
Chow, E. Y.↗
Bayesian inference in geomagnetism
The inverse problem in empirical geomagnetic modeling is investigated, with critical examination of recently published studies. Particular attention is given to the use of Bayesian inference (BI) to select the damping parameter lambda in the uniqueness portion of the inverse problem. The mathematical bases of BI and stochastic inversion are explored, with consideration of bound-softening problems and resolution in linear Gaussian BI. The problem of estimating the radial magnetic field B(r) at the earth core-mantle boundary from surface and satellite measurements is then analyzed in detail, with specific attention to the selection of lambda in the studies of Gubbins (1983) and Gubbins and Bloxham (1985). It is argued that the selection method is inappropriate and leads to lambda values much larger than those that would result if a reasonable bound on the heat flow at the CMB were assumed.
Backus, George E.↗
A Bayesian classification of the IRAS LRS Atlas
The availability of a reclassification of the IRAS LRS Atlas of spectra using a new Bayesian classification procedure (AutoClass) is announced. The classes of objects which result from the application of the AutoClass algorithm include many of the previously known LRS classes. New classes which have interesting astronomical and astrophysical interpretations were also found. Techniques, such as the AutoClass algorithm, have a bright future in the arena of astronomical classification problems.
Goebel, J.↗
Neural network classification - A Bayesian interpretation
The relationship between minimizing a mean squared error and finding the optimal Bayesian classifier is reviewed. This provides a theoretical interpretation for the process by which neural networks are used in classification. A number of confidence measures are proposed to evaluate the performance of the neural network classifier within a statistical framework.
Wan, Eric A.↗
Iterative Bayesian Classification In Polarimetric SAR
In improved scheme for Bayesian classification of picture elements in polarimetric synthetic-aperture radar image of terrain, priori probability that given picture element belongs to given class, adjusted according to spatial variation of statistical properties of image data. Accuracy increases dramatically in first few iterations. Scheme involves sequence of classifications. In first, a priori probability that element belongs to class taken to be constant over the whole image. In subsequent classifications, adaptive a priori probabilities calculated for each picture element.
Van Zyl, Jakob J.↗
Data analysis using scale-space filtering and Bayesian probabilistic reasoning
This paper describes a program for analysis of output curves from Differential Thermal Analyzer (DTA). The program first extracts probabilistic qualitative features from a DTA curve of a soil sample, and then uses Bayesian probabilistic reasoning to infer the mineral in the soil. The qualifier module employs a simple and efficient extension of scale-space filtering suitable for handling DTA data. We have observed that points can vanish from contours in the scale-space image when filtering operations are not highly accurate. To handle the problem of vanishing points, perceptual organizations heuristics are used to group the points into lines. Next, these lines are grouped into contours by using additional heuristics. Probabilities are associated with these contours using domain-specific correlations. A Bayes tree classifier processes probabilistic features to infer the presence of different minerals in the soil. Experiments show that the algorithm that uses domain-specific correlation to infer qualitative features outperforms a domain-independent algorithm that does not.
Kulkarni, Deepak↗
Bayesian classification theory
The task of inferring a set of classes and class descriptions most likely to explain a given data set can be placed on a firm theoretical foundation using Bayesian statistics. Within this framework and using various mathematical and algorithmic approximations, the AutoClass system searches for the most probable classifications, automatically choosing the number of classes and complexity of class descriptions. A simpler version of AutoClass has been applied to many large real data sets, has discovered new independently-verified phenomena, and has been released as a robust software package. Recent extensions allow attributes to be selectively correlated within particular classes, and allow classes to inherit or share model parameters though a class hierarchy. We summarize the mathematical foundations of AutoClass.
Hanson, Robin↗
Development of a Weibull posterior distribution by combining a Weibull prior with an actual failure distribution using Bayesian inference
A Bayesian inference process for system logistical planning is presented which provides a method for incorporating actual failures with prediction data for an ongoing and improving reliability estimates. The process uses the Weibull distribution, and provides a means for examining and updating logistical and maintenance support needs.
Giuntini, Michael E.↗
Bayesian classification of polarimetric SAR images using adaptive a priori probabilities
The problem of classifying earth terrain by observed polarimetric scattering properties is tackled with an iterative Bayesian scheme using a priori probabilities adaptively. The first classification is based on the use of fixed and not necessarily equal a priori probabilities, and successive iterations change the a priori probabilities adaptively. The approach is applied to an SAR image in which a single water body covers 10 percent of the image area. The classification accuracy for ocean, urban, vegetated, and total area increase, and the percentage of reclassified pixels decreases greatly as the iteration number increases. The iterative scheme is found to improve the a posteriori classification accuracy of maximum likelihood classifiers by iteratively using the local homogeneity in polarimetric SAR images. A few iterations can improve the classification accuracy significantly without sacrificing key high-frequency detail or edges in the image.
Van Zyl, J. J.↗
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.↗