scholarly journals A Bayesian Approach for Maintenance Action Recommendation

2020 ◽  
Vol 4 (2) ◽  
Author(s):  
Vassilis Katsouros ◽  
Vassilis Papavassiliou ◽  
Christos Emmanouilidis
Keyword(s):  
Bayesian Inference ◽  
Bayesian Approach ◽  
A Priori ◽  
Training Data ◽  
Maximum A Posteriori ◽  
Problem Type ◽  
A Posteriori ◽  
Problem Types

This paper presents a Bayesian approach for maintenance action recommendation tested on the PHM 2013 Data Challenge dataset. The Challenge focused on maintenance action recommendation based on historical cases and the algorithms were evaluated on their ability to recommend confirmed problem types. The proposed approach is based on a Bayesian inference methodology and deals with recommending an already known problem type for each case. The recommender can be viewed as a classifier among the confirmed problem types. For each such problem type class the a priori probabilities for the events which characterize the problem type from the training data are estimated. When testing cases are presented, the recommender calculates the a posteriori probabilities for each of the confirmed problem types and suggests the type of problem that corresponds to the maximum a posteriori (MAP) probability.

scholarly journals Ozone profile smoothness as a priori information in the inversion of limb measurements

2004 ◽  
Vol 22 (10) ◽  
pp. 3411-3420 ◽  
Author(s):  
V. F. Sofieva ◽  
J. Tamminen ◽  
H. Haario ◽  
E. Kyrölä ◽  
M. Lehtinen
Keyword(s):  
A Priori ◽  
Optimal Estimation ◽  
Maximum A Posteriori ◽  
A Posteriori ◽  
A Priori Information ◽  
Ozone Profile ◽  
Stellar Occultation ◽  
Atmospheric Profiles ◽  
Priori Information ◽  
Typical Measurement

Abstract. In this work we discuss inclusion of a priori information about the smoothness of atmospheric profiles in inversion algorithms. The smoothness requirement can be formulated in the form of Tikhonov-type regularization, where the smoothness of atmospheric profiles is considered as a constraint or in the form of Bayesian optimal estimation (maximum a posteriori method, MAP), where the smoothness of profiles can be included as a priori information. We develop further two recently proposed retrieval methods. One of them - Tikhonov-type regularization according to the target resolution - develops the classical Tikhonov regularization. The second method - maximum a posteriori method with smoothness a priori - effectively combines the ideas of the classical MAP method and Tikhonov-type regularization. We discuss a grid-independent formulation for the proposed inversion methods, thus isolating the choice of calculation grid from the question of how strong the smoothing should be. The discussed approaches are applied to the problem of ozone profile retrieval from stellar occultation measurements by the GOMOS instrument on board the Envisat satellite. Realistic simulations for the typical measurement conditions with smoothness a priori information created from 10-years analysis of ozone sounding at Sodankylä and analysis of the total retrieval error illustrate the advantages of the proposed methods. The proposed methods are equally applicable to other profile retrieval problems from remote sensing measurements.

METHOD OF COMPENSATION OF IONOSPHERE ERRORS OF SPACE OBJECTS COORDINATES DEFINITION BY MEANS OF TWO POSITION RADAR OBSERVATION

2018 ◽  
pp. 45-49
Author(s):  
P. S. Galkin ◽  
V. N. Lagutkin
Keyword(s):  
Probability Density ◽  
A Priori ◽  
Position Estimation ◽  
Estimation Accuracy ◽  
Posteriori Probability ◽  
Maximum A Posteriori ◽  
A Posteriori ◽  
Space Object ◽  
A Posteriori Probability ◽  
Space Objects

The algorithm of estimation and compensation of ionosphere influence on the measurement of parameters of the motion of space objects in two-position radar system with account of radio physical effects depending on elevation angles and the operating frequency is developed. It is assumed that the observed space object is traсked object, the orbital parameters which are well known, including the dependence of the velocity of the point on the orbit, and the uncertainty of the current coordinates of the object is caused mainly by forecast error of its position of in orbit (longitudinal error). To estimate the true position of space object in the orbit and the parameter, determining the influence of the ionosphere, a joint optimal processing of measurement of ranges to the object, obtained by two separated radars, taking into account the relevant ionospheric propagation delays and available a priori data on observable object trajectory. Estimation of unknown parameters are obtained on the basis of the criterion of maximum a posteriori probability density for these parameters, taking into account the measured and a priori data. The task of searching for maximum a posteriori probability density is reduced to task of searching of minimum weighted sum of squares, for the solution of which the cascade algorithm of iteration through is implemented in the work. Estimation accuracy of the position of space objects in orbit after compensation of ionosphere influence have been studied by Monte-Carlo method. Dependencies of mean square error of the position estimation of space objects upon elevation angles, operation frequency and solar activity have been obtained. It is shown that the effectiveness of the algorithm increases with the spatial base of measurements (for a fixed orbit of the object).

scholarly journals Bayesian Analysis of Mixtures of Factor Analyzers

2001 ◽  
Vol 13 (5) ◽  
pp. 993-1002 ◽  
Author(s):  
Akio Utsugi ◽  
Toru Kumagai
Keyword(s):  
Bayesian Inference ◽  
Bayesian Analysis ◽  
Gibbs Sampler ◽  
Simulation Experiment ◽  
Estimation Algorithm ◽  
Deterministic Algorithm ◽  
Maximum A Posteriori ◽  
A Posteriori ◽  
Conjugate Priors ◽  
Posteriori Estimation

For Bayesian inference on the mixture of factor analyzers, natural conjugate priors on the parameters are introduced, and then a Gibbs sampler that generates parameter samples following the posterior is constructed. In addition, a deterministic estimation algorithm is derived by taking modes instead of samples from the conditional posteriors used in the Gibbs sampler. This is regarded as a maximum a posteriori estimation algorithm with hyperparameter search. The behaviors of the Gibbs sampler and the deterministic algorithm are compared on a simulation experiment.

Bayesian Inference Explains Perception of Unity and Ventriloquism Aftereffect: Identification of Common Sources of Audiovisual Stimuli

2007 ◽  
Vol 19 (12) ◽  
pp. 3335-3355 ◽  
Author(s):  
Yoshiyuki Sato ◽  
Taro Toyoizumi ◽  
Kazuyuki Aihara
Keyword(s):  
Bayesian Inference ◽  
Computational Model ◽  
Audiovisual Integration ◽  
Experimental Results ◽  
Auditory Stimuli ◽  
Maximum A Posteriori ◽  
A Posteriori ◽  
Spatial Frame ◽  
Ventriloquism Aftereffect ◽  
Audiovisual Stimuli

We study a computational model of audiovisual integration by setting a Bayesian observer that localizes visual and auditory stimuli without presuming the binding of audiovisual information. The observer adopts the maximum a posteriori approach to estimate the physically delivered position or timing of presented stimuli, simultaneously judging whether they are from the same source or not. Several experimental results on the perception of spatial unity and the ventriloquism effect can be explained comprehensively if the subjects in the experiments are regarded as Bayesian observers who try to accurately locate the stimulus. Moreover, by adaptively changing the inner representation of the Bayesian observer in terms of experience, we show that our model reproduces perceived spatial frame shifts due to the audiovisual adaptation known as the ventriloquism aftereffect.

scholarly journals Information Collecting and Dissemination in the Network of Taxpayers: Bayesian Approach

2021 ◽  
Vol 14 ◽  
pp. 236-256
Author(s):  
Suriya Sh. Kumacheva ◽  
◽  
Galina A. Tomilina ◽  
Keyword(s):  
Bayesian Approach ◽  
A Priori ◽  
Repeated Game ◽  
Social Connections ◽  
Tax Revenue ◽  
A Posteriori ◽  
A Posteriori Estimate ◽  
In The Beginning ◽  
Information Collecting ◽  
The Bayesian Approach

The current research is based on the assumption that the result of tax inspections is not only collection of taxes and fines. The information about audited taxpayers is also collected and helps to renew a priori knowledge of each agent's evasion propensity and obtain new a posteriori estimate of this propensity. In the beginning of the following tax period the fiscal authority can correct auditing strategy using updated information on every taxpayer. Each inspection is considered as a repeated game, in which the choice of agents to audit is associated with their revealed tendency to evade. Taxpayers also renew the information on the number of inspected neighbors using their social connections, represented by networks of various con gurations, and estimate the probability of auditing before the next tax period. Thus, the application of the Bayesian approach to the process of collecting and disseminating information in the network of taxpayers allows to optimize the audit scheme, reducing unnecessary expenses of tax authority and eventually increasing net tax revenue. To illustrate the application of the approach described above to the indicated problem, numerical simulation and scenario analysis were carried out.

Neural Network Classifiers Estimate Bayesian a posteriori Probabilities

1991 ◽  
Vol 3 (4) ◽  
pp. 461-483 ◽  
Author(s):  
Michael D. Richard ◽  
Richard P. Lippmann
Keyword(s):  
Neural Network ◽  
Network Performance ◽  
A Priori ◽  
Training Data ◽  
Estimation Accuracy ◽  
A Posteriori ◽  
Multiple Networks ◽  
Risk Functions ◽  
Alternative Measures ◽  
Neural Network Classifiers

Many neural network classifiers provide outputs which estimate Bayesian a posteriori probabilities. When the estimation is accurate, network outputs can be treated as probabilities and sum to one. Simple proofs show that Bayesian probabilities are estimated when desired network outputs are 1 of M (one output unity, all others zero) and a squared-error or cross-entropy cost function is used. Results of Monte Carlo simulations performed using multilayer perceptron (MLP) networks trained with backpropagation, radial basis function (RBF) networks, and high-order polynomial networks graphically demonstrate that network outputs provide good estimates of Bayesian probabilities. Estimation accuracy depends on network complexity, the amount of training data, and the degree to which training data reflect true likelihood distributions and a priori class probabilities. Interpretation of network outputs as Bayesian probabilities allows outputs from multiple networks to be combined for higher level decision making, simplifies creation of rejection thresholds, makes it possible to compensate for differences between pattern class probabilities in training and test data, allows outputs to be used to minimize alternative risk functions, and suggests alternative measures of network performance.

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