scholarly journals On the Estimation of the Credibility Factor: A Bayesian Approach

1995 ◽  
Vol 25 (2) ◽  
pp. 137-151 ◽  
Author(s):  
René Schnieper
Keyword(s):  
Bayesian Approach ◽  
Statistical Models ◽  
Random Variables ◽  
Weighted Average ◽  
Credibility Theory ◽  
Structure Parameters ◽  
A Posteriori ◽  
Unknown Parameters ◽  
Practical Applications ◽  
Posterior Mean

AbstractIn practical applications of Credibility Theory the structure parameters usually have to be estimated from the data. This leads to an estimator of the a posteriori mean which is often biased and where the credibility factor depends on the data. A more coherent approach to the problem would be to also treat the unknown parameters as random variables and to simultaneously estimate the a posteriori mean and the structure parameters. Different statistical models are proposed which allow for such a solution. These models all lead to an estimation of the posterior mean which is a weighted average of the prior mean and of the observed mean, the weights depending on the observations.

An entropy-based global sensitivity analysis for the structures with both fuzzy variables and random variables

2012 ◽  
Vol 227 (2) ◽  
pp. 195-212 ◽  
Author(s):  
Tang Zhangchun ◽  
Lu Zhenzhou ◽  
Pan Wang ◽  
Zhang Feng
Keyword(s):  
Failure Probability ◽  
Uncertainty Propagation ◽  
Random Variables ◽  
Uncertain Variable ◽  
Importance Measure ◽  
Similar Measure ◽  
Practical Applications ◽  
Fuzzy Variables ◽  
Global Sensitivity ◽  
Uncertain Variables

Based on the entropy of the uncertain variable, a novel importance measure is proposed to identify the effect of the uncertain variables on the system, which is subjected to the combination of random variables and fuzzy variables. For the system with the mixture of random variables and fuzzy variables, the membership function of the failure probability can be obtained by the uncertainty propagation theory first. And then the effect of each input variable on the output response of the system can be evaluated by measuring the shift between entropies of two membership functions of the failure probability, obtained before and after the uncertainty elimination of the input variable. The intersecting effect of the multiple input variables can be calculated by the similar measure. The mathematical properties of the proposed global sensitivity indicators are investigated and proved in detail. A simple example is first employed to demonstrate the procedure of solving the proposed global sensitivity indicators and then the influential variables of four practical applications are identified by the proposed global sensitivity indicators.

scholarly journals An asymptotic optimal design

1991 ◽  
Vol 4 (4) ◽  
pp. 357-361 ◽  
Author(s):  
Kamel Rekab
Keyword(s):  
Optimal Design ◽  
Bayesian Approach ◽  
Sequential Design ◽  
Asymptotically Optimal ◽  
Posterior Mean ◽  
Normal Populations

The problem of designing an experiment to estimate the product of the means of two normal populations is considered. A Bayesian approach is adopted in which the product of the means is estimated by its posterior mean. A fully sequential design is proposed and shown to be asymptotically optimal.

scholarly journals Integer variables estimation problems: the Bayesian approach

1997 ◽  
Vol 40 (5) ◽  
Author(s):  
F. Sansò ◽  
G. Venuti
Keyword(s):  
Bayesian Approach ◽  
Estimation Procedure ◽  
Least Square ◽  
Unknown Parameters ◽  
Ordinary Least Square ◽  
Integer Variables ◽  
Cycle Slips ◽  
Estimation Problems ◽  
Continuous Range ◽  
Gps Observations

In geodesy as well as in geophysics there are a number of examples where the unknown parameters are partly constrained to be integer numbers, while other parameters have a continuous range of possible values. In all such situations the ordinary least square principle, with integer variates fixed to the most probable integer value, can lead to paradoxical results, due to the strong non-linearity of the manifold of admissible values. On the contrary an overall estimation procedure assigning the posterior distribution to all variables, discrete and continuous, conditional to the observed quantities, like the so-called Bayesian approach, has the advantage of weighting correctly the possible errors in choosing different sets of integer values, thus providing a more realistic and stable estimate even of the continuous parameters. In this paper, after a short recall of the basics of Bayesian theory in section 2, we present the natural Bayesian solution to the problem of assessing the estimable signal from noisy observations in section 3 and the Bayesian solution to cycle slips detection and repair for a stream of GPS measurements in section 4. An elementary synthetic example is discussed in section 3 to illustrate the theory presented and more elaborate, though synthetic, examples are discussed in section 4 where realistic streams of GPS observations, with cycle slips, are simulated and then back processed.

Some new approaches to probability distributions

1980 ◽  
Vol 12 (04) ◽  
pp. 903-921 ◽  
Author(s):  
S. Kotz ◽  
D. N. Shanbhag
Keyword(s):  
Probability Distributions ◽  
Random Variables ◽  
Representation Theorems ◽  
Practical Applications ◽  
New Approaches ◽  
Characterization Of Distributions ◽  
Stability Theorems ◽  
Conditional Expectations

We develop some approaches to the characterization of distributions of real-valued random variables, useful in practical applications, in terms of conditional expectations and hazard measures. We prove several representation theorems generalizing earlier results, and establish stability theorems for two general characteristics introduced in this paper.

Mining in Music Databases

2011 ◽  
pp. 340-374
Author(s):  
Ioannis Karydis ◽  
Alexandros Nanopoulos ◽  
Yannis Manolopoulos
Keyword(s):  
Data Mining ◽  
Statistical Models ◽  
Complex Structure ◽  
Digital Audio ◽  
Practical Applications ◽  
Acoustic Data ◽  
Music Classification ◽  
Musical Scores ◽  
Music Databases ◽  
Music Data Mining

This chapter provides a broad survey of music data mining, including clustering, classification and pattern discovery in music. The data studied is mainly symbolic encodings of musical scores, although digital audio (acoustic data) is also addressed. Throughout the chapter, practical applications of music data mining are presented. Music data mining addresses the discovery of knowledge from music corpora. This chapter encapsulates the theory and methods required in order to discover knowledge in the form of patterns for music analysis and retrieval, or statistical models for music classification and generation. Music data, with their temporal, highly structured and polyphonic character, introduce new challenges for data mining. Additionally, due to their complex structure and their subjectivity to inaccuracies caused by perceptual effects, music data present challenges in knowledge representation as well.

Solution of the inverse elastography problem for parametric classes of inclusions with a posteriori error estimate

2018 ◽  
Vol 26 (4) ◽  
pp. 493-499 ◽  
Author(s):  
Alexander S. Leonov ◽  
Alexander N. Sharov ◽  
Anatoly G. Yagola
Keyword(s):  
Error Estimate ◽  
Young’S Modulus ◽  
Young's Modulus ◽  
Posteriori Error ◽  
Theory Of Elasticity ◽  
A Posteriori Error Estimate ◽  
Posteriori Error Estimate ◽  
A Posteriori ◽  
Unknown Parameters ◽  
A Posteriori Error

Abstract This article presents the solution of a special inverse elastography problem: knowing vertical displacements of compressed biological tissue to find a piecewise constant distribution of Young’s modulus in an investigated specimen. Our goal is to detect homogeneous inclusions in the tissue, which can be interpreted as oncological. To this end, we consider the specimen as two-dimensional elastic solid, displacements of which satisfy the differential equations of the linear static theory of elasticity in the plain strain statement. The inclusions to be found are specified by parametric functions with unknown geometric parameters and unknown Young’s modulus. Reducing this inverse problem to the search for all unknown parameters, we solve it applying the modified method of extending compacts by V. K. Ivanov and I. N. Dombrovskaya. A posteriori error estimate is carried out for the obtained approximate solutions.

Vehicle yaw-inertia- and mass-independent adaptive steering control

2009 ◽  
Vol 223 (9) ◽  
pp. 1101-1108 ◽  
Author(s):  
J Wang ◽  
M F Hsieh
Keyword(s):  
Adaptive Control ◽  
Tracking Error ◽  
Stability Control ◽  
Driving Safety ◽  
Control Law ◽  
Steering Control ◽  
Tracking Accuracy ◽  
Unknown Parameters ◽  
Practical Applications ◽  
Adaptive Control Law

This paper describes a vehicle stability control (VSC) system using a vehicle yaw-inertia- and mass-independent adaptive control law. As a primary vehicle active control system, VSC can significantly improve vehicle driving safety for passenger cars and enhance trajectory tracking accuracy for other applications such as autonomous, surveillance, and mobile robot vehicles. For the designs of vehicle dynamic control systems, vehicle yaw inertia and mass are two of the most important parameters. However, in practical applications, vehicle yaw inertia and mass often change with vehicle payload and load distribution. In this paper, an adaptive control law is proposed to treat the vehicle yaw inertia and mass as unknown parameters and automatically address their variations. For the proposed adaptive control law, asymptotic stability of the yaw rate tracking error was proved by a Lyapunov-like analysis for certain vehicle architectures under some reasonable assumptions. The performance of the yaw-inertia- and mass-independent adaptive VSC system was evaluated under several driving conditions (i.e. double lane changing on a slippery surface and braking on a split- μ surface tests) through simulation studies using a high-fidelity full-vehicle model provided by CarSim®.

Determination of the Number of Input Data Through Bi-Objective Confidence-Based Design Optimization

2019 ◽  
Author(s):  
Yongsu Jung ◽  
Hyunkyoo Cho ◽  
Zunyi Duan ◽  
Ikjin Lee
Keyword(s):  
Design Optimization ◽  
Statistical Models ◽  
Input Data ◽  
Operating Cost ◽  
Optimal Number ◽  
Practical Applications ◽  
Reliability Based Design ◽  
Input Model Uncertainty ◽  
Stochastic Sensitivity Analysis

Abstract The confidence of reliability indicates that reliability has randomness induced by any epistemic uncertainties, and these uncertainties can be reduced and manipulated by additional knowledge. In this paper, the uncertainty of input statistical models is mainly treated in the context of confidence-based design optimization (CBDO). Thus, the objective of this paper is to determine the optimal number of data for reliability-based design optimization (RBDO) under input model uncertainty. The uncertainty of input statistical models due to insufficient data is frequent in practical applications since collecting and testing samples of random variables requires engineering efforts. There are two ways to increase the confidence of reliability to be satisfied, which are shifting design vector and supplementing input data. The purpose of this research is to find balanced optimum accounting for a trade-off between two operations since both operations lead to the growth of overall cost. Therefore, it is necessary to optimally distribute the resources to two costs which are denoted as the operating cost of design vector and the development cost of acquiring new data. In this study, two types of costs are integrated as a bi-objective function, satisfying the probabilistic constraint for the confidence of reliability. The number of data is regarded as design variable to be optimized, and stochastic sensitivity analysis of reliability with respect to the number of data is developed. The proposed bi-objective CBDO can determine the optimal number of input data based on the current dataset. Then, the designers decide the additional number of tests for collecting input data according to the optimum of bi-objective CBDO to minimize the overall cost.

Design of Nonovershoot MRACS With Application to D.C. Servo Motor System

1991 ◽  
Vol 113 (1) ◽  
pp. 75-81 ◽  
Author(s):  
K. Tamura ◽  
K. Ogata ◽  
P. N. Nikiforuk
Keyword(s):  
Adaptive Control ◽  
Motor System ◽  
Position Control ◽  
Input Sequence ◽  
Control Input ◽  
Servo Motor ◽  
Unknown Parameters ◽  
Practical Applications ◽  
Existence Region ◽  
Model Reference Adaptive

Excessive overshoots in a transient response are undesirable in a model reference adaptive control system (MRACS) and have to be avoided in practical applications. This paper discusses the design of an MRACS with no overshoot. In this design a d-step ahead estimator is introduced to evaluate the expected maximum and minimum values of the plant output. According to these estimates, the adaptive control input is adjusted so that the output has no overshoot. For the estimator and the input adjustment an existence region of the unknown plant parameters must be known. It is obvious that the smaller the existence region is, the better is the estimation and adjustment, and, consequently, the MRACS performance. First, an algorithm which successively reduces the region is presented. An initial polyhedron region V(0), which includes the unknown parameters, assumed to be given. The volume of V(k) containing the unknown parameters is then successively reduced by a projection-type algorithm which uses the input and output of the plant. Next, the design of an MRACS is discussed in which this region V(k) plays an important role. The proposed controller generates an adaptive control input sequence which makes the plant output follow the reference output without any overshoot. The proposed MRACS was applied to the adaptive position control of a D.C. servo motor system with an unknown load. Experimental results demonstrate the usefulness of the proposed design.

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