Bayesian Estimation and Hierarchical Bayesian Estimation of Zero-failure Data

The zero_failure data research is a new field in the recent years, but it is required urgently in practical projects, so the work has more theory and practical values. In this paper, for zero_failure data (t i,n i) at moment t i , if the prior distribution of the failure probability p i=p{T【t i} is quasi_exponential distribution, the author gives the p i Bayesian estimation and hierarchical Bayesian estimation and the reliability under zero_failure date condition is also obtained.

E-Bayesian Estimation of the Products Reliability when Testing Reveals no Failure

This paper develops a new method, named E-Bayesian estimation method, to estimate the reliability parameters. The E-Bayesian estimation method of the reliability are derived for the zero-failure data from the product with Binomial distribution. Firstly, for the product reliability, the definitions of E-Bayesian estimation were given, and on the base, expressions of the E-Bayesian estimation and hierarchical Bayesian estimation of the products reliability was given. Secondly, discuss properties of the E-Bayesian estimation. Finally, the new method is applied to a real zero-failure data set, and as can be seen, it is both efficient and easy to operate.

Single channel signal component separation using Bayesian estimation

A Bayesian estimation method to separate multicomponent signals with single channel observation is presented in this paper. By using the basis function projection, the component separation becomes a problem of limited parameter estimation. Then, a Bayesian model for estimating parameters is set up. The reversible jump MCMC （Monte Carlo Markov Chain） algorithmis adopted to perform the Bayesian computation. The method can jointly estimate the parameters of each component and the component number. Simulation results demonstrate that the method has low SNR threshold and better performance.

SAR Images Despeckling Based on Bayesian Estimation and Fuzzy Shrinkage in Wavelet Domains

An efficient despeclding algorithm is proposed based on stationary wavelet transform （SWT） for synthetic aperture radar （SAR） images. The statistical model of wavelet coefficients is analyzed and its performance is modeled with a mixture density of two zero-mean Gaussian distributions. A fuzzy shrinkage factor is derived based on the minimum mean square error （MMSE） criteria with Bayesian estimation. In the case above, the ideas of region division and fuzzy shrinkage arc adopted according to the interscale dependencies among wavelet coefficients. The noise-free wavelet coefficients are estimated accurately. Experimental results show that the algorithm proposed is superior to the refined Lee filter, wavelet soft thresbolding shrinkage and SWT shrinkage algorithms in terms of smoothing effects and edges preservation.

E-Bayesian estimation for competing risk model under progressively hybrid censoring

This paper considers the Bayesian and expected Bayesian（E-Bayesian） estimations of the parameter and reliability function for competing risk model from Gompertz distribution under Type-I progressively hybrid censoring scheme（PHCS）. The estimations are obtained based on Gamma conjugate prior for the parameter under squared error（SE） and Linex loss functions. The simulation results are provided for the comparison purpose and one data set is analyzed.

Bayesian Estimation for the Order of INAR(q)Model

In this paper, we consider the problem of determining the order ofINAR（Q） model on the basis of the Bayesian estimation theory. The Bayesian es-timator for the order is given with respect to a squared-error loss function. The consistency of the estimator is discussed. The results of a simulation study for the estimation method are presented.

Speech Signal Detection Based on Bayesian Estimation by Observing Air-Conducted Speech under Existence of Surrounding Noise with the Aid of Bone-Conducted Speech

In order to apply speech recognition systems to actual circumstances such as inspection and maintenance operations in industrial factories to recording and reporting routines at construction sites, etc. where hand-writing is difficult, some countermeasure methods for surrounding noise are indispensable. In this study, a signal detection method to remove the noise for actual speech signals is proposed by using Bayesian estimation with the aid of bone-conducted speech. More specifically, by introducing Bayes’ theorem based on the observation of air-conducted speech contaminated by surrounding background noise, a new type of algorithm for noise removal is theoretically derived. In the proposed speech detection method, bone-conducted speech is utilized in order to obtain precise estimation for speech signals. The effectiveness of the proposed method is experimentally confirmed by applying it to air- and bone-conducted speeches measured in real environment under the existence of surrounding background noise.

Dynamic Bayesian estimation of displacement parameters of continuous curve box based on Novozhilov theory

The finite strip controlling equation of pinned curve box was deduced on basis of Novozhilov theory and with flexibility method, and the problem of continuous curve box was resolved. Dynamic Bayesian error function of displacement parameters of continuous curve box was found. The corresponding formulas of dynamic Bayesian expectation and variance were derived. After the method of solving the automatic search of step length was put forward, the optimization estimation computing formulas were also obtained by adapting conjugate gradient method. Then the steps of dynamic Bayesian estimation were given in detail. Through analysis of a Classic example, the criterion of judging the precision of the known information is gained as well as some other important conclusions about dynamic Bayesian stochastic estimation of displacement parameters of continuous curve box.

Bayesian estimation for nonlinear stochastic hybrid systems with state dependent transitions

The Bayesian approach is considered as the most general formulation of the state estimation for dynamic systems. However, most of the existing Bayesian estimators of stochastic hybrid systems only focus on the Markov jump system, few liter- ature is related to the estimation problem of nonlinear stochastic hybrid systems with state dependent transitions. According to this problem, a new methodology which relaxes quite a restrictive as- sumption that the mode transition process must satisfy Markov properties is proposed. In this method, a general approach is presented to model the state dependent transitions, the state and output spaces are discreted into cell space which handles the nonlinearities and computationally intensive problem offline. Then maximum a posterior estimation is obtained by using the Bayesian theory. The efficacy of the estimator is illustrated by a simulated example .

Weibull-Bayesian Estimation Based on Maximum Ranked Set Sampling with Unequal Samples

A modification of ranked set sampling (RSS) called maximum ranked set sampling with unequal sample (MRSSU) is considered for the Bayesian estimation of scale parameter α of the Weibull distribution. Under this method, we use Linex loss function, conjugate and Jeffreys prior distributions to derive the Bayesian estimate of α. In order to measure the efficiency of the obtained Bayesian estimates with respect to the Bayesian estimates of simple random sampling (SRS), we compute the bias, mean squared error (MSE) and asymptotic relative efficiency of the obtained Bayesian estimates using simulation. It is shown that the proposed estimates are found to be more efficient than the corresponding one based on SRS.

Prediction of Point in Time with High Crash Risk by Integration of Bayesian Estimation of Drowsiness, Tracking Error, and Subjective Drowsiness

The aim of this study was to predict drivers＇ drowsy states with high risk of encountering a crash and prevent drivers from continuing to drive under such drowsy states with high risk of crash. While the participants were required to carry out a simulated driving task, EEG （Electro encephalography） （EEG-MPF and EEG-α/β）, ECG （Electrocradiogram） （RRV3）, t racking error, an d subjective rating on drowsiness were measured. On the basis of such measurements, an attempt was made to predict the point in time with high crash risk using Bayesian estimation of posterior probability of drowsiness, tracking error, and subjective drowsiness. As a result of applying the proposed method to the data of each participant, it was verified that the proposed method could predict the point in time with high crash risk before the point in time of crash.

A Noise Suppression Method for Speech Signal by Jointly Using Bayesian Estimation and Fuzzy Theory

Speech recognition systems have been applied to inspection and maintenance operations in industrial factories to recording and reporting routines at construction sites, etc. where hand-writing is difficult. In these actual circumstances, some countermeasure methods for surrounding noise are indispensable. In this study, a new method to remove the noise for actual speech signal was proposed by using Bayesian estimation with the aid of bone-conducted speech and fuzzy theory. More specifically, by introducing Bayes’ theorem based on the observation of air-conducted speech contaminated by surrounding background noise, a new type of algorithm for noise removal was theoretically derived. In the proposed noise suppression method, bone-conducted speech signal with the reduced high-frequency components was regarded as fuzzy observation data, and a stochastic model for the bone-conducted speech was derived by applying the probability measure of fuzzy events. The proposed method was applied to speech signals measured in real environment with low SNR, and better results were obtained than an algorithm based on observation of only air-conducted speech.

A fault segment location method for distribution networks based on spiking neural P systems and Bayesian estimation

With the increasing scale of distribution networks and the mass access of distributed generation,traditional central-ized fault location methods can no longer meet the performance requirements of speed and high accuracy.There-fore,this paper proposes a fault segment location method based on spiking neural P systems and Bayesian estimation for distribution networks with distributed generation.First,the distribution network system topology is decoupled into single-branch networks.A spiking neural P system with excitatory and inhibitory synapses is then proposed to model the suspected faulty segment,and its matrix reasoning algorithm is executed to obtain a preliminary set of location results.Finally,the Bayesian estimation and contradiction principle are applied to verify and correct the ini-tial results to obtain the final location results.Simulation results based on the IEEE 33-node system validate the feasi-bility and effectiveness of the proposed method.

Bayesian Estimation and Model Selection for the Spatiotemporal Autoregressive Model with Autoregressive Conditional Heteroscedasticity Errors

The spatial and spatiotemporal autoregressive conditional heteroscedasticity(STARCH) models receive increasing attention. In this paper, we introduce a spatiotemporal autoregressive(STAR) model with STARCH errors, which can capture the spatiotemporal dependence in mean and variance simultaneously. The Bayesian estimation and model selection are considered for our model. By Monte Carlo simulations, it is shown that the Bayesian estimator performs better than the corresponding maximum-likelihood estimator, and the Bayesian model selection can select out the true model in most times. Finally, two empirical examples are given to illustrate the superiority of our models in fitting those data.

Stochastic Volatility Modeling based on Doubly Truncated Cauchy Distribution and Bayesian Estimation for Chinese Stock Market

In order to measure the uncertainty of financial asset returns in the stock market, this paper presents a new model, called SV-dt C model, a stochastic volatility(SV) model assuming that the stock return has a doubly truncated Cauchy distribution, which takes into account the high peak and fat tail of the empirical distribution simultaneously. Under the Bayesian framework, a prior and posterior analysis for the parameters is made and Markov Chain Monte Carlo(MCMC) is used for computing the posterior estimates of the model parameters and forecasting in the empirical application of Shanghai Stock Exchange Composite Index(SSECI) with respect to the proposed SV-dt C model and two classic SV-N(SV model with Normal distribution)and SV-T(SV model with Student-t distribution) models. The empirical analysis shows that the proposed SV-dt C model has better performance by model checking, including independence test(Projection correlation test), Kolmogorov-Smirnov test(K-S test) and Q-Q plot. Additionally, deviance information criterion(DIC) also shows that the proposed model has a significant improvement in model fit over the others.

Bayesian and Non-Bayesian Analysis for the Sine Generalized Linear Exponential Model under Progressively Censored Data

This article introduces a novel variant of the generalized linear exponential(GLE)distribution,known as the sine generalized linear exponential(SGLE)distribution.The SGLE distribution utilizes the sine transformation to enhance its capabilities.The updated distribution is very adaptable and may be efficiently used in the modeling of survival data and dependability issues.The suggested model incorporates a hazard rate function(HRF)that may display a rising,J-shaped,or bathtub form,depending on its unique characteristics.This model includes many well-known lifespan distributions as separate sub-models.The suggested model is accompanied with a range of statistical features.The model parameters are examined using the techniques of maximum likelihood and Bayesian estimation using progressively censored data.In order to evaluate the effectiveness of these techniques,we provide a set of simulated data for testing purposes.The relevance of the newly presented model is shown via two real-world dataset applications,highlighting its superiority over other respected similar models.

Hierarchical Bayesian Estimation of the Products Reliability Based on Zero-Failure Data

With the development of science and technology, the products reliability is higher and higher. So for high reliability products, zero\|failure data situation appears often in the time ended reliability tests. In this paper, the hierarchical Bayesian estimation of the products reliability is given under the conditions of the Binomial distribution with zero\|failure data and the prior distribution of the reliability being quasi\|Beta distribution. The authors also give a practical calculating example using the theory.

Target threat estimation based on discrete dynamic Bayesian networks with small samples

The accuracy of target threat estimation has a great impact on command decision-making.The Bayesian network,as an effective way to deal with the problem of uncertainty,can be used to track the change of the target threat level.Unfortunately,the traditional discrete dynamic Bayesian network(DDBN)has the problems of poor parameter learning and poor reasoning accuracy in a small sample environment with partial prior information missing.Considering the finiteness and discreteness of DDBN parameters,a fuzzy k-nearest neighbor(KNN)algorithm based on correlation of feature quantities(CF-FKNN)is proposed for DDBN parameter learning.Firstly,the correlation between feature quantities is calculated,and then the KNN algorithm with fuzzy weight is introduced to fill the missing data.On this basis,a reasonable DDBN structure is constructed by using expert experience to complete DDBN parameter learning and reasoning.Simulation results show that the CF-FKNN algorithm can accurately fill in the data when the samples are seriously missing,and improve the effect of DDBN parameter learning in the case of serious sample missing.With the proposed method,the final target threat assessment results are reasonable,which meets the needs of engineering applications.

Exponentiated Generalized Inverse Flexible Weibull Distribution:Bayesian and Non-Bayesian Estimation Under Complete and TypeⅡCensored Samples with Applications

In this paper,a new 4-parameter exponentiated generalized inverse flexible Weibull distribution is proposed.Some of its statistical properties are studied.The aim of this paper is to estimate the model parameters via several approaches,namely,maximum likelihood,maximum product spacing and Bayesian.According to Bayesian approach,several techniques are used to get the Bayesian estimators,namely,standard error function,Linex loss function and entropy loss function.The estimation herein is based on complete and censored samples.Markov Chain Monte Carlo simulation is used to discuss the behavior of the estimators for each approach.Finally,two real data sets are analyzed to obtain the flexibility of the proposed model.

Three-dimensional color photon counting microscopy using Bayesian estimation with adaptive priori information

In this Letter, we propose a novel three-dimeusional （3D） color microscopy for microorganisms under photon- starved conditions using photon counting integral imaging and Bayesian estimation with adaptive priori infor- mation. In photon counting integral imaging, 3D images can be visualized using maximum likelihood estimation （MLE）. However, since MLE does not consider a priori information of objects, the visual quality of 3D images may not be accurate. In addition, the only grayscale image can be reconstructed. Therefore, to enhance the visual quality of 3D images, we propose photon counting microscopy using maximum a posteriori with adaptive priori information. In addition, we consider a wavelength of each basic color channel to reconstruct 3D color images. To verify our proposed method, we carry out optical experiments.