Bayesian Classifier Based on Robust Kernel Density Estimation and Harris Hawks Optimisation

In real-world applications, datasets frequently contain outliers, which can hinder the generalization ability of machine learning models. Bayesian classifiers, a popular supervised learning method, rely on accurate probability density estimation for classifying continuous datasets. However, achieving precise density estimation with datasets containing outliers poses a significant challenge. This paper introduces a Bayesian classifier that utilizes optimized robust kernel density estimation to address this issue. Our proposed method enhances the accuracy of probability density distribution estimation by mitigating the impact of outliers on the training sample’s estimated distribution. Unlike the conventional kernel density estimator, our robust estimator can be seen as a weighted kernel mapping summary for each sample. This kernel mapping performs the inner product in the Hilbert space, allowing the kernel density estimation to be considered the average of the samples’ mapping in the Hilbert space using a reproducing kernel. M-estimation techniques are used to obtain accurate mean values and solve the weights. Meanwhile, complete cross-validation is used as the objective function to search for the optimal bandwidth, which impacts the estimator. The Harris Hawks Optimisation optimizes the objective function to improve the estimation accuracy. The experimental results show that it outperforms other optimization algorithms regarding convergence speed and objective function value during the bandwidth search. The optimal robust kernel density estimator achieves better fitness performance than the traditional kernel density estimator when the training data contains outliers. The Naïve Bayesian with optimal robust kernel density estimation improves the generalization in the classification with outliers.

Bayesian partial pooling to reduce uncertainty in overcoring rock stress estimation

The state of in situ stress is a crucial parameter in subsurface engineering,especially for critical projects like nuclear waste repository.As one of the two ISRM suggested methods,the overcoring(OC)method is widely used to estimate the full stress tensors in rocks by independent regression analysis of the data from each OC test.However,such customary independent analysis of individual OC tests,known as no pooling,is liable to yield unreliable test-specific stress estimates due to various uncertainty sources involved in the OC method.To address this problem,a practical and no-cost solution is considered by incorporating into OC data analysis additional information implied within adjacent OC tests,which are usually available in OC measurement campaigns.Hence,this paper presents a Bayesian partial pooling(hierarchical)model for combined analysis of adjacent OC tests.We performed five case studies using OC test data made at a nuclear waste repository research site of Sweden.The results demonstrate that partial pooling of adjacent OC tests indeed allows borrowing of information across adjacent tests,and yields improved stress tensor estimates with reduced uncertainties simultaneously for all individual tests than they are independently analysed as no pooling,particularly for those unreliable no pooling stress estimates.A further model comparison shows that the partial pooling model also gives better predictive performance,and thus confirms that the information borrowed across adjacent OC tests is relevant and effective.

Joint Multi-Domain Channel Estimation Based on Sparse Bayesian Learning for OTFS System

Since orthogonal time-frequency space(OTFS)can effectively handle the problems caused by Doppler effect in high-mobility environment,it has gradually become a promising candidate for modulation scheme in the next generation of mobile communication.However,the inter-Doppler interference(IDI)problem caused by fractional Doppler poses great challenges to channel estimation.To avoid this problem,this paper proposes a joint time and delayDoppler(DD)domain based on sparse Bayesian learning(SBL)channel estimation algorithm.Firstly,we derive the original channel response(OCR)from the time domain channel impulse response(CIR),which can reflect the channel variation during one OTFS symbol.Compare with the traditional channel model,the OCR can avoid the IDI problem.After that,the dimension of OCR is reduced by using the basis expansion model(BEM)and the relationship between the time and DD domain channel model,so that we have turned the underdetermined problem into an overdetermined problem.Finally,in terms of sparsity of channel in delay domain,SBL algorithm is used to estimate the basis coefficients in the BEM without any priori information of channel.The simulation results show the effectiveness and superiority of the proposed channel estimation algorithm.

Bayesian Set Estimation with Alternative Loss Functions: Optimality and Regret Analysis

Decision-theoretic interval estimation requires the use of loss functions that, typically, take into account the size and the coverage of the sets. We here consider the class of monotone loss functions that, under quite general conditions, guarantee Bayesian optimality of highest posterior probability sets. We focus on three specific families of monotone losses, namely the linear, the exponential and the rational losses whose difference consists in the way the sizes of the sets are penalized. Within the standard yet important set-up of a normal model we propose: 1) an optimality analysis, to compare the solutions yielded by the alternative classes of losses;2) a regret analysis, to evaluate the additional loss of standard non-optimal intervals of fixed credibility. The article uses an application to a clinical trial as an illustrative example.

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.

Nonlinear Bayesian Estimation： From Kalman Filtering to a Broader Horizon

This article presents an up-to-date tutorial review of nonlinear Bayesian estimation. State estimation for nonlinear systems has been a challenge encountered in a wide range of engineering fields, attracting decades of research effort. To date,one of the most promising and popular approaches is to view and address the problem from a Bayesian probabilistic perspective,which enables estimation of the unknown state variables by tracking their probabilistic distribution or statistics(e.g., mean and covariance) conditioned on a system's measurement data.This article offers a systematic introduction to the Bayesian state estimation framework and reviews various Kalman filtering(KF)techniques, progressively from the standard KF for linear systems to extended KF, unscented KF and ensemble KF for nonlinear systems. It also overviews other prominent or emerging Bayesian estimation methods including Gaussian filtering, Gaussian-sum filtering, particle filtering and moving horizon estimation and extends the discussion of state estimation to more complicated problems such as simultaneous state and parameter/input estimation.

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.

Bayesian network model for traffic flow estimation using prior link flows

In order to estimate traffic flow a Bayesian network BN model using prior link flows is proposed.This model sets link flows as parents of the origin-destination OD flows. Under normal distribution assumptions the model considers the level of total traffic flow the variability of link flows and the violation of the conservation law.Using prior link flows the prior distribution of all the variables is determined. By updating some observed link flows the posterior distribution is given.The variances of the posterior distribution normally decrease with the progressive update of the link flows. Based on the posterior distribution point estimations and the corresponding probability intervals are provided. To remove inconsistencies in OD matrices estimation and traffic assignment a combined BN and stochastic user equilibrium model is proposed in which the equilibrium solution is obtained through iterations.Results of the numerical example demonstrate the efficiency of the proposed BN model and the combined method.

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.

Direction-of-arrival estimation for co-located multiple-input multiple-output radar using structural sparsity Bayesian learning

This paper addresses the direction of arrival （DOA） estimation problem for the co-located multiple-input multiple- output （MIMO） radar with random arrays. The spatially distributed sparsity of the targets in the background makes com- pressive sensing （CS） desirable for DOA estimation. A spatial CS framework is presented, which links the DOA estimation problem to support recovery from a known over-complete dictionary. A modified statistical model is developed to ac- curately represent the intra-block correlation of the received signal. A structural sparsity Bayesian learning algorithm is proposed for the sparse recovery problem. The proposed algorithm, which exploits intra-signal correlation, is capable being applied to limited data support and low signal-to-noise ratio （SNR） scene. Furthermore, the proposed algorithm has less computation load compared to the classical Bayesian algorithm. Simulation results show that the proposed algorithm has a more accurate DOA estimation than the traditional multiple signal classification （MUSIC） algorithm and other CS recovery algorithms.

DOA estimation based on multi-frequency joint sparse Bayesian learning for passive radar

This paper considers multi-frequency passive radar and develops a multi-frequency joint direction of arrival(DOA)estimation algorithm to improve estimation accuracy and resolution.The developed algorithm exploits the sparsity of targets in the spatial domain.Specifically,we first extract the required frequency channel data and acquire the snapshot data through a series of preprocessing such as clutter suppression,coherent integration,beamforming,and constant false alarm rate(CFAR)detection.Then,based on the framework of sparse Bayesian learning,the target’s DOA is estimated by jointly extracting the multi-frequency data via evidence maximization.Simulation results show that the developed algorithm has better estimation accuracy and resolution than other existing multi-frequency DOA estimation algorithms,especially under the scenarios of low signalto-noise ratio(SNR)and small snapshots.Furthermore,the effectiveness is verified by the field experimental data of a multi-frequency FM-based passive radar.

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.

Application of Bayesian Compressive Sensing in IR-UWB Channel Estimation

Due to the sparse nature of the impulse radio ultra-wideband(IR-UWB)communication channel in the time domain,compressive sensing(CS)theory is very suitable for the sparse channel estimation. Besides the sparse nature,the IR-UWB channel has shown more features which can be taken into account in the channel estimation process,such as the clustering structures. In this paper,by taking advantage of the clustering features of the channel,a novel IR-UWB channel estimation scheme based on the Bayesian compressive sensing(BCS)framework is proposed,in which the sparse degree of the channel impulse response is not required. Extensive simulation results show that the proposed channel estimation scheme has obvious advantages over the traditional scheme,and the final demodulation performance,in terms of Bit Error Rate(BER),is therefore greatly improved.

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.