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Nested error regression models are useful tools for the analysis of grouped data, especially in the context of small area estimation. This paper suggests a nested error regression model using uncertain random effects in which the random effect in each area is expressed as a mixture of a normal distribution and a positive mass at 0. For the estimation of the model parameters and prediction of the random effects, an objective Bayesian inference is proposed by setting non-informative prior distributions on the model parameters. Under mild sufficient conditions, it is shown that the posterior distribution is proper and the posterior variances are finite, confirming the validity of posterior inference. To generate samples from the posterior distribution, a Gibbs sampling method is provided with familiar forms for all the full conditional distributions. This paper also addresses the problem of predicting finite population means, and a sampling-based method is suggested to tackle this issue. Finally, the proposed model is compared with the conventional nested error regression model through simulation and empirical studies. [ABSTRACT FROM AUTHOR]

Rolling element bearings are one of the most common components used in machines and they are used to support rotating shafts. Unexpected bearing failures may cause machine breakdown which results in economic loss. Detection of bearing faults is crucial to prevent bearing failures. Vibration based signal processing methods have been proven to be effective in identifying different bearing faults. Among different signal processing methods, wavelet analysis is widely investigated because it is able to highlight the similarity between wavelet functions with different wavelet parameters and impulses caused by bearing faults. In wavelet analysis, two topics are of great concern. The first is how to choose a suitable wavelet mother function for bearing fault diagnosis. In recent studies, an anti-symmetric real Laplace wavelet or impulse response wavelet has been experimentally proven to have a high similarity with impulses caused by bearing faults. Therefore, anti-symmetric real Laplace wavelet is chosen as the wavelet mother function in this paper. The second is how to determine the optimal wavelet parameters so as to enhance the ability of wavelet analysis. Based on the anti-symmetric real Laplace wavelet, smoothness index based Bayesian inference is proposed in this paper to establish joint posterior probability density functions of wavelet parameters, which reflect graphical relationships between wavelet parameters. The smoothness index is chosen because it is not only able to quantify bearing fault signals, but also has upper and lower bounds, compared with other metrics, such as wavelet entropy, Shannon entropy, kurtosis, sparsity measurement, etc. For Bayesian inference, a general particle filter is adopted to iteratively calculate and update joint posterior probability density functions of wavelet parameters. Once the joint posterior probability density functions of wavelet parameters are available, the optimal wavelet parameters are determined and an optimal wavelet filtering is conducted to extract bearing fault signatures. Real case studies are investigated to illustrate how the proposed method works. The results show that the proposed method can determine joint posterior probability density functions of wavelet parameters and is effective in identifying different bearing faults. [ABSTRACT FROM AUTHOR]

We introduce the papers of the JAS Special Issue: Radiocarbon Dating that were presented at the First Frison Institute Symposium at the 2013 Society for American Archaeology annual meeting. Papers here fall into two categories that reflect two growing trends in archaeology: the use of summed probability distributions as measures of human population, and the use of Bayesian statistics to refine radiocarbon age estimates. While caution is required, these two methods combined offer archaeology the possibility of tracking change in the size of human populations through time and across space. [ABSTRACT FROM AUTHOR]

Model updating using measured system dynamic response has a wide range of applications in system response evaluation and control, health monitoring, or reliability and risk assessment. In this paper, we are interested in model updating of a linear dynamic system with non-classical damping based on incomplete modal data including modal frequencies, damping ratios and partial complex mode shapes of some of the dominant modes. In the proposed algorithm, the identification model is based on a linear structural model where the mass and stiffness matrix are represented as a linear sum of contribution of the corresponding mass and stiffness matrices from the individual prescribed substructures, and the damping matrix is represented as a sum of individual substructures in the case of viscous damping, in terms of mass and stiffness matrices in the case of Rayleigh damping or a combination of the former. To quantify the uncertainties and plausibility of the model parameters, a Bayesian approach is developed. A new Gibbs-sampling based algorithm is proposed that allows for an efficient update of the probability distribution of the model parameters. In addition to the model parameters, the probability distribution of complete mode shapes is also updated. Convergence issues and numerical issues arising in the case of high-dimensionality of the problem are addressed and solutions to tackle these problems are proposed. The effectiveness and efficiency of the proposed method are illustrated by numerical examples with complex modes. [ABSTRACT FROM AUTHOR]

In this paper, we generalize the Wishart distribution utilizing a fresh approach that leads to the hypergeometric Wishart generator distribution with the Wishart generator and the Wishart as special cases. Important statistical characteristics are derived. The significance of this generator distribution is further demonstrated by assuming a special case as a prior for the underlying matrix variate normal model. [ABSTRACT FROM AUTHOR]

A novel variational Bayesian mixture of experts model for robust regression of bifurcating and piece-wise continuous processes is introduced. The mixture of experts model is a powerful model which probabilistically splits the input space allowing different models to operate in the separate regions. However, current methods have no fail-safe against outliers. In this paper, a robust mixture of experts model is proposed which consists of Student- t mixture models at the gates and Student- t distributed experts, trained via Bayesian inference. The Student- t distribution has heavier tails than the Gaussian distribution, and so it is more robust to outliers, noise and non-normality in the data. Using both simulated data and real data obtained from the Z24 bridge this robust mixture of experts performs better than its Gaussian counterpart when outliers are present. In particular, it provides robustness to outliers in two forms: unbiased parameter regression models, and robustness to overfitting/complex models. [ABSTRACT FROM AUTHOR]

Parametric uncertainties are encountered in the simulations of many physical systems, and may be reduced by an inverse modeling procedure that calibrates the simulation results to observations on the real system being simulated. Following Bayes' rule, a general approach for inverse modeling problems is to sample from the posterior distribution of the uncertain model parameters given the observations. However, the large number of repetitive forward simulations required in the sampling process could pose a prohibitive computational burden. This difficulty is particularly challenging when the posterior is multimodal. We present in this paper an adaptive importance sampling algorithm to tackle these challenges. Two essential ingredients of the algorithm are: 1) a Gaussian mixture (GM) model adaptively constructed as the proposal distribution to approximate the possibly multimodal target posterior, and 2) a mixture of polynomial chaos (PC) expansions, built according to the GM proposal, as a surrogate model to alleviate the computational burden caused by computational-demanding forward model evaluations. In three illustrative examples, the proposed adaptive importance sampling algorithm demonstrates its capabilities of automatically finding a GM proposal with an appropriate number of modes for the specific problem under study, and obtaining a sample accurately and efficiently representing the posterior with limited number of forward simulations. [ABSTRACT FROM AUTHOR]

Abstract: The focus of this paper is Bayesian modal parameter recursive estimation based on an interacting Kalman filter algorithm with decoupled distributions for frequency and damping. Interacting Kalman filter is a combination of two widely used Bayesian estimation methods: the particle filter and the Kalman filter. Some sensitivity analysis techniques are also proposed in order to deduce a recursive estimate of modal parameters from the estimates of the damping/stiffness coefficients. [Copyright &y& Elsevier]