Stochastic Extinction in an SIRS Epidemic Model Incorporating Media Coverage

We extend the classical SIRS epidemic model incorporating media coverage from a deterministic framework to a stochastic differential equation (SDE) and focus on how environmental fluctuations of the contact coefficient affect the extinction of the disease. We give the conditions of existence of unique positive solution and the stochastic extinction of the SDE model and discuss the exponential p-stability and global stability of the SDE model. One of the most interesting findings is that if the intensity of noise is large, then the disease is prone to extinction, which can provide us with some useful control strategies to regulate disease dynamics

Bayesian analysis of series system with dependent causes of failure

Most studies of series system assume the causes of failure are independent, which may not hold in practice. In this paper, dependent causes of failure are considered by using a Marshall–Olkin bivariate Weibull distribution. We derived four reference priors based on several grouping orders. Gibbs sampling combined with the rejection sampling algorithm and Metropolis–Hastings algorithm is developed to obtain the estimates of the unknown parameters. The proposed approach is compared with the maximum-likelihood method via simulation. We find that the root-mean-squared errors of the Bayesian estimates are much smaller for the case of small sample size, and that the coverage probabilities of the Bayesian estimates are much closer to the nominal levels. Finally, a real data-set is analysed for illustration

Reference analysis for Birnbaum-Saunders distribution

In this paper we consider the Bayesian estimators for the unknown parameters of the Birnbaum-Saunders distribution under the reference prior. The Bayesian estimators cannot be obtained in closed forms. An approximate Bayesian approach is proposed using the idea of Lindley and Gibbs sampling procedure is also used to obtain the Bayesian estimators. These results are compared using Monte Carlo simulations with the maximum likelihood method and another approximate Bayesian approach Laplace's approximation. Two real data sets are analyzed for illustrative purposes.

Statistical inference for zero-and-one-inflated poisson models

In this paper, a zero-and-one-inflated Poisson (ZOIP) model is studied. The maximum likelihood estimation and the Bayesian estimation of the model parameters are obtained based on data augmentation method. A simulation study based on proposed sampling algorithm is conducted to assess the performance of the proposed estimation for various sample sizes. Finally, two real data-sets are analysed to illustrate the practicability of the proposed method

Bayesian Inference of System Reliability for Multicomponent Stress-Strength Model under Marshall-Olkin Weibull Distribution

Industrial systems often have redundant structures for improving reliability and avoiding sudden failures, and a parallel system is one of the special redundant systems. In this paper, we consider the problem of reliability estimation for a parallel system when one stress variable is involved, which is called the multicomponent stress-strength model. The parallel system contains two components, and their joint lifetime follows a Marshall–Olkin bivariate Weibull distribution, while the stress variable is assumed to be the Weibull distribution. Due to the complicated form of the likelihood function, a data augmentation method is proposed, and then the Gibbs sampling algorithm is constructed to obtain the Bayesian estimation of the system reliability. The proposed method is evaluated by a simulated dataset and Monte Carlo simulation study. The simulation results show that the proposed method performs well in terms of relative bias, mean squared error and frequentist coverage probability

Bayesian Inference of System Reliability for Multicomponent Stress-Strength Model under Marshall-Olkin Weibull Distribution

Industrial systems often have redundant structures for improving reliability and avoiding sudden failures, and a parallel system is one of the special redundant systems. In this paper, we consider the problem of reliability estimation for a parallel system when one stress variable is involved, which is called the multicomponent stress-strength model. The parallel system contains two components, and their joint lifetime follows a Marshall–Olkin bivariate Weibull distribution, while the stress variable is assumed to be the Weibull distribution. Due to the complicated form of the likelihood function, a data augmentation method is proposed, and then the Gibbs sampling algorithm is constructed to obtain the Bayesian estimation of the system reliability. The proposed method is evaluated by a simulated dataset and Monte Carlo simulation study. The simulation results show that the proposed method performs well in terms of relative bias, mean squared error and frequentist coverage probability

Bias reduction in the two-stage method for degradation data analysis

Degradation data are usually collected for assessing the reliability of the product. We propose a new two-stage method to analyze degradation data. The degradation path is fitted by the nonlinear mixed effects model in the first stage, and the parameters in lifetime distribution are estimated by maximizing the asymptotic marginal distribution of pseudo lifetimes in the second stage. The new method has many advantages: (i) it does not require the distributions on random effects, (ii) the historical information about lifetime distribution of the product can be incorporated easily, and thus the estimated lifetime distribution has a closed form, (iii) bias correction term is automatically embedded into the asymptotic marginal distribution of pseudo lifetime. Finally, simulation studies and real data analysis are performed for illustration

A Spatial-Temporal ARMA Model of the Incidence of Hand, Foot, and Mouth Disease in Wenzhou, China

To investigate the variability of HFMD in each county of Wenzhou, a spatial-temporal ARMA model is presented, and a general Bayesian framework is given for parameter estimation. The proposed model has two advantages: (i) allowing time series to be correlated, thus it can describe the series both spatially and temporally; (ii) implementing forecast easily. Based on the HFMD data in Wenzhou, we find that HFMD had positive spatial autocorrelation and the incidence seasonal peak was between May and July. In the county-level analysis, we find that after first-order difference the spatial-temporal ARMA (0,0)×(1,0)12 model provides an adequate fit to the data