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Traffic intensity is one of the most critical parameters of single-server Markovian queues. This paper deals with the Bayesian inference for the M/M/1 queue by sampling from the posterior distribution. The No-U-Turn Sampler (NUTS) is a recently developed Markov Chain Monte Carlo (MCMC) algorithm, which is proposed to compute the traffic intensity by observing the number of customers in the system at the departure epoch. Numerical results show that the NUTS outperforms the other algorithms in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a Bayesian statistical inference approach for multiple break-points threshold autoregressive moving average model with exogenous inputs (MB-TARMAX) which change in state space and time domain. Based on the appropriate prior information of parameters, we give the full conditional posterior distribution of parameters including the thresholds and break-points. In order to obtain the estimates of parameters, we employ the Markov chain Monte Carlo (MCMC) method via Gibbs sampler with Metropolis-Hastings algorithm. Compared with Metropolis-Hastings algorithm, we apply Hamiltonian Monte Carlo algorithm to avoid the slow space exploration from simple random walk and improve the sampling efficiency. As applications, we demonstrate the effectiveness of our method from simulation experiments and a real example. [ABSTRACT FROM AUTHOR]

Two types of outliers that may occur in data are considered in this paper: additive outliers (AO) and innovational outliers (IO). We have generalized the two types of contaminations AO and IO to the multiple case for an autoregressive model of order p with a regression trend. We adopt the Bayesian approach combined with Gibbs sampling to jointly estimate the model parameters and the outliers on the first hand, and on the other hand we use a test based on p-values and other discrimination Bayesian criteria to detect the location and the magnitude of the two types of outliers. An intensive simulation study is presented for illustrating the performance of the method relative to maximum likelihood estimation, mainly for small sample sizes. Our method is applied to a real data set. [ABSTRACT FROM AUTHOR]

Gibbs samplings is a Markov Chain Monte Carlo technique for estimating conditional probabilities in Bayesian networks. A major problem of Gibbs sampling is the dependency of the generated chain of samples. Thus the estimates are biased unless the initial value of the chain is drawn from the target distribution. One elegant method to overcome the initial bias is regenerative samplings. We reported elsewhere the "stationary minorization condition" that makes any Markov Chain Monte Carlo technique regenerative. In this paper, we show how this condition can be easily met in the simulations of any Bayesian network. [ABSTRACT FROM AUTHOR]

This paper presents a Bayesian analysis of linear mixed models for quantile regression using a modified Cholesky decomposition for the covariance matrix of random effects and an asymmetric Laplace distribution for the error distribution. We consider several novel Bayesian shrinkage approaches for both fixed and random effects in a linear mixed quantile model using extended L 1 penalties. To improve mixing of the Markov chains, a simple and efficient partially collapsed Gibbs sampling algorithm is developed for posterior inference. We also extend the framework to a Bayesian mixed expectile model and develop a Metropolis–Hastings acceptance–rejection (MHAR) algorithm using proposal densities based on iteratively weighted least squares estimation. The proposed approach is then illustrated via both simulated and real data examples. Results indicate that the proposed approach performs very well in comparison to the other approaches. [ABSTRACT FROM AUTHOR]

This paper proposes a new panel autoregressive model named as merged panel autoregressive (M-PAR) model that explains the desired inferences of merger and acquisition (M&A) concept. Bayesian analysis of the M-PAR model is introduced to show the impact of the merger series in the acquire series and then obtain the Bayesian estimator under different loss functions. It is noticed that the conditional posterior distribution of all model parameters appears in standard distribution form, so the Gibbs sampler algorithm is applied for Bayesian computation. Various Bayesian testing procedures are performed to understand the influence of the merged variables into the acquired variable. The proposed model is evaluated based on simulation exercises, with the result shows that the merged variable has a significant impact on the M&A series. On the empirical application, banking indicators of the Indian banking system are analyzed to support our model. [ABSTRACT FROM AUTHOR]

In this paper, a web-based shiny application called the 'PAR(1) Model Analysis'— that allows the modelling, estimation and prediction of a periodic autoregressive time series with scale mixtures of skew-normal innovations, a general and quite flexible class of error distributions—is presented. The class of scale mixtures of skew-normal distributions is often used for statistical procedures of analysing symmetrical and asymmetrical data. The formulation of the scale of a mixture of skew-normal periodic autoregressive models and the estimating methods, which will be applied in the web application, is briefly explained. The embedded tools in the web application and their applications on data analysis are fully described, and finally, a real data example is completely analysed by using this app to illustrate its handling. [ABSTRACT FROM AUTHOR]

In the noncontractual setting of customer-base analysis, heterogeneity parameters in purchase model and lifetime model are usually assumed to follow some familiar parametric distribution such as gamma or log-normal distribution. But, in many applications, these assumptions may be questionable because the true distributions of heterogeneity parameters are usually unknown. To this end, this paper relaxes these assumptions imposed on heterogeneity parameters to develop a nonparametric approach to purchase model and lifetime model, in which unknown distributions of heterogeneity parameters are approximated by a truncated Dirichlet process prior. A nonparametric empirical Bayesian method is developed to obtain Bayesian estimations of unknown parameters in the proposed nonparametric models. The blocked Gibbs sampler is presented to draw observations required for Bayesian inference from the corresponding posterior distributions of the components of parameters. Extensive simulation studies and a CDNOW data set are presented to illustrate the newly developed methodologies. [ABSTRACT FROM AUTHOR]

Recently, Feizjavadian and Hashemi (Analysis of dependent competing risks in presence of progressive hybrid censoring using Marshall–Olkin bivariate Weibull distribution. Comput Stat Data Anal. 2015;82:19–34) provided a classical inference of a competing risks data set using Marshall–Olkin bivariate Weibull distribution when the failure of an unit at a particular time point can happen due to more than one cause. The aim of this paper is to provide the Bayesian analysis of the same model based on a very flexible Gamma–Dirichlet (GD) prior on the scale parameters. The Bayesian inference has certain advantages over the classical inference in this case. We provide the Bayes estimates of the unknown parameters and the associated highest posterior density credible intervals based on Gibbs sampling technique. We further consider the Bayesian inference of the model parameters assuming partially ordered GD prior on the scale parameters when one cause is more severe than the other cause. We have extended the results for different censoring schemes also. [ABSTRACT FROM AUTHOR]