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AbstractIn this paper, we propose combining the stochastic blockmodel and the smooth graphon model, two of the most prominent modeling approaches in statistical network analysis. Stochastic blockmodels are generally used for clustering networks into groups of actors with homogeneous connectivity behavior. Smooth graphon models, on the other hand, assume that all nodes can be arranged on a one-dimensional scale such that closeness implies a similar behavior in connectivity. Both frameworks belong to the class of node-specific latent variable models, entailing a natural relationship. While these two modeling concepts have developed independently, this paper proposes their generalization towards stochastic block smooth graphon models. This combined approach enables to exploit the advantages of both worlds. Employing concepts of the EM-type algorithm allows to develop an appropriate estimation routine, where MCMC techniques are used to accomplish the E-step. Simulations and real-world applications support the practicability of our novel method and demonstrate its advantages. The paper is accompanied by supplementary material covering details about computation and implementation. [ABSTRACT FROM AUTHOR]

In this paper, estimation and prediction inference of power Muth distribution, with the progressive censoring data, are described. The maximum likelihood and Bayesian approaches of the unknown parameters are considered. Several Bayesian estimators are obtained against different symmetric and asymmetric loss functions, such as squared error, linex and general entropy. Also, the asymptotic confidence intervals and highest posterior density credible intervals of them are derived. Most focus of this paper is Bayesian prediction of the removed units in multiple stages of the progressively censored sample, so that, the Gibbs and Metropolis samplers are used, to reach this end. To compare the performance of different methods, Mont Carlo simulation is employed. Moreover, one practical data set is analyzed for illustrative purposes. [ABSTRACT FROM AUTHOR]

AbstractIt is well known that Bridge regression Knight et al. (2000) enjoys superior theoretical properties when compared to traditional LASSO. However, the current latent variable representation of its Bayesian counterpart, based on the exponential power prior, is computationally expensive in higher dimensions. In this paper, we show that the Bridge prior has a closed form scale mixture of normal decomposition for α=(12)γ,γ∈{1,2,…} . We call these types of priors L12 prior for short. We develop an efficient partially collapsed Gibbs sampling scheme for computation using the L12 prior and study theoretical properties when p > n. In addition, we introduce a non-separable Bridge penalty function inspired by the fully Bayesian formulation and a novel, efficient coordinate descent algorithm. We prove the algorithm’s convergence and show that the local minimizer from our optimisation algorithm has an oracle property. Finally, simulation studies were carried out to illustrate the performance of the new algorithms. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new class of heterogeneous spatial autoregressive models (heterogeneous SAR models) where the variance parameters are modeled in terms of covariates. In order to estimate the model parameters, as well as their corresponding standard error estimates, we proposed a computational efficient MCMC method which combines the Gibbs sampler with Metropolis-Hastings algorithm. The proposed estimate method is illustrated through numerous simulations and is applied to the Boston housing data. [ABSTRACT FROM AUTHOR]

Interval-valued data have been widely used in both academic and industry research areas. With the development of computational statistics, the Bayesian methods are growing rapidly. Based on the existing theoretical researches, this paper tries to establish a Bayesian framework for interval-valued data, which contains the determination of Jeffreys' prior, posterior inferences, and posterior predictive checking methods. First, Jeffreys' prior for interval-valued data is proposed for the first time. Then, the posterior conditional distribution is derived, and posterior samples are obtained by using Gibbs sampling methods. Based on posterior samples, we obtain the Bayesian point and credible interval estimations for interval-valued data. Finally, we propose a posterior predictive checking method for interval-valued data based on novel test quantities. If the posterior predictive checking method shows that the data do not meet the distribution assumptions, we suggest the use of a data transformation. The effectiveness of our method is demonstrated by simulations and two cardiological data sets. [ABSTRACT FROM AUTHOR]

The noterate is a tool for predicting home mortgage rates, it is often skewed and has missing information. The noterate could be affected by incomplete or inaccurate data, thus leading to inaccurate predictions. Financial organizations including mortgage companies or banks need to consider the risk of uncertainty carefully and make a more accurate prediction based on some suitable models. To deal with this situation, in this paper we compared six computational statistical methods, including the ordinary least square model, maximum likelihood estimation, maximum a posterior, bootstrapping, Metropolis-Hastings, and Gibbs sampling method on a mortgage dataset. Based on the k fold cross-validation technique and four metrics including mean absolute error (MAE), mean squared error (MSE), root mean squared error (RMSE), and mean absolute percentage error (MAPE), the bootstrapping method outperforms other methods. In practice, this method is recommended for predicting noterate. [ABSTRACT FROM AUTHOR]

In this paper, we obtain the stress-strength reliability estimation under balanced joint Type-II progressive censoring scheme for independent samples from two different populations. We simultaneously place two independent samples where the experimental units follow Weibull distributions with common shape parameter β and different scale parameters α, λ, respectively. The maximum likelihood estimators of the unknown parameters are derived. Further, the Bayesian inference is considered using Lindley's approximation and Gibbs sampling method. Extensive simulations are performed to see the effectiveness of the proposed estimation methods. Further, we derive the optimal censoring scheme in the Bayesian framework by using the variable neighbourhood search method proposed by [Bhattacharya et al. On optimum life-testing plans under type-ii progressive censoring scheme using variable neighbourhood search algorithm. Test. 2016;25(2):309–330]. Further, some simulation schemes are provided to compare the performances of the estimations under the jointly censored samples versus two separate censored samples. [ABSTRACT FROM AUTHOR]

In this paper, the Bayesian and non-Bayesian estimation of $$\psi = P(X \gt Y)$$ ψ = P (X > Y) based on the progressively first-failure censored data is considered. The $$X$$ X and $$Y$$ Y are strength and stress random variables and follow the Topp-Leone distributions, respectively. The maximum likelihood and Bayes estimators of $$\psi $$ ψ are derived. The Bayes estimators under generalized entropy loss function are computed using Lindley's approximation and Gibbs sampling methods. Different interval estimates like asymptotic, bootstrap confidence, Bayesian credible, and highest posterior density credible intervals of $$\psi $$ ψ are constructed. Furthermore, a Monte Carlo numerical study is conducted to check the performance of various estimators developed. Finally, an application of algorithm real data is considered for illustrative purposes. [ABSTRACT FROM AUTHOR]

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]

Applications of circular regression models are ubiquitous in many disciplines, particularly in meteorology, biology and geology. In circular regression models, variable selection problem continues to be a remarkable open question. In this paper, we address variable selection in linear-circular regression models where uni-variate linear dependent and a mixed set of circular and linear independent variables constitute the data set. We consider Bayesian lasso which is a popular choice for variable selection in classical linear regression models. We show that Bayesian lasso in linear-circular regression models is not able to produce robust inference as the coefficient estimates are sensitive to the choice of hyper-prior setting for the tuning parameter. To eradicate the problem, we propose a robustified Bayesian lasso that is based on an empirical Bayes (EB) type methodology to construct a hyper-prior for the tuning parameter while using Gibbs Sampling. This hyper-prior construction is computationally more feasible than the hyper-priors that are based on correlation measures. We show in a comprehensive simulation study that Bayesian lasso with EB-GS hyper-prior leads to a more robust inference. Overall, the method offers an efficient Bayesian lasso for variable selection in linear-circular regression while reducing model complexity. [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]

In the context of both cognitive and affective tests, items are usually designed to involve more than two responses, for which polytomous models are applicable. The purpose of this paper is to propose a highly effective Pólya-Gamma Gibbs sampling algorithm based on auxiliary variables to estimate the multidimensional graded response model that has been widely used in psychological, educational, and health-related assessment. The strategy is based on the Pólya Gamma family of distributions which provides a closed-form posterior distribution for logistic-based models. With the introduction of the two latent variables, the full conditional distributions are tractable, and consequently the Gibbs sampling is easy to implement. Nice features including empirical performance of the proposed methodology are demonstrated by simulation studies. Finally, two empirical data sets were analysed to demonstrate the efficiency and utility of the proposed method. [ABSTRACT FROM AUTHOR]

In last few decades some researchers have extended existing time series models to fit high frequency time series characterized by exhibiting multiple seasonalities. In the Bayesian framework, most of the work in this direction is only at the level of double seasonality. Therefore, in this paper we have the objective to fill part of this gap by extending autoregressive models to fit time series that have three layers of seasonality, i.e., triple seasonal autoregressive (TSAR) models, and introducing the Bayesian estimation for these models using the Gibbs sampling algorithm. In order to achieve this objective, we first assume the model errors are normally distributed and employ the normal-gamma and g priors for the model parameters. We then derive the full conditional posterior distributions to be multivariate normal for the model coefficients and inverse gamma for the model variance. Using these closed-form conditional posterior distributions, we propose the Gibbs sampling algorithm to approximate empirically the joint posterior of the TSAR model parameters, enabling us easily to carry out the Bayesian estimation of TSAR models. By employing the g prior for the model parameters, we execute an extensive simulation study to evaluate the efficiency of the proposed Bayesian estimation of TSAR models, and we then apply our work to real-world hourly electricity load time series datasets in six European countries. [ABSTRACT FROM AUTHOR]

In this paper, a highly effective slice sampling algorithm is proposed to estimate the graded response model that has been widely used in educational psychological assessments. The new algorithm not only avoids the Metroplis–Hastings algorithm boring adjustment the turning parameters to achieve an appropriate acceptance probability, but also overcomes the dependence of the traditional Gibbs sampling algorithm on the conjugate prior distribution. Three simulation studies are conducted and a detailed analysis of sexual compulsivity scale (SCS) data is carried out to further illustrate the proposed methodology. [ABSTRACT FROM AUTHOR]

The classical autoregressive type models are widely used in time series modelling. Recently, a class of models known as generalized autoregressive, recognized by an additional parameter, has been proposed in order to reveal some hidden features which cannot be characterized by the standard autoregressive models. In this paper, the generalized autoregressive models are extended to the vector-valued autoregressive models which provide a flexible framework for modelling the dependent data. The properties of the new model such as stationary conditions, some explicit form of the auto-covariance function and the spectral density matrices are investigated. Unknown parameters are then estimated and compared with other kinds of traditional methods. The numerical results obtained by means of simulation studies are then reported. Finally, the traditional autoregressive model and generalized autoregressive model are fitted to a well-known bivariate time series, respectively, and the performance of the proposed models and the estimation methods are discussed. [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]

This paper proposes simulation protocols in terms of an auto-calibration strategy for the parameterisation of Gibbs ensemble Monte Carlo simulations for Lennard–Jones fluids. The proposed simulation protocols have been deduced from various approaches proposed in literature and have been tested against pure LJ fluids and their mixtures. These simulation protocols are intended to reduce or avoid time-consuming pre-simulations by adjusting the trial move limits, the number of attempted transfers, or the probability of attempted transfer during the equilibration phase, and can serve as a starting point for simulating more complex molecules, beyond LJ-fluids. This new approach aims to adjust simulation parameters to ensure a sufficient amount of successful trial moves as suggested in literature. It is similar to a previously proposed trial move adjustment and can easily be implemented in existing simulation code. Abbreviations: BWR EoS: Benedict–Webb–Rubin equation of state; CBMC: Configurational-bias Monte Carlo; EoS: Equation of state; GEMC: Gibbs ensemble Monte Carlo; LJ: Lennard–Jones; M1; M2; M3: Abbreviations for the three simulated mixtures; MC: Monte Carlo; PAT: Probability of attempted transfer; TL: Translation within a box (GEMC move); TR: Transfer to the other box (GEMC move); t-PR EoS: Volume-translated Peng-Robinson equation of state [ABSTRACT FROM AUTHOR]

This paper proposes a flexible stochastic volatility model with jumps and leverage effect by introducing a generalized hyperbolic skew Student's t-distribution (GHST), which can capture the skewness, heavy-tailedness and leptokurtosis of asset returns. Monte Carlo Markov Chain algorithm combining Gibbs sampler and Metropolis-Hastings algorithm is used for parameter estimation and the method is illustrated with simulated data and CSI300 and S&P500 indices. Meantime, we investigate the sensitivity of Bayesian estimates to prior distributions of parameters in jump component and GHST distribution. [ABSTRACT FROM AUTHOR]

In this paper, we propose clustering algorithms based on finite mixture and infinite mixture models of exponential approximation to the Multinomial Generalized Dirichlet (EMGD), Multinomial Beta-Liouville (EMBL) and Multinomial Shifted- Scaled Dirichlet (EMSSD) with Bayesian inference. The finite mixtures have already shown superior performance in real data sets clustering using the Expectation--Maximization approach. The proposed approaches in this paper are based on a Monte Carlo simulation technique namely Gibbs sampling algorithm including an additional Metropolis--Hastings step, and we utilize exponential family conjugate prior information to construct their posterior relying on Bayesian theory. Furthermore, we also present the infinite models based on Dirichlet processes, which results in clustering algorithms that do not require the specification of the number of mixture components to be given in advance and selects it in a principled manner. The performance of our Bayesian approaches was evaluated in some challenging real-world applications concerning text sentiment analysis, fake news detection, and human face gender recognition. [ABSTRACT FROM AUTHOR]

The paper provides a Bayesian alternative to transform the abridged age-specific fertility data into an unabridged one. A model suitable for a binary type of fertility data is considered for the study. The success probabilities of the considered model are assumed to vary in accordance with some established parametric age-specific fertility models. Bayes analysis is done using uniform priors for the unknown parameters of the considered models. Since the posterior analysis involves analytically intractable form of integrals, the paper employs the Gibbs sampler algorithm with intermediate Metropolis-Hastings steps to draw the corresponding posterior samples. Numerical illustration is provided using grouped age-specific fertility rate data. Finally, a few standard Bayesian model comparison tools are used in order to recommend an appropriate model for the data in hand, keeping in view the intended objectives. [ABSTRACT FROM AUTHOR]

The Ising model is a graphical model that has played an essential role in network psychometrics. It has been used as a theoretical model to conceptualize psychological concepts and as a statistical model to analyze psychological data. Using graphical models such as the Ising model to analyze psychological data has been heavily critiqued since these data often come from cross-sectional applications. An often voiced concern is the inability of the Ising model to express heterogeneity in the population. The idiographic approach has been posed as an alternative and aims to infer individual network structures. While idiographic networks overcome population heterogeneity, it is unclear how they aggregate into established cross-sectional phenomena. This paper establishes a formal bridge between idiographic and cross-sectional network approaches of the Ising model. We ascertain unique topological structures that characterize individuals and aggregate into an Ising model cross-sectionally. This new formulation supports population heterogeneity while being consistent with cross-sectional phenomena. The proposed theory also establishes a new statistical framework for analyzing populations of idiographic networks for binary variables. The Ising model and the divide and color model are special cases of this new framework. We introduce a Gibbs sampling algorithm to estimate models from this new framework. [ABSTRACT FROM AUTHOR]

In this paper, we propose a multilevel multidimensional item response model for studying the relations among multiple abilities and covariates in a hierarchical data structure. As an example, this study is well suited to examining the scenario in which a test measures multidimensional latent traits (e.g., reading ability, cognitive ability, and computing ability) and in which students are nested within classes or schools. The new model can recover the correlations among multidimensional abilities, along with the correlation between person- and school-level covariates and abilities. A fully Gibbs sampling algorithm within the Markov chain Monte Carlo (MCMC) framework is proposed for parameter estimation. A unique form of the deviance information criterion (DIC) is used as a model comparison index. Two simulation studies show that the estimation method is suitable in recovering all model parameters. [ABSTRACT FROM AUTHOR]

Efficient estimation for a stochastic volatility (SV) model has been actively pursued in recent years. In this paper, a new Markov chain Monte Carlo (MCMC) algorithm based on a combination of Kalman filtering and the auxiliary sufficiency interweaving strategy (ASIS) is studied. Compared to other MCMC strategies like Stan algorithm ("Rstan") and the Gibbs algorithm ("R2Winbugs"), it is shown from finite-sample studies that the MCMC interweaving strategy improves both the estimation accuracy and the computation speed. We also applied the final selected algorithm, i.e., KMA5 algorithm, to the return rate of The Chinese CSI 300 Index (the Shanghai and Shenzhen 300 stock index in China), which further verifies the validity and accuracy of the new method. [ABSTRACT FROM AUTHOR]

The Bayesian lasso is well-known as a Bayesian alternative for Lasso. Although the advantage of the Bayesian lasso is capable of full probabilistic uncertain quantification for parameters, the corresponding posterior distribution can be sensitive to outliers. To overcome such problem, robust Bayesian regression models have been proposed in recent years. In this paper, we consider the robust and efficient estimation for the Bayesian Huberized lasso regression in fully Bayesian perspective. A new posterior computation algorithm for the Bayesian Huberized lasso regression is proposed. The proposed approximate Gibbs sampler is based on the approximation of full conditional distribution and it is possible to estimate a tuning parameter for robustness of the pseudo-Huber loss function. Some theoretical properties of the posterior distribution are also derived. We illustrate performance of the proposed method through simulation studies and real data examples. [ABSTRACT FROM AUTHOR]

Mechanical components containing internal complexities in free vibration mode are analyzed through generalized bases made of global piecewise smooth functions. Such bases introduced in 2002, as GPSFs, were made adaptive in 2015 to reduce the computational efforts (A-GPSFs) while, a recent study in 2018 used supplementary analytical conditions along with A-GPSFs to study free vibrations of thin-walled beams and plates. In this paper, generalized bases of A-GPSFs are introduced (i) in a self-contained manner, id est, without needing any supplementary analytical conditions and even (ii) extending the possibility of modeling mechanical components containing internal jumps. It is shown how such generalized A-GPSFs can be used to model continuous functions which have different degrees of smoothness; even discontinuous functions (i.e. containing jumps) can be modeled and always without involving significant approximations or letting rise to any Gibbs phenomenon. Thus, a free vibration analysis of mechanical components including internal complexities of engineering interest becomes part of a simple unified procedure based on a global approximation where unknown eigenvalues and eigenfunctions can be singled out only through generalized bases of A-GPSFs; the results of previous formulations are then obtained as particular cases. The efficiency and ability of the proposed models result from the comparison between calculated eigen-parameters and those of other models presented in the open literature. [ABSTRACT FROM AUTHOR]

This paper is an effort to obtain the point estimators and interval estimators for the unknown parameters, reliability and hazard rate functions of bathtub-shaped distribution based on generalized progressive hybrid censoring. We first derive the maximum likelihood estimators for the quantities and compute the estimates using Newton iterative method. Observed Fisher's information matrix is obtained and then the asymptotic confidence intervals are constructed. Besides, two bootstrap confidence intervals are proposed for the quantities. The Bayesian estimators are acquired under squared error loss function using Lindley method and Metropolis-Hastings method with Gibbs sampling, and Bayesian credible intervals are constructed based on Markov Chain Monte Carlo (MCMC) samples as well. Finally, extensive simulation studies are conducted to compare the performance of the estimators and a real data set is analyzed for illustrative purpose. [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]

Frailty models are generally used to model heterogeneity and dependence between individuals. The distribution of the frailty variable is often assumed to be continuous. However, there are situations where a discretely-distributed frailty may be appropriate. On the other hand, when a cure rate is present in survival data, these continuous distributions may not be appropriate since individuals with long-term survival times encompass zero frailty. Having zero frailty can be interpreted as being immune or cured (long-term survivors). In this paper, we propose a new multivariate survival model induced by frailty for multivariate lifetime data in the presence of surviving fractions and examine some of its properties. The inferential approach exploits the Bayesian methods. We provide some simulation results to assess the performance of the proposed model. Furthermore, we illustrate the performance of the proposed model by means of a real data set. [ABSTRACT FROM AUTHOR]

The reciprocal LASSO estimate for linear regression corresponds to a posterior mode when independent inverse Laplace priors are assigned on the regression coefficients. This paper studies reciprocal LASSO in quantile regression from a Bayesian perspective. Simple and efficient Gibbs sampling algorithms are developed for posterior inference using a scale mixture of inverse uniforms (or double Pareto densities), which can be further decomposed as a scale mixture of truncated normals. Slight modifications of this approach lead to Bayesian analogues of other related estimation methods, including reciprocal adaptive LASSO, reciprocal bridge, and reciprocal adaptive bridge. Empirical evidence of the attractiveness of the method is demonstrated via extensive simulation studies and two real data applications. Results show that the proposed methods perform quite well under a variety of scenarios. [ABSTRACT FROM AUTHOR]

The extreme value distribution was developed for modeling extreme-order statistics or extreme events. In this study, we discuss the distribution of the largest extreme. The main objective of this paper is to determine the best estimators of the unknown parameters of the extreme value distribution. Thus, both classical and Bayesian methods are used. The classical estimation methods under consideration are maximum likelihood estimators, moment's estimators, least squares estimators, and weighted least squares estimators, percentile estimators, the ordinary least squares estimators, best linear unbiased estimators, L-moments estimators, trimmed L-moments estimators, and Bain and Engelhardt estimators. We also propose new estimators for the unknown parameters. Bayesian estimators of the parameters are derived by using Lindley's approximation and Markov Chain Monte Carlo methods. The asymptotic confidence intervals are considered by using maximum likelihood estimators. The Bayesian credible intervals are also obtained by using Gibbs sampling. The performances of these estimation methods are compared with respect to their biases and mean square errors through a simulation study. The maximum daily flood discharge (annual) data sets of the Meriç River and Feather River are analyzed at the end of the study for a better understanding of the methods presented in this paper. [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]

Due to the diversity of mobile network technologies, the volume of data that has to be observed by mobile operators in a daily basis has become enormous. This huge volume has become an obstacle to mobile networks management. This paper aims to provide a simplified representation of these data for an easier analysis. A model-based co-clustering algorithm for mixed data, functional and binary, is therefore proposed. Co-clustering aims to identify block patterns in a dataset from a simultaneous clustering of rows and columns. The proposed approach relies on the latent block model, and three algorithms are compared for its inference: stochastic EM within Gibbs sampling, classification EM and variational EM. The proposed model is the first co-clustering algorithm for mixed data that deals with functional and binary features. The model has proven its efficiency on simulated data and on real data extracted from live 4G mobile networks. [ABSTRACT FROM AUTHOR]

The joint censoring scheme is of great importance when the motive of study is to compare the relative merits of products in relation of their service times. In last few years, progressive censoring received considerable attention in order to save cost and time of the experiment. This paper deals with inferences for Lindley populations, when joint progressive type-II censoring scheme is applied on two samples in a joint manner. Here, the maximum likelihood estimators of parameters are derived along with their associated confidence intervals which are dependent on the Fisher's information matrix. The boot-p and boot-t confidence intervals are also obtained. Bayes estimators of the unknown parameters assuming gamma priors are calculated. The concept of importance sampling technique and Gibbs sampling technique are used as the Bayes estimators cannot be calculated in closed form. HPD credible intervals are also constructed. A Monte Carlo simulation study is performed to measure the efficiency of the estimates. A real data set is given for illustrative purpose. Finally some criteria for an optimum censoring scheme are discussed. [ABSTRACT FROM AUTHOR]

Missing data is a common problem in general applied studies, and specially in clinical trials. For implementing sensitivity analysis, several multiple imputation methods exist, like sequential imputation, which restricts to monotone missingness, and Bayesian, where the imputation and analysis models differ, entailing overestimation of variance. Also, full conditional specification provides a conditional interpretation of sensitivity parameters, requiring further calibration to get the desired marginal interpretation. We propose in this paper a multiple imputation procedure, based on a multivariate linear regression model, which keeps compatibility in sensitivity analysis under intermittent missingness, providing a marginal interpretation of the elicited parameters. Simulation studies show that the method behaves well with longitudinal data and remains robust under demanding constraints. We conclude the possibility of situations not covered by the existing methods and well suited for our proposal, which allows more efficient handling of a given multivariate linear regression structure. Its use is illustrated in a real case study, where a sensitivity analysis is accomplished. [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 this paper, we develop a variable selection framework with the spike-and-slab prior distribution via the hazard function of the Cox model. Specifically, we consider the transformation of the score and information functions for the partial likelihood function evaluated at the given data from the parameter space into the space generated by the logarithm of the hazard ratio. Thereby, we reduce the nonlinear complexity of the estimation equation for the Cox model and allow the utilization of a wider variety of stable variable selection methods. Then, we use a stochastic variable search Gibbs sampling approach via the spike-and-slab prior distribution to obtain the sparsity structure of the covariates associated with the survival outcome. Additionally, we conduct numerical simulations to evaluate the finite-sample performance of our proposed method. Finally, we apply this novel framework on lung adenocarcinoma data to find important genes associated with decreased survival in subjects with the disease. [ABSTRACT FROM AUTHOR]

Logistic mixed-effects models are widely used to study the relationship between the binary response and covariates for longitudinal data analysis, where the random effects are typically assumed to have a fully parametric distribution. As this assumption is likely limited or unreasonable in a multitude of practical researches, a semiparametric Bayesian approach for relaxing it is developed in this paper. In the context of binomial distribution logistic mixed-effects models, a general Bayesian framework is presented in which a semiparametric hierarchical modelling with an approximate truncated Dirichlet process prior distribution is specified for the random effects. The stick-breaking prior and the blocked Gibbs sampler using Pólya-Gamma mixture are employed to efficiently sample in the posterior analysis. Besides, a procedure calculating DIC for Bayesian model comparison is addressed. The methodology is demonstrated through simulation studies and a real example. [ABSTRACT FROM AUTHOR]

In this application note paper, we propose and examine the performance of a Bayesian approach for a homoscedastic nonlinear regression (NLR) model assuming errors with two-piece scale mixtures of normal (TP-SMN) distributions. The TP-SMN is a large family of distributions, covering both symmetrical/ asymmetrical distributions as well as light/heavy tailed distributions, and provides an alternative to another well-known family of distributions, called scale mixtures of skew-normal distributions. The proposed family and Bayesian approach provides considerable flexibility and advantages for NLR modelling in different practical settings. We examine the performance of the approach using simulated and real data. [ABSTRACT FROM AUTHOR]

One of the fundamental problems in Bayesian statistics is the approximation of the posterior distribution. Gibbs sampler and coordinate ascent variational inference are renownedly utilized approximation techniques that rely on stochastic and deterministic approximations. In this paper, we define fundamental sets of densities frequently used in Bayesian inference. We shall be concerned with the clarification of the two schemes from the set-theoretical point of view. This new way provides an alternative mechanism for analyzing the two schemes endowed with pedagogical insights. [ABSTRACT FROM AUTHOR]

This paper describes a comprehensive survival analysis for the inverse Gaussian distribution employing Bayesian and Fiducial approaches. It focuses on making inferences on the inverse Gaussian (IG) parameters μ and λ and the average remaining time of censored units. A flexible Gibbs sampling approach applicable in the presence of censoring is discussed and illustrations with Type II, progressive Type II, and random rightly censored observations are included. The analyses are performed using both simulated IG data and empirical data examples. Further, the bootstrap comparisons are made between the Bayesian and Fiducial estimates. It is concluded that the shape parameter ( ϕ = λ / μ) of the inverse Gaussian distribution has the most impact on the two analyses, Bayesian vs. Fiducial, and so does the size of censoring in data to a lesser extent. Overall, both these approaches are effective in estimating IG parameters and the average remaining lifetime. The suggested Gibbs sampler allowed a great deal of flexibility in implementation for all types of censoring considered. [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]

This paper develops a novel and efficient algorithm for Bayesian inference in inverse Gamma stochastic volatility models. It is shown that by conditioning on auxiliary variables, it is possible to sample all the volatilities jointly directly from their posterior conditional density, using simple and easy to draw from distributions. Furthermore, this paper develops a generalized inverse gamma process with more flexible tails in the distribution of volatilities, which still allows for simple and efficient calculations. Using several macroeconomic and financial datasets, it is shown that the inverse gamma and generalized inverse gamma processes can greatly outperform the commonly used log normal volatility processes with Student's t errors or jumps in the mean equation. [ABSTRACT FROM AUTHOR]

In this paper, a multicomponent system which has k independent and identical strength components X 1 , X 2 , ... , X k is considered. Each component is exposed to a common random stress Y when distributions are generalized logistic. This system is operating or failing only if at least s out of k ( 1 ≤ s ≤ k ) strength variables exceeds the random stress. The Bayesian and classical inferences of multicomponent stress-strength reliability under the generalized logistic distribution are studied. The small sample comparison of the reliability estimates is made through Monte Carlo simulation and asymptotic confidence interval is obtained based on maximum likelihood estimation. Also the highest posterior density credible interval is calculated based on Bayesian estimation with Gibbs and Metropolis Hastings algorithms. Finally analysis of a real data set has been presented for illustrative purposes too. [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]

One of the major challenges in modern day statistics is to formulate models and develop inferential procedures to understand the complex multivariate relationships present in high-dimensional datasets. In this paper, we address the issue of model determination for DAGs, with respect to a given ordering of the variables, together with the corresponding parameter estimation. For this, we use a hierarchical mixture prior and develop a Gibbs sampling algorithm to carry out the posterior computations. We first focus on the Gaussian DAG models and calculate the posterior probability of being the edge between two nodes. We then extend our idea to construct a DAG for discrete data under the assumption that the data generated by discretization of the marginal distributions of a latent multivariate Gaussian distribution via a set of predetermined threshold values. Results show that the proposed method has high accuracy. The source code is available at [ABSTRACT FROM AUTHOR]

Analysis of some real phenomena involve directional variables that by their nature are defined only in certain subsets of the k-dimensional unit sphere, S k. For example, when working with axial data, the support of the associated directional variables turns out to be the interval (0 , π ]. Thus, from a methodological point of view it is important to have probability distributions defined in bounded subsets of S k. Specifically, in order to describe directional variables restricted to the first orthant, in this paper we introduce the Multivariate Projected Gamma model (MPG). This model is flexible enough and treats observations as projections onto the unit sphere of unobserved responses from a multivariate distribution which is generated as a product of k independent univariate Gamma distributions. Inference about the parameters of the model is based on samples from the corresponding joint posterior density, which is obtained using a Gibbs sampling after the introduction of suitable latent variables. The proposed methodology is illustrated using simulated data sets as well as a real data set. [ABSTRACT FROM AUTHOR]

Recently, Lee and Cha proposed two general classes of discrete bivariate distributions. They have discussed some general properties and some specific cases of their proposed distributions. In this paper we have considered one model, namely bivariate discrete Weibull distribution, which has not been considered in the literature yet. The proposed bivariate discrete Weibull distribution is a discrete analogue of the Marshall–Olkin bivariate Weibull distribution. We study various properties of the proposed distribution and discuss its interesting physical interpretations. The proposed model has four parameters, and because of that it is a very flexible distribution. The maximum likelihood estimators of the parameters cannot be obtained in closed forms, and we have proposed a very efficient nested EM algorithm which works quite well for discrete data. We have also proposed augmented Gibbs sampling procedure to compute Bayes estimates of the unknown parameters based on a very flexible set of priors. Two data sets have been analyzed to show how the proposed model and the method work in practice. We will see that the performances are quite satisfactory. Finally, we conclude the paper. [ABSTRACT FROM AUTHOR]

The paper employs a linear Bayesian procedure to simultaneously estimate regression parameters and variance parameter in a linear model with equality constraints. We obtain the expression of the linear Bayesian estimator (LBE) for the parameter vector, which consists of the regression parameters and the variance parameter, without specifying the specific form of the prior. The superiorities of the proposed LBE over some classical estimators are established in terms of mean squared error matrix criterion. Monte Carlo simulations and a numerical example are presented to compare its performances with those of the usual Bayesian estimator and the Lindley approximation as well. [ABSTRACT FROM AUTHOR]

Ranked data arise in many areas of application ranging from the ranking of up-regulated genes for cancer to the ranking of academic statistics journals. Complications can arise when rankers do not report a full ranking of all entities; for example, they might only report their top-M ranked entities after seeing some or all entities. It can also be useful to know whether rankers are equally informative, and whether some entities are effectively judged to be exchangeable. Revealing subgroup structure in the data may also be helpful in understanding the distribution of ranker views. In this paper, we propose a flexible Bayesian nonparametric model for identifying heterogeneous structure and ranker reliability in ranked data. The model is a weighted adapted nested Dirichlet (WAND) process mixture of Plackett–Luce models and inference proceeds through a simple and efficient Gibbs sampling scheme for posterior sampling. The richness of information in the posterior distribution allows us to infer many details of the structure both between ranker groups and between entity groups (within-ranker groups). Our modeling framework also facilitates a flexible representation of the posterior predictive distribution. This flexibility is important as we propose to use the posterior predictive distribution as the basis for addressing the rank aggregation problem, and also for identifying lack of model fit. The methodology is illustrated using several simulation studies and real data examples. for this article are available online. [ABSTRACT FROM AUTHOR]