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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, studies of competing risks model are considered when the observations are left-truncated and right-censored data. When the failure times of the competing risks are distributed by a generalized inverted exponential model with same scale but different shape parameters with partially observed failure causes, statistical inference for the unknown model parameters is discussed from classical and Bayesian approaches, respectively. Maximum likelihood estimators of the unknown parameters, along with associated existence and uniqueness, are established, and the asymptotic likelihood theory is also used to construct the confidence interval via the observed Fisher information matrix. Moreover, Bayesian estimates and the corresponding highest posterior density credible intervals are also obtained based a flexible Gamma-Beta prior, and a Gibbs sampling technique is constructed to compute associated estimates. Further, under a general practical assumption with order-restriction parameter case, classical and Bayesian estimations are also established under order restriction situations, respectively. Extensive Monte-Carlo simulations are carried out to investigate the performances of our results and two real-life examples are analyzed to show the applicability of the proposed methods. [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]

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, 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, 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]

This research investigates the reliability estimation in multicomponent stress-strength model when both the stress and strengths are drawn from Weighted Exponential-Lindley distribution. Reliability assessment is carried out using classical and Bayesian approaches. The Bayes estimates of the reliability in the multicomponent stress-strength model are derived under a squared error loss function using informative and non-informative priors for the parameters. Further, Lindley's approximation and Gibbs sampling method are used to develop Bayes estimators for the system's reliability due to the lack of explicit forms. Additionally, an asymptotic confidence interval and the highest probability density credible interval are constructed to gauge system performance. A simulation study is conducted to assess the performance of reliability estimators. Finally, a real data set is analysed for illustrative purposes. [ABSTRACT FROM AUTHOR]

In the stress-strength reliability literature, although identical components assumption may not be realistic due to the structure of a system, independent and identically distributed components have been commonly used. In this study, we aim to contribute to the literature by studying of non-identical distributed components in a consecutive k-out of-n system when both stress and strength components follow the proportional hazard rate models. Estimation methods for the stress-strength reliability of this system are investigated from frequentist and Bayesian perspectives. Maximum likelihood and uniformly minimum variance unbiased estimations are obtained in the frequentist approach. Based on the suitability of the structure, approximate Bayes estimates methods: Lindley's approximation, Markov Chain Monte Carlo through Metropolis-Hastings or Gibbs sampling algorithms and exact Bayes estimates are derived. Asymptotic confidence and highest posterior density credible intervals are also constructed for all cases. We provide comprehensive simulation experiments for investigating the performances of the considered estimates. Wind speed data from NASA's satellite data source project are used in the application of the considered model and methods. We present the comparison of wind energy potentials of two districts on the Aegean coast of Turkey using our model structure after determining their wind speed distributions. [ABSTRACT FROM AUTHOR]

Mediation analysis is widely applied in various fields of science, such as psychology, epidemiology, and sociology. In practice, many psychological and behavioral phenomena are dynamic, and the corresponding mediation effects are expected to change over time. However, most existing mediation methods assume a static mediation effect over time, which overlooks the dynamic nature of mediation effect. To address this issue, we propose dynamic mediation models that can capture the dynamic nature of the mediation effect. Specifically, we model the path parameters of mediation models as auto-regressive (AR) processes of time that can vary over time. Additionally, we define the mediation effect under the potential outcome framework, and examine its identification and causal interpretation. Bayesian methods utilizing Gibbs sampling are adopted to estimate unknown parameters in the proposed dynamic mediation models. We further evaluate our proposed models and methods through extensive simulations and illustrate their application through a real data application. [ABSTRACT FROM AUTHOR]