Search Results (39)

Identifying the most appropriate lag structure for double seasonal autoregressive models is a fundamental demanding task in time series analysis. Classical model selection tools such as the Akaike information criteria are well known to be inconsistent for identifying the true lag structure. At the same time, standard Bayesian formulations almost invariably assume normality that is often violated in the presence of heavy tails, isolated outliers, or contaminated observations. This paper addresses both limitations simultaneously by proposing a unified Bayesian framework for the best-subset selection of multiplicative double seasonal autoregressive models under the scale-mixtures of normal family of error distributions. Adopting an extended stochastic search variable selection, we assign mixture-normal priors to all primitive autoregressive coefficient vectors and derive tractable closed-form conditional posterior distributions for all model parameters. Building on these results, we design an efficient Markov chain Monte Carlo algorithm integrating Gibbs sampling and Metropolis–Hastings updates for simultaneous subset identification and parameter estimation under heavy-tailed errors. A comprehensive simulation study and real-data applications to hourly electricity demand in the Czech Republic and Germany demonstrate that the proposed algorithm consistently outperforms classical information criteria, particularly when innovations are heavy-tailed. Full article

Autoregressive models with exogenous variables (ARX) constitute a fundamental class of dynamic regression models used extensively for time series analysis across a wide range of applications. A pervasive limitation of the existing Bayesian analyses of ARX models is their near-exclusive reliance on the Gaussian error assumption, which is routinely violated in empirical applications exhibiting heavy-tailed innovations, distributional outliers, or excess kurtosis. To address this deficiency, we develop a rigorous Bayesian estimation framework for these models whose errors are drawn from the scale-mixtures of normal (SMN) family, which is a rich, symmetric, heavy-tailed class of distributions. Exploiting the hierarchical stochastic representation of the SMN family through observation-specific latent scale-mixing variables, the ARX model is embedded in an augmented data structure that restores Gaussian conditional structure. Under three distinct prior formulations—namely, normal-gamma, Zellner’s g-prior, and Jeffreys’ prior—we derive closed-form full conditional posterior distributions for the ARX coefficient vector and the error scale parameter, which follow multivariate normal and inverse-gamma distributions, respectively. In addition, for the SMN-specific shape parameters, we derive the full conditional posteriors for each distribution in the family, and some of them are non-standard distributions handled by embedding Metropolis-Hastings steps within the Gibbs sampler. The resulting hybrid MCMC algorithm is validated through a comprehensive simulation study spanning three ARX model configurations and all three SMN special cases. A real macroeconomic application to US consumer price inflation demonstrates the practical utility of the framework, confirming heavy-tailed residuals and yielding precise, well-calibrated posterior estimates. Full article

This study investigates statistical inference for upper record ranked set sampling (URRSS) data from the Kies distribution. In multiple-cycle URRSS settings where the heterogeneity across cycles is non-ignorable, both classical and Bayesian approaches are adopted to estimate the unknown model parameters and associated reliability metrics. Likelihood-based point and interval estimates are derived for these parameters and reliability indices, and the existence and uniqueness of the maximum likelihood estimators for the Kies distribution parameters are rigorously established. Moreover, a hierarchical Bayesian framework is developed to accommodate cycle-specific variability, with a Metropolis–Hastings algorithm embedded within a Gibbs sampler proposed to facilitate posterior computation in complex scenarios. The performance of the suggested methods is assessed through extensive simulation studies, supplemented by two real-world data applications that demonstrate their practical utility. Numerical results show that the proposed estimators perform well overall, with the hierarchical Bayesian approach showing a particular advantage when uncertainty about the cycle effect is present. Full article

We study inference and prediction for two populations whose lifetimes follow two-parameter Birnbaum–Saunders distributions under a joint progressive Type-II censoring scheme. We derive the observed-data likelihood and obtain maximum likelihood estimates via an EM algorithm that treats progressively removed lifetimes as missing data. Bayesian inference is developed using importance sampling and a hybrid Gibbs–Metropolis–Hastings sampler, leading to Bayes estimators, credible intervals, and posterior predictive summaries. We further construct prediction intervals for the unobserved lifetimes removed at multiple censoring stages. Monte Carlo experiments under several censoring patterns and parameter configurations compare the frequentist and Bayesian procedures. A tuberculosis survival dataset illustrates model adequacy, parameter estimation, and prediction of removed units under joint progressive censoring. Full article

We propose a new random change point model that utilizes routinely recorded individual-level HIV viral load data to estimate the timing of antiretroviral therapy (ART) initiation in people living with HIV. The change point distribution is assumed to follow a zero-inflated exponential distribution for the longitudinal data, which is also subject to left-censoring, and the underlying data-generating mechanism is a nonlinear mixed-effects model. We extend the Stochastic EM (StEM) algorithm by combining a Gibbs sampler with a Metropolis–Hastings sampling. We apply the method to real HIV data to infer the timing of ART initiation since diagnosis. Additionally, we conduct simulation studies to assess the performance of our proposed method. Full article

In this paper, a new generalization of continuous distributions using the Marshall–Olkin distribution as a generator is proposed and studied. Many important mathematical properties are derived from the proposed distribution, including moments, the moment generating function, order statistics, entropy, and the quantile function. Two different estimation methods are used, namely, maximum likelihood estimation and Bayesian methods. A Monte Carlo simulation is conducted to estimate the parameters and study the behavior of the proposed distribution. Bayesian estimation is obtained using the Gibbs sampler and Metropolis–Hastings algorithm. Finally, two real-world datasets are used to compare the performance of non-Bayesian and Bayesian methods. Full article

This paper investigates statistical methods for estimating unknown lifetime parameters using a progressive first-failure censoring dataset. The failure mode’s lifetime distribution is modeled by the odd-generalized-exponential–inverse-Weibull distribution. Maximum-likelihood estimators for the model parameters, including the survival, hazard, and inverse hazard rate functions, are obtained, though they lack closed-form expressions. The Newton–Raphson method is used to compute these estimations. Confidence intervals for the parameters are approximated via the normal distribution of the maximum-likelihood estimation. The Fisher information matrix is derived using the missing information principle, and the delta method is applied to approximate the confidence intervals for the survival, hazard rate, and inverse hazard rate functions. Bayes estimators were calculated with the squared error, linear exponential, and general entropy loss functions, utilizing independent gamma distributions for informative priors. Markov-chain Monte Carlo sampling provides the highest-posterior-density credible intervals and Bayesian point estimates for the parameters and reliability characteristics. This study evaluates these methods through Monte Carlo simulations, comparing Bayes and maximum-likelihood estimates based on mean squared errors for point estimates, average interval widths, and coverage probabilities for interval estimators. A real dataset is also analyzed to illustrate the proposed methods. Full article

Neyman–Scott rectangular pulse is a stochastic rainfall model with five parameters. The impacts of initial values and optimization methods on the parameter estimation of the Neyman–Scott rectangular pulse model were investigated using both the method of moments and the method of maximum likelihood. The estimates using the method of moments were influenced by the optimization method and were sensitive to the initial values and the aggregation scale of the data. Thus, by using frequentist estimation methods, we cannot guarantee the unique values as estimates. The aim of this study is to find more reliable unique values as estimates using a Bayesian approach. In this approach, parameters are estimated from the posterior distribution, and model performance is assessed by comparing observed values with fitted values. Slice sampling within the Gibbs sampler algorithm demonstrates superior convergence and model fitting, yielding unique estimates for the model parameters. The main conclusion of this study is that Bayesian estimation methods outperform other estimation methods in terms of providing reliable and stable estimates that improve rainfall generation accuracy. Full article

This paper proposes a semiparametric spatial lag model and develops a Bayesian estimation method for this model. In the estimation of the model, the paper combines Reversible Jump Markov Chain Monte Carlo (RJMCMC) algorithm, random walk Metropolis sampler, and Gibbs sampling techniques to sample all the parameters. The paper conducts numerical simulations to validate the proposed Bayesian estimation theory using a numerical example. The simulation results demonstrate satisfactory estimation performance of the parameter part and the fitting performance of the nonparametric function under different spatial weight matrix settings. Furthermore, the paper applies the constructed model and its estimation method to an empirical study on the relationship between economic growth and carbon emissions in China, illustrating the practical application value of the theoretical results. Full article

Many semiparametric spatial autoregressive (SSAR) models have been used to analyze spatial data in a variety of applications; however, it is a common phenomenon that heteroscedasticity often occurs in spatial data analysis. Therefore, when considering SSAR models in this paper, it is allowed that the variance parameters of the models can depend on the explanatory variable, and these are called heterogeneous semiparametric spatial autoregressive models. In order to estimate the model parameters, a Bayesian estimation method is proposed for heterogeneous SSAR models based on B-spline approximations of the nonparametric function. Then, we develop an efficient Markov chain Monte Carlo sampling algorithm on the basis of the Gibbs sampler and Metropolis–Hastings algorithm that can be used to generate posterior samples from posterior distributions and perform posterior inference. Finally, some simulation studies and real data analysis of Boston housing data have demonstrated the excellent performance of the proposed Bayesian method. Full article

This paper focuses on a joint model to analyze longitudinal proportional and survival data. We utilize a logit transformation on the longitudinal proportional data and employ a partially linear mixed-effect model. With this model, we estimate the unknown function of time using the B-splines technique. Additionally, we introduce a centered Dirichlet process mixture model (CDPMM) to capture the random effects, allowing for a flexible distribution. The survival data are assumed using a Cox proportional hazard model, and the sharing random effects joint model is developed for the two types of data. We develop a Bayesian Lasso (BLasso) approach that combines the Gibbs sampler and the Metropolis–Hastings algorithm. The proposed method allows for the estimation of unknown parameters and the selection of significant covariates simultaneously. We evaluate the performance of our proposed methods through simulation studies and also provide an illustration of our methodologies using an example from the MA.5 research experiment. Full article

Seasonal autoregressive (SAR) models have many applications in different fields, such as economics and finance. It is well known in the literature that these models are nonlinear in their coefficients and that their Bayesian analysis is complicated. Accordingly, choosing the best subset of these models is a challenging task. Therefore, in this paper, we tackled this problem by introducing a Bayesian method for selecting the most promising subset of the SAR models. In particular, we introduced latent variables for the SAR model lags, assumed model errors to be normally distributed, and adopted and modified the stochastic search variable selection (SSVS) procedure for the SAR models. Thus, we derived full conditional posterior distributions of the SAR model parameters in the closed form, and we then introduced the Gibbs sampler, along with SSVS, to present an efficient algorithm for the Bayesian subset selection of the SAR models. In this work, we employed mixture–normal, inverse gamma, and Bernoulli priors for the SAR model coefficients, variance, and latent variables, respectively. Moreover, we introduced a simulation study and a real-world application to evaluate the accuracy of the proposed algorithm. Full article

We study a joint model where logistic regression is applied to binary longitudinal data with a mismeasured time-varying covariate that is modeled using a mechanistic nonlinear model. Multiple random effects are necessary to characterize the trajectories of the covariate and the response variable, leading to a high dimensional integral in the likelihood. To account for the computational challenge, we propose a stochastic expectation-maximization (StEM) algorithm with a Gibbs sampler coupled with Metropolis–Hastings sampling for the inference. In contrast with previous developments, this algorithm uses single imputation of the missing data during the Monte Carlo procedure, substantially increasing the computing speed. Through simulation, we assess the algorithm’s convergence and compare the algorithm with more classical approaches for handling measurement errors. We also conduct a real-world data analysis to gain insights into the association between CD4 count and viral load during HIV treatment. Full article

Censored data are frequently found in diverse fields including environmental monitoring, medicine, economics and social sciences. Censoring occurs when observations are available only for a restricted range, e.g., due to a detection limit. Ignoring censoring produces biased estimates and unreliable statistical inference. The aim of this work is to contribute to the modelling of time series of counts under censoring using convolution closed infinitely divisible (CCID) models. The emphasis is on estimation and inference problems, using Bayesian approaches with Approximate Bayesian Computation (ABC) and Gibbs sampler with Data Augmentation (GDA) algorithms. Full article

Under the Bayesian framework, this study proposes a Tweedie compound Poisson partial linear mixed model on the basis of Bayesian P-spline approximation to nonparametric function for longitudinal semicontinuous data in the presence of nonignorable missing covariates and responses. The logistic regression model is simultaneously used to specify the missing response and covariate mechanisms. A hybrid algorithm combining the Gibbs sampler and the Metropolis–Hastings algorithm is employed to produce the joint Bayesian estimates of unknown parameters and random effects as well as nonparametric function. Several simulation studies and a real example relating to the osteoarthritis initiative data are presented to illustrate the proposed methodologies. Full article