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The Lomax distribution is one of the well-known distributions that is used to fit heavy-tailed data. In this paper, we investigate the estimation of Shannon entropy of the Lomax distribution using noninformative priors. Some important priors including Jeffreys prior, reference priors and probability matching priors are presented. We demonstrate that the reference and matching priors for the Lomax entropy do not match the reference and probability matching priors of the Lomax parameters, regardless of which parameter of interest is considered. The propriety and the existence of the expectation of the posterior under each prior are validated, respectively. A simulation study is conducted to assess the frequentist performance of the proposed Bayesian estimates in terms of the mean squared error and coverage probability. Finally, the approach is applied to three real data sets for illustrative purposes. [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]

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]

Heston's model and Bates’ model are very important in option pricing. It is mentioned in Mendoza's paper [Bayesian estimation and option mispricing (job market paper). Cambridge, MA: Massachusetts Institute of Technology; 2011] that Mexican Stock Exchange introduced options over its main index (the Índice de Precios y Cotizaciones) in 2004 which used Heston's model to price options on days when there was no trading. The estimation of the parameters in both models is not easy. One of the methods is Markov chain Monte Carlo algorithm (MCMC for short). In this paper, we adopt Li, Wells and Yu's MCMC algorithm [A Bayesian analysis of return dynamics with levy jumps. Rev Financ Stud. 2008;21(5):2345–2377]. We provide the necessary derivation utilizing prior distributions since they are otherwise unavailable in the literature. As Li et al. used their model to analyse S&P 500 data from 2 January 1980 to 29 December 2000, we likewise recreate their analysis, this time using data from 1987 to 2012. We would like to involve the financial crisis and analyse how stable the method is while applying to the financial crisis. Unlike Li et al., we find that the estimation is very sensitive to the prior distribution assumption. In addition, we have R-code available by request. We hope to offer tools for people doing empirical research in financial mathematics or quantitative finance. [ABSTRACT FROM PUBLISHER]

In this paper, we study computation of the range of posterior expectations that arise from robust Bayesian statistics. We compute supremum and infimum of the posterior expectations, when allowing uncertainty for the choice of the likelihood function, or uncertainty for the choice of the prior distribution. In the standard approach of sensitivity analysis, posterior statistics is computed a multiple number of times for each choice of the uncertainty scenarios, which might involve heavy computation due to running Monte Carlo sampling many times. Our paper proposes a more efficient computational method that only requires one Monte Carlo sample for all possible choices of the uncertainty scenarios. The proposed computational method involves three steps (with the mnemonic PSI):(Prior step.) Introduce an auxiliary hyperprior distribution on a parameter λ that indexes the uncertainty.(Sampling step.) For any parameter of interest h, we derive a sample of from the joint posterior distribution given the observed data, using a Monte Carlo method. 1(Inference step.) Based on this posterior sample of , we estimate the range of posterior expectations (and similarly the range for any posterior quantile). [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]

In Bayesian semi-parametric analyses of time-to-event data, non-parametric process priors are adopted for the baseline hazard function or the cumulative baseline hazard function for a given finite partition of the time axis. However, it would be controversial to suggest a general guideline to construct an optimal time partition. While a great deal of research has been done to relax the assumption of the fixed split times for other non-parametric processes, to our knowledge, no methods have been developed for a gamma process prior, which is one of the most widely used in Bayesian survival analysis. In this paper, we propose a new Bayesian framework for proportional hazards models where the cumulative baseline hazard function is modelled a priori by a gamma process. A key feature of the proposed framework is that the number and position of interval cutpoints are treated as random and estimated based on their posterior distributions. [ABSTRACT FROM AUTHOR]

This paper deals with random sign-censoring data (RSCD) which may be observed under repair alert models (RAMs) for implementing age-dependent maintenance policies on engineering devices. A general family for lifetime distributions of devices is considered and estimates of parameters are derived on the basis of RSCD via the likelihood and the Bayesian approaches. In recent literature, the cumulative repair alert function (CRAF), denoted by, of the RAMs is considered proportional to the cumulative hazard rate function of the device lifetime. This paper also suggests a polynomial form for the CRAFfor modelling purposed. A comparison between the two kinds of CRAFs under the RAMs is given for a real data set from Mendenhall and Hader [Estimation of parameters of mixed exponentially distributed failure time distributions from censored life test data. Biometrika. 1958;45:504–520] The data are times to failure for a type of communication transmitter-receivers of a single commercial airline. Some special cases including exponential, Weibull and Pareto distributions are studied in a great detail. [ABSTRACT FROM PUBLISHER]

The paper proposes a Bayesian quantile regression method for hierarchical linear models. Existing approaches of hierarchical linear quantile regression models are scarce and most of them were not from the perspective of Bayesian thoughts, which is important for hierarchical models. In this paper, based on Bayesian theories and Markov Chain Monte Carlo methods, we introduce Asymmetric Laplace distributed errors to simulate joint posterior distributions of population parameters and across-unit parameters and then derive their posterior quantile inferences. We run a simulation as the proposed method to examine the effects on parameters induced by units and quantile levels; the method is also applied to study the relationship between Chinese rural residents' family annual income and their cultivated areas. Both the simulation and real data analysis indicate that the method is effective and accurate. [ABSTRACT FROM AUTHOR]

Traditional Item Response Theory models assume the distribution of the abilities of the population in study to be Gaussian. However, this may not always be a reasonable assumption, which motivates the development of more general models. This paper presents a generalized approach for the distribution of the abilities in dichotomous 3-parameter Item Response models. A mixture of normal distributions is considered, allowing for features like skewness, multimodality and heavy tails. A solution is proposed to deal with model identifiability issues without compromising the flexibility and practical interpretation of the model. Inference is carried out under the Bayesian Paradigm through a novel MCMC algorithm. The algorithm is designed in a way to favour good mixing and convergence properties and is also suitable for inference in traditional IRT models. The efficiency and applicability of our methodology is illustrated in simulated and real examples. [ABSTRACT FROM AUTHOR]

In most practical applications, the quality of count data is often compromised due to errors-in-variables (EIVs). In this paper, we apply Bayesian approach to reduce bias in estimating the parameters of count data regression models that have mismeasured independent variables. Furthermore, the exposure model is misspecified with a flexible distribution, hence our approach remains robust against any departures from normality in its true underlying exposure distribution. The proposed method is also useful in realistic situations as the variance of EIVs is estimated instead of assumed as known, in contrast with other methods of correcting bias especially in count data EIVs regression models. We conduct simulation studies on synthetic data sets using Markov chain Monte Carlo simulation techniques to investigate the performance of our approach. Our findings show that the flexible Bayesian approach is able to estimate the values of the true regression parameters consistently and accurately. [ABSTRACT FROM AUTHOR]

The accelerated degradation test (ADT) is an effective method for evaluating the lifetime of high-reliability products. In this paper, a doubly accelerated degradation model based on the inverse Gaussian process is proposed to characterize the ADT data, and then an objective Bayesian approach is presented to analyze the model. Some important noninformative priors including the Jeffreys prior and reference priors under different group orderings are derived. The propriety of the posterior distributions under each prior is validated. A simulation study is carried out to show the superiority of objective Bayesian approach compared with the parametric Bootstrap method. Finally, the approach is applied to analyze a carbon film data. [ABSTRACT FROM AUTHOR]

In Bayesian model calibration, evaluation of the likelihood function usually involves finding the inverse and determinant of a covariance matrix. When Markov Chain Monte Carlo (MCMC) methods are used to sample from the posterior, hundreds of thousands of likelihood evaluations may be required. In this paper, we demonstrate that the structure of the covariance matrix can be exploited, leading to substantial time savings in practice. We also derive two simple equations for approximating the inverse of the covariance matrix in this setting, which can be computed in near-quadratic time. The practical implications of these strategies are demonstrated using a simple numerical case study and the "quack" R package. For a covariance matrix with 1000 rows, application of these strategies for a million likelihood evaluations leads to a speedup of roughly 4000 compared to the naive implementation [ABSTRACT FROM AUTHOR]

When assessing the compatibility of an assumed model and the observed data, one popular method is the posterior predictive p-value (ppp). However, the posterior predictive p-values typically do not have uniform distributions and tend to be conservative when detecting the misfit of the assumed model. In this paper, we consider a calibrated p-value which is initially proposed in Hjort et al. [Post-processing posterior predictive p-values. J Am Stat Assoc. 2006;1011157–1174]. We further explore its theoretical properties by proving the asymptotic uniformity of the calibrated p-value under some mild conditions. For testing hypotheses under local Pitman alternatives, we investigate its power performance in the asymptotic sense. Theoretical analysis and simulation results show that the calibrated p-value enjoys some desirable properties and is superior to the original posterior predictive p-values. [ABSTRACT FROM AUTHOR]

The inverse generalized gamma (IGG) distribution can be particularly useful for modelling reliability (survival) data with an upside-down bathtub hazard rate function. The mathematical properties and estimation methods are not known in the literature. In this paper, we provide Bayesian inferences for the IGG distribution parameters using non-informative priors, namely, the Jeffreys prior and the reference prior. Extensive numerical simulations are conducted to investigate the performance of the proposed estimation method when compared with the classical inference. Finally, the potentiality of the IGG model is analysed by employing real environmental data. [ABSTRACT FROM AUTHOR]

In this paper, we study the identification of Bayesian regression models, when an ordinal covariate is subject to unidirectional misclassification. Xia and Gustafson [Bayesian regression models adjusting for unidirectional covariate misclassification. Can J Stat. 2016;44(2):198–218] obtained model identifiability for non-binary regression models, when there is a binary covariate subject to unidirectional misclassification. In the current paper, we establish the moment identifiability of regression models for misclassified ordinal covariates with more than two categories, based on forms of observable moments. Computational studies are conducted that confirm the theoretical results. We apply the method to two datasets, one from the Medical Expenditure Panel Survey (MEPS), and the other from Translational Research Investigating Underlying Disparities in Acute Myocardial infarction Patients Health Status (TRIUMPH). [ABSTRACT FROM PUBLISHER]

This paper presents an extension of mean-squared forecast error (MSFE) model averaging for integrating linear regression models computed on data frames of various lengths. Proposed method is considered to be a preferable alternative to best model selection by various efficiency criteria such as Bayesian information criterion (BIC), Akaike information criterion (AIC), F-statistics and mean-squared error (MSE) as well as to Bayesian model averaging (BMA) and naïve simple forecast average. The method is developed to deal with possibly non-nested models having different number of observations and selects forecast weights by minimizing the unbiased estimator of MSFE. Proposed method also yields forecast confidence intervals with a given significance level what is not possible when applying other model averaging methods. In addition, out-of-sample simulation and empirical testing proves efficiency of such kind of averaging when forecasting economic processes. [ABSTRACT FROM PUBLISHER]

In this paper, we consider some problems of estimation and reconstruction based on middle censored competing risks data. It is assumed that the lifetime distributions of the latent failure times are independent and exponential distributed with different parameters and also that the censoring mechanism is independent. The maximum likelihood estimators (MLEs) of the unknown parameters are obtained. We then use the asymptotic distribution of the MLEs to construct approximate confidence intervals. Based on gamma priors, Lindley's approximation method is applied to obtain the Bayesian estimates of the unknown parameters under squared error loss function. Since it is not possible to construct the credible intervals, we propose and implement the Gibbs sampling technique to construct the credible intervals. Several point reconstructors for failure time of censored units are provided. Finally, a simulation study is given by Monte-Carlo simulations to evaluate the performances of the different methods and a data set is analysed to illustrate the proposed procedures. [ABSTRACT FROM PUBLISHER]

A parachute is a kind of decelerator that requires very high reliability. Inflation is a primary step that causes the failure of a parachute structure, especially for a slot parachute. If success/failure data from the airdrop experiment or numerical simulation are to be used for assessing the reliability of a parachute, a series of experiments or simulations is necessary. However, this process is unacceptable in engineering because of the high cost required. A new assessment method is proposed in this paper, and a novel simulation method of slot-parachute inflation is investigated to obtain strength test data. In the assessment method, strength test data are used as the prior information and integrated with inflation simulation information to assess parachute reliability using the Bayesian theory. This method is derived from a strict mathematical theory. The assessment results are consistent with the parachute's actual performance. The simulation results demonstrate the effectiveness of the proposed approaches. [ABSTRACT FROM PUBLISHER]

Competing risks arise when an individual is exposed to the several causes of failure. In this case, the recorded data includes two components, the failure times and the cause of failure indicators. Such data may suffer from censoring in the former part and missingness in the latter part. Prior researches have ignored the missing mechanism when analysing such data which might lead to invalid statistical inferences. Since the ignorability assumption is unverifiable from the available data, the sensitivity analysis is recommended. In this paper, the Bayesian index of local sensitivity to non-ignorability (ISNI) is derived to quantify the sensitivity of Bayesian estimators to the ignorability assumption for hybrid censored incomplete competing risks data when the lifetimes follow exponential, Weibull, and generalized exponential distributions. Also, some simulation studies are conducted to evaluate the performance of the proposed Bayesian ISNI in different missing and competing risks scenarios. Finally, a real-world example is analysed for illustrative purposes. [ABSTRACT FROM AUTHOR]

Item response theory (IRT) models are commonly used in educational and psychological testing to assess the (latent) ability of examinees and the effectiveness of the test items in measuring this underlying trait. The focus of this paper is on the assessment of item fit for unidimensional IRT models for dichotomous items using a Bayesian method. This paper will illustrate and compare the effectiveness of several discrepancy measures, used within the posterior predictive model check procedure, in detecting misfitted items. The effectiveness of the different discrepancy measures are illustrated in a simulation study using artificially altered simulated data. Using the best discrepancy measure among those studied, this method was applied to real data coming from a mathematics placement exam. [ABSTRACT FROM PUBLISHER]

This paper presents the posterior analysis of a new family defined in the literature as modified Weibull distribution. This family is a modification of the two-parameter Weibull model in the sense that it, besides covering increasing and decreasing hazard rates, also represents bathtub-shaped behaviour. Both the Gibbs sampler and the Metropolis algorithms have been used to provide complete analysis of the concerned posterior surfaces. The paper also considers examining the issue of model validation using predictive simulation ideas and the Bayesian p-value. Finally, numerical illustration has been provided based on two real data sets. [ABSTRACT FROM AUTHOR]

In recent years, there has been a considerable interest to study count time series with a dependence structure and appearance of excess of zeros values. Such series are commonly encountered in diverse disciplines, such as economics, financial research, environmental science, public health, among others. In this paper, we propose a stationary p-order integer-valued autoregressive process with zero-inflated Poisson innovations, called the ZINAR(p) times series model. We study some of its theoretical properties and develop a Markov chain Monte Carlo (MCMC) algorithm for inferring parameters from Bayesian perspectives. Finally, we demonstrate the utility of proposed ZINAR(p) model through simulated and real data examples. [ABSTRACT FROM AUTHOR]

Bayesian hierarchical spatio-temporal models are becoming increasingly important due to the increasing availability of space-time data in various domains. In this paper we develop a user friendlyRpackage,spTDyn, for spatio-temporal modelling. It can be used to fit models with spatially varying and temporally dynamic coefficients. The former is used for modelling the spatially varying impact of explanatory variables on the response caused by spatial misalignment. This issue can arise when the covariates only vary over time, or when they are measured over a grid and hence do not match the locations of the response point-level data. The latter is to examine the temporally varying impact of explanatory variables in space-time data due, for example, to seasonality or other time-varying effects. ThespTDynpackage uses Markov chain Monte Carlo sampling written inC, which makes computations highly efficient, and the interface is written inRmaking these sophisticated modelling techniques easily accessible to statistical analysts. The models and software, and their advantages, are illustrated using temperature and ozone space-time data. [ABSTRACT FROM PUBLISHER]

In this paper, we discuss a progressively censored inverted exponentiated Rayleigh distribution. Estimation of unknown parameters is considered under progressive censoring using maximum likelihood and Bayesian approaches. Bayes estimators of unknown parameters are derived with respect to different symmetric and asymmetric loss functions using gamma prior distributions. An importance sampling procedure is taken into consideration for deriving these estimates. Further highest posterior density intervals for unknown parameters are constructed and for comparison purposes bootstrap intervals are also obtained. Prediction of future observations is studied in one- and two-sample situations from classical and Bayesian viewpoint. We further establish optimum censoring schemes using Bayesian approach. Finally, we conduct a simulation study to compare the performance of proposed methods and analyse two real data sets for illustration purposes. [ABSTRACT FROM AUTHOR]

Periodic autoregressive (PAR) models with symmetric innovations are widely used on time series analysis, whereas its asymmetric counterpart inference remains a challenge, because of a number of problems related to the existing computational methods. In this paper, we use an interesting relationship between periodic autoregressive and vector autoregressive (VAR) models to study maximum likelihood and Bayesian approaches to the inference of a PAR model with normal and skew-normal innovations, where different kinds of estimation methods for the unknown parameters are examined. Several technical difficulties which are usually complicated to handle are reported. Results are compared with the existing classical solutions and the practical implementations of the proposed algorithms are illustrated via comprehensive simulation studies. The methods developed in the study are applied and illustrate a real-time series. The Bayes factor is also used to compare the multivariate normal model versus the multivariate skew-normal model. [ABSTRACT FROM AUTHOR]

Spatial data analysis has become more and more important in the studies of ecology and economics during the last decade. One focus of spatial data analysis is how to select predictors, variance functions and correlation functions. However, in general, the true covariance function is unknown and the working covariance structure is often misspecified. In this paper, our target is to find a good strategy to identify the best model from the candidate set using model selection criteria. This paper is to evaluate the ability of some information criteria (corrected Akaike information criterion, Bayesian information criterion (BIC) and residual information criterion (RIC)) for choosing the optimal model when the working correlation function, the working variance function and the working mean function are correct or misspecified. Simulations are carried out for small to moderate sample sizes. Four candidate covariance functions (exponential, Gaussian, Matern and rational quadratic) are used in simulation studies. With the summary in simulation results, we find that the misspecified working correlation structure can still capture some spatial correlation information in model fitting. When the sample size is large enough, BIC and RIC perform well even if the the working covariance is misspecified. Moreover, the performance of these information criteria is related to the average level of model fitting which can be indicated by the average adjustedRsquare (), and overall RIC performs well. [ABSTRACT FROM PUBLISHER]

In this paper, we consider a special finite mixture model named Combination of Uniform and shifted Binomial (CUB), recently introduced in the statistical literature to analyse ordinal data expressing the preferences of raters with regards to items or services. Our aim is to develop a variable selection procedure for this model using a Bayesian approach. Bayesian methods for variable selection and model choice have become increasingly popular in recent years, due to advances in Markov chain Monte Carlo computational algorithms. Several methods have been proposed in the case of linear and generalized linear models (GLM). In this paper, we adapt to the CUB model some of these algorithms: the Kuo–Mallick method together with its ‘metropolized’ version and the Stochastic Search Variable Selection method. Several simulated examples are used to illustrate the algorithms and to compare their performance. Finally, an application to real data is introduced. [ABSTRACT FROM PUBLISHER]

Interval-censored data arise when a failure time say,Tcannot be observed directly but can only be determined to lie in an interval obtained from a series of inspection times. The frequentist approach for analysing interval-censored data has been developed for some time now. It is very common due to unavailability of software in the field of biological, medical and reliability studies to simplify the interval censoring structure of the data into that of a more standard right censoring situation by imputing the midpoints of the censoring intervals. In this research paper, we apply the Bayesian approach by employing Lindley's 1980, and Tierney and Kadane 1986 numerical approximation procedures when the survival data under consideration are interval-censored. The Bayesian approach to interval-censored data has barely been discussed in literature. The essence of this study is to explore and promote the Bayesian methods when the survival data been analysed are is interval-censored. We have considered only a parametric approach by assuming that the survival data follow a loglogistic distribution model. We illustrate the proposed methods with two real data sets. A simulation study is also carried out to compare the performances of the methods. [ABSTRACT FROM AUTHOR]

Interval-censored survival data arise often in medical applications and clinical trials [Wang L, Sun J, Tong X. Regression analyis of case II interval-censored failure time data with the additive hazards model. Statistica Sinica. 2010;20:1709-1723]. However, most of existing interval-censored survival analysis techniques suffer from challenges such as heavy computational cost or non-proportionality of hazard rates due to complicated data structure [Wang L, Lin X. A Bayesian approach for analyzing case 2 interval-censored data under the semiparametric proportional odds model. Statistics & Probability Letters. 2011;81:876-883; Banerjee T, Chen M-H, Dey DK, et al. Bayesian analysis of generalized odds-rate hazards models for survival data. Lifetime Data Analysis. 2007;13:241-260]. To address these challenges, in this paper, we introduce a flexible Bayesian non-parametric procedure for the estimation of the odds under interval censoring, case II. We use Bernstein polynomials to introduce a prior for modeling the odds and propose a novel and easy-to-implement sampling manner based on the Markov chain Monte Carlo algorithms to study the posterior distributions. We also give general results on asymptotic properties of the posterior distributions. The simulated examples show that the proposed approach is quite satisfactory in the cases considered. The use of the proposed method is further illustrated by analyzing the hemophilia study data [McMahan CS, Wang L. A package for semiparametric regression analysis of interval-censored data; 2015. [ABSTRACT FROM AUTHOR]

Feature selection arises in many areas of modern science. For example, in genomic research, we want to find the genes that can be used to separate tissues of different classes (e.g. cancer and normal). One approach is to fit regression/classification models with certain penalization. In the past decade, hyper-LASSO penalization (priors) have received increasing attention in the literature. However, fully Bayesian methods that use Markov chain Monte Carlo (MCMC) for regression/classification with hyper-LASSO priors are still in lack of development. In this paper, we introduce an MCMC method for learning multinomial logistic regression with hyper-LASSO priors. Our MCMC algorithm uses Hamiltonian Monte Carlo in a restricted Gibbs sampling framework. We have used simulation studies and real data to demonstrate the superior performance of hyper-LASSO priors compared to LASSO, and to investigate the issues of choosing heaviness and scale of hyper-LASSO priors. [ABSTRACT FROM AUTHOR]

In this paper, we consider the Bayesian analysis of binary time series with different priors, namely normal, Students' t, and Jeffreys prior, and compare the results with the frequentist methods through some simulation experiments and one real data on daily rainfall in inches at Mount Washington, NH. Among Bayesian methods, our results show that the Jeffreys prior perform better in most of the situations for both the simulation and the rainfall data. Furthermore, among weakly informative priors considered, Student's t prior with 7 degrees of freedom fits the data most adequately. [ABSTRACT FROM AUTHOR]

The existing studies on spatial dynamic panel data model (SDPDM) mainly focus on the normality assumption of response variables and random effects. This assumption may be inappropriate in some applications. This paper proposes a new SDPDM by assuming that response variables and random effects follow the multivariate skew-normal distribution. A Markov chain Monte Carlo algorithm is developed to evaluate Bayesian estimates of unknown parameters and random effects in skew-normal SDPDM by combining the Gibbs sampler and the Metropolis-Hastings algorithm. A Bayesian local influence analysis method is developed to simultaneously assess the effect of minor perturbations to the data, priors and sampling distributions. Simulation studies are conducted to investigate the finite-sample performance of the proposed methodologies. An example is illustrated by the proposed methodologies. [ABSTRACT FROM AUTHOR]

In sequential plays with two players, the players have the opportunity to use information on opponents’ past moves in selecting a move for the current stage. Strategies for Player II are considered in our study, in particular, play against the random past (PRP) strategy. In this paper, PRP strategy will be reviewed and discussed. Hannan consistency of PRP strategy in term of regret (difference in average loss and an envelope loss) on k-extended Bayes envelope risk problem in matching binary bits game will be shown. The simulation of two-experts selection problem on real experts’ forecasting data of IBM share earnings confirms the consistency of PRP strategy. [ABSTRACT FROM AUTHOR]

The lasso is a popular technique of simultaneous estimation and variable selection in many research areas. The marginal posterior mode of the regression coefficients is equivalent to estimates given by the non-Bayesian lasso when the regression coefficients have independent Laplace priors. Because of its flexibility of statistical inferences, the Bayesian approach is attracting a growing body of research in recent years. Current approaches are primarily to either do a fully Bayesian analysis using Markov chain Monte Carlo (MCMC) algorithm or use Monte Carlo expectation maximization (MCEM) methods with an MCMC algorithm in each E-step. However, MCMC-based Bayesian method has much computational burden and slow convergence. Tan et al. [An efficient MCEM algorithm for fitting generalized linear mixed models for correlated binary data. J Stat Comput Simul. 2007;77:929–943] proposed a non-iterative sampling approach, the inverse Bayes formula (IBF) sampler, for computing posteriors of a hierarchical model in the structure of MCEM. Motivated by their paper, we develop this IBF sampler in the structure of MCEM to give the marginal posterior mode of the regression coefficients for the Bayesian lasso, by adjusting the weights of importance sampling, when the full conditional distribution is not explicit. Simulation experiments show that the computational time is much reduced with our method based on the expectation maximization algorithm and our algorithms and our methods behave comparably with other Bayesian lasso methods not only in prediction accuracy but also in variable selection accuracy and even better especially when the sample size is relatively large. [ABSTRACT FROM AUTHOR]

Autoregressive model is a popular method for analysing the time dependent data, where selection of order parameter is imperative. Two commonly used selection criteria are the Akaike information criterion (AIC) and the Bayesian information criterion (BIC), which are known to suffer the potential problems regarding overfit and underfit, respectively. To our knowledge, there does not exist a criterion in the literature that can satisfactorily perform under various situations. Therefore, in this paper, we focus on forecasting the future values of an observed time series and propose an adaptive idea to combine the advantages of AIC and BIC but to mitigate their weaknesses based on the concept of generalized degrees of freedom. Instead of applying a fixed criterion to select the order parameter, we propose an approximately unbiased estimator of mean squared prediction errors based on a data perturbation technique for fairly comparing between AIC and BIC. Then use the selected criterion to determine the final order parameter. Some numerical experiments are performed to show the superiority of the proposed method and a real data set of the retail price index of China from 1952 to 2008 is also applied for illustration. [ABSTRACT FROM AUTHOR]

In this paper, we discuss optimum sample size determination for a bounded linex loss function (blinex). The linex loss function is often used when losses are asymmetric, but it has the disadvantage that it can only be used if the moment-generating function of the posterior distribution exists. Blinex loss has the advantage that it can always be calculated. Also many authors have argued that a bounded loss function is to be preferred. We have obtained the optimum sample size for a number of distributions when the cost of sampling is linear. The form of the posterior risk function does not allow an analytical solution so simulation is necessary. [ABSTRACT FROM PUBLISHER]

In this paper, we discuss the regularization in linear-mixed quantile regression. A hierarchical Bayesian model is used to shrink the fixed and random effects towards the common population values by introducing anl1penalty in the mixed quantile regression check function. A Gibbs sampler is developed to simulate the parameters from the posterior distributions. Through simulation studies and analysis of an age-related macular degeneration (ARMD) data, we assess the performance of the proposed method. The simulation studies and the ARMD data analysis indicate that the proposed method performs well in comparison with the other approaches. [ABSTRACT FROM PUBLISHER]

Quantitative model validation is playing an increasingly important role in performance and reliability assessment of a complex system whenever computer modelling and simulation are involved. The foci of this paper are to pursue a Bayesian probabilistic approach to quantitative model validation with non-normality data, considering data uncertainty and to investigate the impact of normality assumption on validation accuracy. The Box–Cox transformation method is employed to convert the non-normality data, with the purpose of facilitating the overall validation assessment of computational models with higher accuracy. Explicit expressions for the interval hypothesis testing-based Bayes factor are derived for the transformed data in the context of univariate and multivariate cases. Bayesian confidence measure is presented based on the Bayes factor metric. A generalized procedure is proposed to implement the proposed probabilistic methodology for model validation of complicated systems. Classic hypothesis testing method is employed to conduct a comparison study. The impact of data normality assumption and decision threshold variation on model assessment accuracy is investigated by using both classical and Bayesian approaches. The proposed methodology and procedure are demonstrated with a univariate stochastic damage accumulation model, a multivariate heat conduction problem and a multivariate dynamic system. [ABSTRACT FROM AUTHOR]

This paper focusses on computing the Bayesian reliability of components whose performance characteristics (degradation - fatigue and cracks) are observed during a specified period of time. Depending upon the nature of degradation data collected, we fit a monotone increasing or decreasing function for the data. Since the components are supposed to have different lifetimes, the rate of degradation is assumed to be a random variable. At a critical level of degradation, the time to failure distribution is obtained. The exponential and power degradation models are studied and exponential density function is assumed for the random variable representing the rate of degradation. The maximum likelihood estimator and Bayesian estimator of the parameter of exponential density function, predictive distribution, hierarchical Bayes approach and robustness of the posterior mean are presented. The Gibbs sampling algorithm is used to obtain the Bayesian estimates of the parameter. Illustrations are provided for the train wheel degradation data. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of estimating unknown parameters of the Burr XII distribution under classical and Bayesian approaches when samples are observed under progressive type-I interval censoring. Under classical approach we employ the stochastic expectation maximization algorithm to obtain maximum likelihood estimators for the unknown parameters and also compute associated interval estimates. Further under Bayesian approach we obtain Bayes estimators with respect to different symmetric, asymmetric and balanced loss functions. In this regard we use Tierney–Kadane and Metropolis–Hastings (MH) algorithm. For illustration purpose we analyse a real data set and conduct a Monte Carlo simulation study to observe the performance of the proposed estimators. Finally we present a discussion on inspection times and optimal censoring. [ABSTRACT FROM PUBLISHER]

The max-stable process is a natural approach for modelling extrenal dependence in spatial data. However, the estimation is difficult due to the intractability of the full likelihoods. One approach that can be used to estimate the posterior distribution of the parameters of the max-stable process is to employ composite likelihoods in the Markov chain Monte Carlo (MCMC) samplers, possibly with adjustment of the credible intervals. In this paper, we investigate the performance of the composite likelihood-based MCMC samplers under various settings of the Gaussian extreme value process and the Brown–Resnick process. Based on our findings, some suggestions are made to facilitate the application of this estimator in real data. [ABSTRACT FROM PUBLISHER]

Segmentation models aim to partition compositionally heterogeneous domains into homogeneous segments which may be reflective of biological function. Due to the latent nature of the segments a natural approach to segmentation that has gained favour recently uses Bayesian hidden Markov models (HMMs). Concomitantly in the last few decades, the free R programming language has become a dominant tool for computational statistics, visualization and data science. Therefore, this paper aims to fully exploit R to fit a Bayesian HMM for DNA segmentation. The joint posterior distribution of parameters in the model to be considered is derived followed by the algorithms that can be used for estimation. Functions following these algorithms (Gibbs Sampling, Data Augmentation and Label Switching) are then fully implemented in R. The methodology is assessed through extensive simulation studies and then being applied to analyse Simian Vacuolating virus (SV40). It is concluded that: (1) the algorithms and functions in R can correctly estimate sequence segmentation if the HMM structure is assumed; (2) the performance of the model improves with sequence length; (3) R is reasonably fast for short to medium sequence lengths and number of segments and (4) the segmentation of SV40 appears to correspond with the two major transcripts, early and late, that regulate the expression of SV40 genes. [ABSTRACT FROM AUTHOR]

In this paper, based on a progressively Type-II right censored sample, we discuss the prediction of k-record values from a future sequence. By considering the parent distribution as exponential, we derive Bayesian prediction intervals as well as Bayesian point predictors for k-record values from a future sequence based on an observed progressively Type-II right censored sample. The corresponding results for ordinary Type-II censored sample and the usual order statistics are then deduced as special cases. A real data set concerning the breakdown times of an insulating fluid in an accelerated life-test is used for illustrating all the results developed here. [ABSTRACT FROM PUBLISHER]

The need to simulate from a univariate density arises in several settings, particularly in Bayesian analysis. An especially efficient algorithm which can be used to sample from a univariate density, fX, is the adaptive accept-reject algorithm. To implement the adaptive accept-reject algorithm, the user has to envelope T ∘ fX, where T is some transformation such that the density g(x) ∝ T-1 (α+β x) is easy to sample from. Successfully enveloping T ∘ fX, however, requires that the user identify the number and location of T ∘ fX's inflection points. This is not always a trivial task. In this paper, we propose an adaptive accept-reject algorithm which relieves the user of precisely identifying the location of T ∘ fX's inflection points. This new algorithm is shown to be efficient and can be used to sample from any density such that its support is bounded and its log is three-times differentiable. [ABSTRACT FROM AUTHOR]

System characteristics of a redundant repairable system are studied from a Bayesian viewpoint with different types of priors assumed for the unknown parameters. The system consists of two primary units, one standby unit, and one repair facility which is activated when switching to standby fails. Times to failure and times to repair of the operating units are assumed to follow exponential distributions. When time to failure and time to repair have uncertain parameters, a Bayesian approach is adopted to evaluate system characteristics. Monte Carlo simulation is used to derive the posterior distribution for the mean time to system failure and steady-state availability. Some numerical experiments are performed to illustrate the results derived in this paper. [ABSTRACT FROM AUTHOR]

This paper proposes a two-sided monitoring algorithm of changes in the exponential family. We adopt a Bayesian approach which uses a loss function and takes into account the run length of the process. It also extends the monitoring scheme proposed in [Harrison, P.J., Veerapen, P.P., 1994, A Bayesian decision approach to model monitoring and Cusums. Journal of Forecasting, 13, 29-36.] The algorithm is illustrated with several examples, which analyze the power of the monitor. [ABSTRACT FROM AUTHOR]

In this paper, E-Bayesian and hierarchical Bayesian estimations of the shape parameter, when the underlying distribution belongs to the proportional reversed hazard rate model, are considered. Maximum likelihood, Bayesian and E-Bayesian estimates of the unknown parameter and reliability function are obtained based on record values. The Bayesian estimates are derived based on squared error and linear–exponential loss functions. It is pointed out that some previously obtained order relations of E-Bayesian estimates are inadequate and these results are improved. The relationship between E-Bayesian and hierarchical Bayesian estimations is obtained under the same loss functions. The comparison of the derived estimates is carried out by using Monte Carlo simulations. A real data set is analysed for an illustration of the findings. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to develop a full Bayesian analysis for the Birnbaum–Saunders (BS) regression model based on scale mixtures of the normal (SMN) distribution with right-censored survival data. The BS distributions based on SMN models are a very general approach for analysing lifetime data, which has as special cases the Student-t-BS, slash-BS and the contaminated normal-BS distributions, being a flexible alternative to the use of the corresponding BS distribution or any other well-known compatible model, such as the log-normal distribution. A Gibbs sample algorithm with Metropolis–Hastings algorithm is used to obtain the Bayesian estimates of the parameters. Moreover, some discussions on the model selection to compare the fitted models are given and case-deletion influence diagnostics are developed for the joint posterior distribution based on the Kullback–Leibler divergence. The newly developed procedures are illustrated on a real data set previously analysed under BS regression models. [ABSTRACT FROM AUTHOR]

Semiparametric reproductive dispersion mixed model (SPRDMM) is a natural extension of the reproductive dispersion model and the semiparametric mixed model. In this paper, we relax the normality assumption of random effects in SPRDMM and use a truncated and centred Dirichlet process prior to specify random effects, and present the Bayesian P-spline to approximate the smoothing unknown function. A hybrid algorithm combining the block Gibbs sampler and the Metropolis–Hastings algorithm is implemented to sample observations from the posterior distribution. Also, we develop Bayesian case deletion influence measure for SPRDMM based on theφ-divergence and present those computationally feasible formulas. Several simulation studies and a real example are presented to illustrate the proposed methodologies. [ABSTRACT FROM AUTHOR]