Point estimation and related classification problems for several Lindley populations with application using COVID-19 data.

The problems of point estimation and classification under the assumption that the training data follow a Lindley distribution are considered. Bayes estimators are derived for the parameter of the Lindley distribution applying the Markov chain Monte Carlo (MCMC), and Tierney and Kadane's [Tierney and Kadane, Accurate approximations for posterior moments and marginal densities, J. Amer. Statist. Assoc. 81 (1986), pp. 82-86] methods. In the sequel, we prove that the Bayes estimators using Tierney and Kadane's approximation and Lindley's approximation both converge to the maximum likelihood estimator (MLE), as n → ∞ , where n is the sample size. The performances of all the proposed estimators are compared with some of the existing ones using bias and mean squared error (MSE), numerically. It has been noticed from our simulation study that the proposed estimators perform better than some of the existing ones. Applying these estimators, we construct several plug-in type classification rules and a rule that uses the likelihood accordance function. The performances of each of the rules are numerically evaluated using the expected probability of misclassification (EPM). Two real-life examples related to COVID-19 disease are considered for illustrative purposes.

A generalized Gompertz promotion time cure model and its fitness to cancer data.

The cure models based on standard distributions like exponential, Weibull, lognormal, Gompertz, gamma, are often used to analyze survival data from cancer clinical trials with long-term survivors. Sometimes, the data is simple, and the standard cure models fit them very well, however, most often the data are complex and the standard cure models don't fit them reasonably well. In this article, we offer a novel generalized Gompertz promotion time cure model and illustrate its fitness to gastric cancer data by three different methods. The generalized Gompertz distribution is as simple as the generalized Weibull distribution and is not computationally as intensive as the generalized F distribution. One detailed real data application is provided for illustration and comparison purposes.

Full Bayesian analysis of double seasonal autoregressive models with real applications.

We present a full Bayesian analysis of multiplicative double seasonal autoregressive (DSAR) models in a unified way, considering identification (best subset selection), estimation, and prediction problems. We assume that the DSAR model errors are normally distributed and introduce latent variables for the model lags, and then we embed the DSAR model in a hierarchical Bayes normal mixture structure. By employing the Bernoulli prior for each latent variable and the mixture normal and inverse gamma priors for the DSAR model coefficients and variance, respectively, we derive the full conditional posterior and predictive distributions in closed form. Using these derived conditional posterior and predictive distributions, we present the full Bayesian analysis of DSAR models by proposing the Gibbs sampling algorithm to approximate the posterior and predictive distributions and provide multi-step-ahead predictions. We evaluate the efficiency of the proposed full Bayesian analysis of DSAR models using an extensive simulation study, and we then apply our work to several real-world hourly electricity load time series datasets in 16 European countries.

A size-of-loss model for the negatively skewed insurance claims data: applications, risk analysis using different methods and statistical forecasting.

The future values of the expected claims are very important for the insurance companies for avoiding the big losses under uncertainty which may be produced from future claims. In this paper, we define a new size-of-loss distribution for the negatively skewed insurance claims data. Four key risk indicators are defined and analyzed under four estimation methods: maximum likelihood, ordinary least squares, weighted least squares, and Anderson Darling. The insurance claims data are modeled using many competitive models and comprehensive comparison is performed under nine statistical tests. The autoregressive model is proposed to analyze the insurance claims data and estimate the future values of the expected claims. The value-at-risk estimation and the peaks-over random threshold mean-of-order-p methodology are considered.

Dealing with missing data under stratified sampling designs where strata are study domains.

A quick count seeks to estimate the voting trends of an election and communicate them to the population on the evening of the same day of the election. In quick counts, the sampling is based on a stratified design of polling stations. Voting information is gathered gradually, often with no guarantee of obtaining the complete sample or even information in all the strata. However, accurate interval estimates with partial information must be obtained. Furthermore, this becomes more challenging if the strata are additionally study domains. To produce partial estimates, two strategies are proposed: (1) a Bayesian model using a dynamic post-stratification strategy and a single imputation process defined after a thorough analysis of historic voting information; additionally, a credibility level correction is included to solve the underestimation of the variance and (2) a frequentist alternative that combines standard multiple imputation ideas with classic sampling techniques to obtain estimates under a missing information framework. Both solutions are illustrated and compared using information from the 2021 quick count. The aim was to estimate the composition of the Chamber of Deputies in Mexico.

Estimation and prediction for Burr type III distribution based on unified progressive hybrid censoring scheme.

The present communication develops the tools for estimation and prediction of the Burr-III distribution under unified progressive hybrid censoring scheme. The maximum likelihood estimates of model parameters are obtained. It is shown that the maximum likelihood estimates exist uniquely. Expectation maximization and stochastic expectation maximization methods are employed to compute the point estimates of unknown parameters. Based on the asymptotic distribution of the maximum likelihood estimators, approximate confidence intervals are proposed. In addition, the bootstrap confidence intervals are constructed. Furthermore, the Bayes estimates are derived with respect to squared error and LINEX loss functions. To compute the approximate Bayes estimates, Metropolis-Hastings algorithm is adopted. The highest posterior density credible intervals are obtained. Further, maximum a posteriori estimates of the model parameters are computed. The Bayesian predictive point, as well as interval estimates, are proposed. A Monte Carlo simulation study is employed in order to evaluate the performance of the proposed statistical procedures. Finally, two real data sets are considered and analysed to illustrate the methodologies established in this paper.

Bayesian heterogeneity in a meta-analysis with two studies and binary data.

The meta-analysis of two trials is valuable in many practical situations, such as studies of rare and/or orphan diseases focussed on a single intervention. In this context, additional concerns, like small sample size and/or heterogeneity in the results obtained, might make standard frequentist and Bayesian techniques inappropriate. In a meta-analysis, moreover, the presence of between-sample heterogeneity adds model uncertainty, which must be taken into consideration when drawing inferences. We suggest that the most appropriate way to measure this heterogeneity is by clustering the samples and then determining the posterior probability of the cluster models. The meta-inference is obtained as a mixture of all the meta-inferences for the cluster models, where the mixing distribution is the posterior model probability. We present a simple two-component form of Bayesian model averaging that is unaffected by characteristics such as small study size or zero-cell counts, and which is capable of incorporating uncertainties into the estimation process. Illustrative examples are given and analysed, using real sparse binomial data.

Inference of multicomponent stress-strength reliability following Topp-Leone distribution using progressively censored data.

In this paper, the inference of multicomponent stress-strength reliability has been derived using progressively censored samples from Topp-Leone distribution. Both stress and strength variables are assumed to follow Topp-Leone distributions with different shape parameters. The maximum likelihood estimate along with the asymptotic confidence interval are developed. Boot-p and Boot-t confidence intervals are also constructed. The Bayes estimates under generalized entropy loss function based on gamma priors using Lindley's, Tierney-Kadane's approximation and Markov chain Monte Carlo methods are derived. A simulation study is considered to check the performance of various estimation methods and different censoring schemes. A real data study shows the applicability of the proposed estimation methods.

Generalized Geographically Weighted Regression Model within a Modularized Bayesian Framework.

Geographically weighted regression (GWR) models handle geographical dependence through a spatially varying coefficient model and have been widely used in applied science, but its general Bayesian extension is unclear because it involves a weighted log-likelihood which does not imply a probability distribution on data. We present a Bayesian GWR model and show that its essence is dealing with partial misspecification of the model. Current modularized Bayesian inference models accommodate partial misspecification from a single component of the model. We extend these models to handle partial misspecification in more than one component of the model, as required for our Bayesian GWR model. Information from the various spatial locations is manipulated via a geographically weighted kernel and the optimal manipulation is chosen according to a Kullback-Leibler (KL) divergence. We justify the model via an information risk minimization approach and show the consistency of the proposed estimator in terms of a geographically weighted KL divergence.

Shrinkage with shrunken shoulders: Gibbs sampling shrinkage model posteriors with guaranteed convergence rates.

Use of continuous shrinkage priors - with a "spike" near zero and heavy-tails towards infinity - is an increasingly popular approach to induce sparsity in parameter estimates. When the parameters are only weakly identified by the likelihood, however, the posterior may end up with tails as heavy as the prior, jeopardizing robustness of inference. A natural solution is to "shrink the shoulders" of a shrinkage prior by lightening up its tails beyond a reasonable parameter range, yielding a regularized version of the prior. We develop a regularization approach which, unlike previous proposals, preserves computationally attractive structures of original shrinkage priors. We study theoretical properties of the Gibbs sampler on resulting posterior distributions, with emphasis on convergence rates of the Pólya-Gamma Gibbs sampler for sparse logistic regression. Our analysis shows that the proposed regularization leads to geometric ergodicity under a broad range of global-local shrinkage priors. Essentially, the only requirement is for the prior πlocal(⋅) on the local scale λ to satisfy πlocal(0)<∞. If πlocal(⋅) further satisfies limλ→0πlocal(λ)/λa<∞ for a>0, as in the case of Bayesian bridge priors, we show the sampler to be uniformly ergodic.

Inference on Nadarajah-Haghighi distribution with constant stress partially accelerated life tests under progressive type-II censoring.

This paper presents methods of estimation of the parameters and acceleration factor for Nadarajah-Haghighi distribution based on constant-stress partially accelerated life tests. Based on progressive Type-II censoring, Maximum likelihood and Bayes estimates of the model parameters and acceleration factor are established, respectively. In addition, approximate confidence interval are constructed via asymptotic variance and covariance matrix, and Bayesian credible intervals are obtained based on importance sampling procedure. For comparison purpose, alternative bootstrap confidence intervals for unknown parameters and acceleration factor are also presented. Finally, extensive simulation studies are conducted for investigating the performance of the our results, and two data sets are analyzed to show the applicabilities of the proposed methods.

A discrete analogue of odd Weibull-G family of distributions: properties, classical and Bayesian estimation with applications to count data.

In the statistical literature, several discrete distributions have been developed so far. However, in this progressive technological era, the data generated from different fields is getting complicated day by day, making it difficult to analyze this real data through the various discrete distributions available in the existing literature. In this context, we have proposed a new flexible family of discrete models named discrete odd Weibull-G (DOW-G) family. Its several impressive distributional characteristics are derived. A key feature of the proposed family is its failure rate function that can take a variety of shapes for distinct values of the unknown parameters, like decreasing, increasing, constant, J-, and bathtub-shaped. Furthermore, the presented family not only adequately captures the skewed and symmetric data sets, but it can also provide a better fit to equi-, over-, under-dispersed data. After producing the general class, two particular distributions of the DOW-G family are extensively studied. The parameters estimation of the proposed family, are explored by the method of maximum likelihood and Bayesian approach. A compact Monte Carlo simulation study is performed to assess the behavior of the estimation methods. Finally, we have explained the usefulness of the proposed family by using two different real data sets.

Bayesian inference in based-kernel regression: comparison of count data of condition factor of fish in pond systems.

The discrete kernel-based regression approach generally provides pointwise estimates of count data that do not account for uncertainty about both parameters and resulting estimates. This work aims to provide probabilistic kernel estimates of count regression function by using Bayesian approach and then allows for a readily quantification of uncertainty. Bayesian approach enables to incorporate prior knowledge of parameters used in discrete kernel-based regression. An application was proposed on count data of condition factor of fish (K) provided from an experimental project that analyzed various pond management strategies. The probabilistic distribution of estimates were contrasted by discrete kernels, as a support to theoretical results on the performance of kernels. More practically, Bayesian credibility intervals of K-estimates were evaluated to compare pond management strategies. Thus, similarities were found between performances of semi-intensive and coupled fishponds, with formulated feed, in comparison with extensive fishponds, without formulated feed. In particular, the fish development was less predictable in extensive fishpond, dependent on natural resources, than in the two other fishponds, supplied in formulated feed.

Bayesian estimation of extropy and goodness of fit tests.

Extropy, a complementary dual of entropy, is considered in this paper. A Bayesian approach based on the Dirichlet process is proposed for the estimation of extropy. A goodness of fit test is also developed. Many theoretical properties of the procedure are derived. Several examples are discussed to illustrate the approach.

Predictive analysis for joint progressive censoring plans: a Bayesian approach.

Comparative lifetime experiments are of particular importance in production processes when one wishes to determine the relative merits of several competing products with regard to their reliability. This paper confines itself to the data obtained by running a joint progressive Type-II censoring plan on samples in a combined manner. The problem of Bayesian predicting failure times of surviving units is discussed in details when parent populations are exponential. Two real data sets are analyzed in order to illustrate all the inferential procedures developed here. When destructive experiments under a censoring scheme finished, the researchers are usually interested to estimate remaining lifetimes of surviving units for sequel experiments. Findings of this paper are useful for these purposes specially when samples are non-homogeneous such as those taken from industrial storages.

Bayesian analyses of an exponential-Poisson and related zero augmented type models.

We consider several alternatives to the continuous exponential-Poisson distribution in order to accommodate the occurrence of zeros. Three of these are modifications of the exponential-Poisson model. One of these remains a fully continuous model. The other models we consider are all semi-continuous models, each with a discrete point mass at zero and a continuous density on the positive values. All of the models are applied to two environmental data sets concerning precipitation, and their Bayesian analyses using MCMC are discussed. This discussion covers convergence of the MCMC simulations and model selection procedures and considerations.

Joint modelling of longitudinal response and time-to-event data using conditional distributions: a Bayesian perspective.

Over the last 20 or more years a lot of clinical applications and methodological development in the area of joint models of longitudinal and time-to-event outcomes have come up. In these studies, patients are followed until an event, such as death, occurs. In most of the work, using subject-specific random-effects as frailty, the dependency of these two processes has been established. In this article, we propose a new joint model that consists of a linear mixed-effects model for longitudinal data and an accelerated failure time model for the time-to-event data. These two sub-models are linked via a latent random process. This model will capture the dependency of the time-to-event on the longitudinal measurements more directly. Using standard priors, a Bayesian method has been developed for estimation. All computations are implemented using OpenBUGS. Our proposed method is evaluated by a simulation study, which compares the conditional model with a joint model with local independence by way of calibration. Data on Duchenne muscular dystrophy (DMD) syndrome and a set of data in AIDS patients have been analysed.

An objective Bayesian approach to estimation in multistage experiments.

This article presents a Bayesian approach to estimation in multistage experiments based on the reference prior theory. The idea of deriving design-dependent priors was first introduced using Jeffreys' criterion. A theoretical framework was then established by showing that explicit reference to the design is fully Bayesian justified and Bayesian objectivity cannot ignore such information. Extending the work to multi-parameter problems, a general form of priors was derived from the reference prior theory. In this article, I evidence the good frequentist properties of the reference posterior estimators with normally distributed data. As a notable advance, I address the issue of the point and the interval estimations upon experiment termination. The approach is applied to a data set collected in a clinical trial in schizophrenia with the possibility to stop the trial early if interim results provide sufficient evidence of efficacy or futility. Finally, I discuss the idea of using the reference posterior estimators as a default choice for objective estimation in multistage experiment.

A Matrix-Variate t Model for Networks.

Networks represent a useful tool to describe relationships among financial firms and network analysis has been extensively used in recent years to study financial connectedness. An aspect, which is often neglected, is that network observations come with errors from different sources, such as estimation and measurement errors, thus a proper statistical treatment of the data is needed before network analysis can be performed. We show that node centrality measures can be heavily affected by random errors and propose a flexible model based on the matrix-variate t distribution and a Bayesian inference procedure to de-noise the data. We provide an application to a network among European financial institutions.

A grouped beta process model for multivariate resting-state EEG microstate analysis on twins.

EEG microstate analysis investigates the collection of distinct temporal blocks that characterize the electrical activity of the brain. Brain activity within each microstate is stable, but activity switches rapidly between different microstates in a nonrandom way. We propose a Bayesian nonparametric model that concurrently estimates the number of microstates and their underlying behaviour. We use a Markov switching vector autoregressive (VAR) framework, where a hidden Markov model (HMM) controls the nonrandom state switching dynamics of the EEG activity and a VAR model defines the behaviour of all time points within a given state. We analyze the resting-state EEG data from twin pairs collected through the Minnesota Twin Family Study, consisting of 70 epochs per participant, where each epoch corresponds to 2 s of EEG data. We fit our model at the twin pair level, sharing information within epochs from the same participant and within epochs from the same twin pair. We capture within twin-pair similarity, using an Indian buffet process, to consider an infinite library of microstates, allowing each participant to select a finite number of states from this library. The state spaces of highly similar twins may completely overlap while dissimilar twins could select distinct state spaces. In this way, our Bayesian nonparametric model defines a sparse set of states that describe the EEG data. All epochs from a single participant use the same set of states and are assumed to adhere to the same state switching dynamics in the HMM model, enforcing within-participant similarity.

L'analyse des micro-états d'un électroencéphalogramme (EEG) porte sur une collection de différents blocs temporels caractérisant l'activité électrique du cerveau. L'activité cérébrale est stable à l'intérieur de chaque bloc, mais elle varie rapidement entre les différents micro-états de façon non aléatoire. Les auteurs proposent un modèle bayésien non paramétrique qui estime simultanément le nombre de micro-états et leur comportement sous-jacent. Ils utilisent le cadre de vecteurs autorégressifs (VAR) markoviens commutants où un modèle de Markov caché (MMC) contrôle les dynamiques de commutations non aléatoires de l'activité de l'EEG et le modèle de VAR définit le comportement à travers le temps pour un état donné. Ils analysent des données d'EEG au repos de paires de jumeaux collectées dans l'étude des jumeaux du Minnesota comportant 70 époques de deux secondes d'EEG chacune pour chaque participant. Les auteurs ajustent leur modèle au niveau des paires de jumeaux, partageant les informations d'un participant et de son jumeau pour une même époque. Ils capturent les similarités dans la paire de jumeaux avec un processus du buffet indien afin de constituer une bibliothèque infinie de micro-états et de permettre à chaque participant de choisir un ensemble fini d'états provenant de celle-ci. L'espace d'états de jumeaux très semblables peut se chevaucher entièrement alors que des jumeaux différents pourraient avoir des espaces distincts. Le modèle bayésien non paramétrique des auteurs définit ainsi un ensemble creux d'états qui décrivent les données d'EEG. Toutes les époques d'un même participant utilisent le même ensemble d'états, et elles doivent adhérer au même régime de changement d'état pour leur dynamique de commutation selon le MMC, forçant ainsi une similarité intra-participant.