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A new Bayesian–inspired statistic for hypothesis testing is proposed which compares two posterior distributions; the observed posterior and the expected posterior under the null model. The Kullback–Leibler divergence between the two posterior distributions yields a test statistic which can be interpreted as a penalized log–Bayes factor with the penalty term converging to a constant as the sample size increases. Hence, asymptotically, the statistic behaves as a Bayes factor. Viewed as a penalized Bayes factor, this approach solves the long standing issue of using improper priors with the Bayes factor, since only posterior summaries are needed for the new statistic. Further motivation for the new statistic is a minimal move from the Bayes factor which requires no tuning nor splitting of data into training and inference, and can use improper priors. Critical regions for the test can be assessed using frequentist notions of Type I error.

Estimating demand for large assortments of differentiated goods requires the specification of a demand system that is sufficiently flexible. However, flexible models are highly parameterized so estimation requires appropriate forms of regularization to avoid overfitting. In this paper, we study the specification of Bayesian shrinkage priors for pairwise product substitution parameters. We use a log-linear demand system as a leading example. Log-linear models are parameterized by own and cross-price elasticities, and the total number of elasticities grows quadratically in the number of goods. Traditional regularized estimators shrink regression coefficients towards zero which can be at odds with many economic properties of price effects. We propose a hierarchical extension of the class of global-local priors commonly used in regression modeling to allow the direction and rate of shrinkage to depend on a product classification tree. We use both simulated data and retail scanner data to show that, in the absence of a strong signal in the data, estimates of price elasticities and demand predictions can be improved by imposing shrinkage to higher-level group elasticities rather than zero.

We propose a likelihood-based Bayesian method that exploits up-to-date sequential Monte Carlo methods to efficiently estimate long-run risk models in which the conditional variance of consumption growth follows either an autoregressive (AR) process or an autoregressive gamma (ARG) process. We use the U.S. quarterly consumption and asset returns data from the postwar period to implement estimation. Our findings are: (1) informative priors on the preference parameters can help to improve model performance; (2) expected consumption growth has a very persistent component, whereas consumption volatility is less persistent; (3) while the ARG-based model performs better than the AR-based one statistically, the latter could fit asset returns better; and (4) the solution method matters more for estimation in the AR-based model than in the ARG-based model.

Given a Wiener process with unknown and unobservable drift, we try to estimate this drift as effectively but also as quickly as possible, in the presence of a quadratic penalty for the estimation error and of a fixed, positive cost per unit of observation time. In a Bayesian framework, where the unobservable drift is assumed to have a known “prior” distribution, this question reduces to choosing judiciously a stopping time for an appropriate diffusion process in natural scale. We establish structural properties of the solution for the corresponding problem of optimal stopping. In particular, we show that, regardless of the prior distribution, the continuation region is monotonically shrinking in time. Moreover, we provide conditions on the prior distribution that guarantee a one-sided stopping region. Lastly, some concrete prior distributions are studied to illustrate the theoretical results.

International audience; A hyperspectral image sequence can be obtained at different time in the same region from a hyperspectral sensor. The environmental change usually leads to variation in endmember reflectance, which has an important influence on unmixing process. In this article, a Bayesian unmixing model considering spectral variability for hyperspectral sequence is proposed, in which composite prior distributions of abundance and endmember variability are developed. The abundance priors consider the continuity of abundance in the temporal and spatial domains, simultaneously. Specifically, in the spatial domain, a data-adaptive variance of the abundance prior distribution is put forward based on local spatial difference. Moreover, the priors of endmember variability in temporal continuity and spectral smoothness are also exploited. Finally, a joint posterior distribution is obtained by the likelihood function and the parameter prior distributions, which can be calculated by the Markov chain Monte Carlo (MCMC) algorithm. Experiments on synthetic and real data sets demonstrate the effectiveness of the proposed approach in terms of abundance, endmember, and its variability estimation accuracy.

The elicitation of power priors, based on the availability of historical data, is realized by raising the likelihood function of the historical data to a fractional power δ , which quantifies the degree of discounting of the historical information in making inference with the current data. When δ is not pre-specified and is treated as random, it can be estimated from the data using Bayesian updating paradigm. However, in the original form of the joint power prior Bayesian approach, certain positive constants before the likelihood of the historical data could be multiplied when different settings of sufficient statistics are employed. This would change the power priors with different constants, and hence the likelihood principle is violated. In this article, we investigate a normalized power prior approach which obeys the likelihood principle and is a modified form of the joint power prior. The optimality properties of the normalized power prior in the sense of minimizing the weighted Kullback–Leibler divergence are investigated. By examining the posteriors of several commonly used distributions, we show that the discrepancy between the historical and the current data can be well quantified by the power parameter under the normalized power prior setting. Efficient algorithms to compute the scale factor is also proposed. In addition, we illustrate the use of the normalized power prior Bayesian analysis with three data examples, and provide an implementation with an R package NPP.

A Bayesian treatment of the proportional hazard (PH) model is revisited using Dirichlet process and gamma process priors for the baseline survival and cumulative hazard functions respectively. Such priors, due to their discrete support, conflict with the absolutely continuous nature of survival responses expressed through the hazard function structure that defines the PH model. We resolve this conflict through the use of a proposed e -grid likelihood approach which we apply to the PH model to consider marginal inference for the regression parameter β using expansions as e ↓ 0 . Using Dirichlet process priors, the e -grid likelihood approach leads to a new explicit marginal posterior density expansion for β which accommodates the most general setting with arbitrary ties and right censoring. In the previously considered case of gamma process priors, the approach extends the results of Kalbfleisch (1978) to deal with arbitrary arrangements of ties and also provides a rigorous justification for his posterior expressions. As in Kalbfleisch (1978), we show that the leading terms of both expansions approximate Cox’s partial likelihood when there are no ties and the process priors are diffuse. The e -grid likelihood approach is similar in concept to the grouped data likelihood approach of Sinha et al. (2003) but differs in the likelihood approximation. Whereas our expansions are Poincare expansions (with relative error O ( e ) as e ↓ 0 ), those of Sinha et al. (2003) are stochastic expansions and not proper Poincare expansion (as we show), so that they lack relative error O ( e ) . Using a flat improper prior for β , the two marginal posterior expressions for β are shown to be integrable for general arrangements of ties and censoring under weak conditions on the design and failures.

Probability theory provides the general framework within which assignments of probabilities of past, present, and future events are coherently modified in the light of observed events or, more generally, new information. Forensic scientists, as an illustrative example, routinely face tasks of reasoning under uncertainty when they seek to assist members of the judiciary in evaluating or interpreting the meaning of items of scientific evidence. As a consequence of the laws of probability theory and related concepts, Bayes’ theorem is the key rule according to which to conduct such reasoning in order to comply with the requirement of rationality. This quantification, though, does not represent the end of the matter as the forensic scientist may also be confronted with questions of how to make a rational choice amongst alternative courses of action. This article presents the role of Bayes’ theorem, and its extension to decision analysis, in categorical and continuous data analysis in forensic science applications. It emphasizes the importance of propositional hierarchies, the role of background information, the interpretation of probability as personal degrees of belief and the personal quantification of the consequences of decisions. The discussion also includes a sketch of some common pitfalls of intuition associated with probabilistic reasoning in legal contexts.

Population-based seroprevalence surveys can provide useful estimates of the number of individuals previously infected with serious acute respiratory syndrome coronavirus 2 (SARS-CoV-2) and still susceptible, as well as contribute to better estimates of the case-fatality rate and other measures of coronavirus disease 2019 (COVID-19) severity. No serological test is 100% accurate, however, and the standard correction that epidemiologists use to adjust estimates relies on estimates of the test sensitivity and specificity often based on small validation studies. We have developed a fully Bayesian approach to adjust observed prevalence estimates for sensitivity and specificity. Application to a seroprevalence survey conducted in New York State in 2020 demonstrates that this approach results in more realistic—and narrower—credible intervals than the standard sensitivity analysis using confidence interval endpoints. In addition, the model permits incorporating data on the geographical distribution of reported case counts to create informative priors on the cumulative incidence to produce estimates and credible intervals for smaller geographic areas than often can be precisely estimated with seroprevalence surveys.

Regression models play a vital role in the study of data regarding survival of subjects. The Cox proportional hazards model for regression analysis has been frequently used in survival modelling. In survival studies, it is also possible that survival time may occur with multiple occurrences of event or competing risks. The situation of competing risks arises when there are more than one mutually exclusive causes of death (or failure) for the person (or subject). In this paper, we developed a parametric regression model using Gompertz distribution via the Cox proportional hazards model with competing risks. We discussed point and interval estimation of unknown parameters and cumulative cause-specific hazard function with maximum-likelihood method and Bayesian method of estimation. The Bayes estimates are obtained based on non-informative priors and symmetric as well as asymmetric loss functions. To observe the finite sample behaviour of the proposed model under both estimation procedures, we carried out a Monte Carlo simulation analysis. To demonstrate our methodology, we also included real data analysis.

Mixture transition distribution time series models build high-order dependence through a weighted combination of first-order transition densities for each one of a specified number of lags. We present a framework to construct stationary transition mixture distribution models that extend beyond linear, Gaussian dynamics. We study conditions for first-order strict stationarity which allow for different constructions with either continuous or discrete families for the first-order transition densities given a pre-specified family for the marginal density, and with general forms for the resulting conditional expectations. Inference and prediction are developed under the Bayesian framework with particular emphasis on flexible, structured priors for the mixture weights. Model properties are investigated both analytically and through synthetic data examples. Finally, Poisson and Lomax examples are illustrated through real data applications.

As agriculture is the backbone of the Indian economy, Government needs a reliable forecast of crop yield for planning new schemes. The most extensively used technique for forecasting crop yield is regression analysis. The significance of parameters is one of the major problems of regression analysis. Non-significant parameters lead to absurd forecast values and these forecast values are not reliable. In such cases, models need to be improved. To improve the models, we have incorporated prior knowledge through the Bayesian technique and investigate the superiority of these models under the Bayesian framework. The Bayesian technique is one of the most powerful methodologies in the modern era of statistics. We have discussed different types of prior (informative, non-informative and conjugate priors). The Markov chain Monte Carlo (MCMC) methodology has been briefly discussed for the estimation of parameters under Bayesian framework. To illustrate these models, production data of banana, mango and wheat yield data are taken under consideration. We compared the traditional regression model with the Bayesian regression model and conclusively infer that the models estimated under Bayesian framework provided superior results as compared to the models estimated under the classical approach.

Estimating incidence of rare cancers is challenging for exceptionally rare entities and in small populations. In a previous study, investigators in the Information Network on Rare Cancers (RARECARENet) provided Bayesian estimates of expected numbers of rare cancers and 95% credible intervals for 27 European countries, using data collected by population-based cancer registries. In that study, slightly different results were found by implementing a Poisson model in integrated nested Laplace approximation/WinBUGS platforms. In this study, we assessed the performance of a Poisson modeling approach for estimating rare cancer incidence rates, oscillating around an overall European average and using small-count data in different scenarios/computational platforms. First, we compared the performance of frequentist, empirical Bayes, and Bayesian approaches for providing 95% confidence/credible intervals for the expected rates in each country. Second, we carried out an empirical study using 190 rare cancers to assess different lower/upper bounds of a uniform prior distribution for the standard deviation of the random effects. For obtaining a reliable measure of variability for country-specific incidence rates, our results suggest the suitability of using 1 as the lower bound for that prior distribution and selecting the random-effects model through an averaged indicator derived from 2 Bayesian model selection criteria: the deviance information criterion and the Watanabe-Akaike information criterion.

In this article, we aim to estimate the parameters of Poisson-Dirichlet mixture model with multigroup data structure by empirical Bayes. The number of mixture components with Bayesian nonparametric process priors is not fixed in advance and it can grow with the increase of data. Empirical Bayes is the useful method to estimate the mixture components without information on them in advance. We give the procedure to construct smooth estimates of base distribution G 0 and estimates of the two parameters α , θ . The performances of estimations for parameters under multigroup data are better than those of the single-group data with the same total size of individuals in the perspectives of bias, standard deviations, and mean squared errors by numerical simulation. Also, we applied Poisson-Dirichlet mixture models to well-known real datasets.

In this paper, Bayes estimators for the shape and scale parameters of Weibull distribution have been obtained using the generalized weighted loss function, based on Exponential priors. Lindley’s approximation has been used effectively in Bayesian estimation. Based on theMonte Carlo simulation method, those estimators are compared depending on the mean squared errors (MSE’s).

In recent years, the finite mixture lifetime models have frequently been used in chemical, physical, social science, biological and other fields due to their methodological development and practical applications. The Bayesian analysis of the mixture models has also developed a significant interest among the statisticians especially in the last decade. However, the most of these contributions are limited to the Bayes estimation for the parameters of lifetime models under singly type I censoring. This paper discusses the Bayesian estimation for the two-component mixture of the lifetime models under doubly censored samples with a particular case for the Burr type VII model. A class of improved priors has been proposed for the posterior estimation. The likelihood function, for doubly censored samples using two-component mixture of life time distributions, has been introduced. The hazard rate function for the mixture model has been compared for different parametric values. The performance of various estimators has been compared under a simulation study along with a real life example.

This paper considers D-optimal designs for linear mixed models involving random effects with unknown distributions. From Bayesian point of view, the Dirichlet process as a prior distribution on the...

This study analyzes the link between temperature and COVID‐19 incidence in a sample of Italian regions during the period that covers the first epidemic wave of 2020. To that end, Bayesian model averaging techniques are used to analyze the relevance of temperature together with a set of additional climatic, demographic, social, and health policy factors. The robustness of individual predictors is measured through posterior inclusion probabilities. The empirical analysis provides conclusive evidence on the role played by temperature given that it appears as one of the most relevant determinants reducing regional coronavirus disease 2019 (COVID‐19) severity. The strong negative link observed in our baseline analysis is robust to the specification of priors, the scale of analysis, the correction of measurement errors in the data due to under‐reporting, the time window considered, and the inclusion of spatial effects in the model. In a second step, we compute relative importance metrics that decompose the variability explained by the model. We find that cross‐regional temperature differentials explain a large share of the observed variation on the number of infections.

The Bayesian approach, a non-classical estimation technique, is very widely used in statistical inference for real world situations. The parameter is considered to be a random variable, and knowledge of the prior distribution is used to update the parameter estimation. Herein, two Bayesian approaches for Poisson parameter estimation by deriving the posterior distribution under the squared error loss or quadratic loss functions are proposed. Their performances were compared with frequentist (maximum likelihood estimator) and Empirical Bayes approaches through Monte Carlo simulations. The mean square error was used as the test criterion for comparing the methods for point estimation; the smallest value indicates the best performing method with the estimated parameter value closest to the true parameter value. Coverage Probabilities (CPs) and average lengths (ALs) were obtained to evaluate the performances of the methods for constructing confidence intervals. The results reveal that the Bayesian approaches were excellent for point estimation when the true parameter value was small (0.5, 1 and 2). In the credible interval comparison, these methods obtained CP values close to the nominal 0.95 confidence level and the smallest ALs for large sample sizes (50 and 100), when the true parameter value was small (0.5, 1 and 2). Doi: 10.28991/esj-2021-01310 Full Text: PDF

In this paper we present a Bayesian approach to estimate the mean of a binary variable and changes in the mean over time, when the variable is subject to misclassification error. These parameters are partially identified and we derive identified sets under various assumptions about the misclassification rates. We apply our method to estimating the prevalence and trend of prescription opioid misuse, using data from the 2002-2014 National Survey on Drug Use and Health. Using a range of priors, the posterior distribution provides evidence that the prevalence of opioid misuse increases multiple times between 2002 and 2012.

This paper considers a general Bayesian test for the multi-sample problem. Specifically, for M independent samples, the interest is to determine whether the M samples are generated from the same multivariate population. First, M Dirichlet processes are considered as priors for the true distributions generated the data. Then, the concentration of the distribution of the total distance between the M posterior processes is compared to the concentration of the distribution of the total distance between the M prior processes through the relative belief ratio. The total distance between processes is established based on the energy distance. Various interesting theoretical results of the approach are derived. Several examples covering the high dimensional case are considered to illustrate the approach.

This article works with an expression of the mean of log Bayes Factor to elucidate its dependence on specified priors. Such explication answers some basic questions about interpreting Bayes Factor ...

Normalized maximum likelihood (NML) distribution of probabilistic model gives the optimal code length function in the sense of minimax regret. Despite its optimal property, the calculation of NML distribution is not easy, and existing efficient methods have been focusing on its asymptotic behavior, or on specific models. This paper gives an efficient way to calculate NML by integral on parameter domain, not on data domain, showing that NML distribution is a Bayesian predictive distribution with a complex prior, based on our novel Fourier expansion approach. Our results provide an integrated way to calculate NML for exponential family and also include a non-asymptotic version of previous work on asymptotic behavior for general cases. The applications of our methodology are not limited to but also include normal distribution, Gamma distribution, Weibull distribution, and von Mises distribution.

International audience; Robust statistical data modelling under potential model mis-specification often requires leaving the parametric world for the nonparametric. In the latter, parameters are infinite dimensional objects such as functions, probability distributions or infinite vectors. In the Bayesian nonparametric approach, prior distributions are designed for these parameters, which provide a handle to manage the complexity of nonparametric models in practice. However, most modern Bayesian nonparametric models seem often out of reach to practitioners, as inference algorithms need careful design to deal with the infinite number of parameters. The aim of this work is to facilitate the journey by providing computational tools for Bayesian nonparametric inference. The article describes a set of functions available in the R package BNPdensity in order to carry out density estimation with an infinite mixture model, including all types of censored data. The package provides access to a large class of such models based on normalized random measures, which represent a generalization of the popular Dirichlet process mixture. One striking advantage of this generalization is that it offers much more robust priors on the number of clusters than the Dirichlet. Another crucial advantage is the complete flexibility in specifying the prior for the scale and location parameters of the clusters, because conjugacy is not required. Inference is performed using a theoretically grounded approximate sampling methodology known as the Ferguson & Klass algorithm. The package also offers several goodness of fit diagnostics such as QQ-plots, including a cross-validation criterion, the conditional predictive ordinate. The proposed methodology is illustrated on a classical ecological risk assessment method called the Species Sensitivity Distribution (SSD) problem, showcasing the benefits of the Bayesian nonparametric framework.

Mixed-effects models are often employed to study individual differences in psychological science. Such analyses commonly entail testing whether between-subjects variability exists and including covariates to explain that variability. We argue that researchers have much to gain by explicitly focusing on the individual in individual differences research. To this end, we propose the spike-and-slab prior distribution for random effect selection in (generalized) mixed-effects models as a means to gain a more nuanced perspective of individual differences. The prior for each random effect is a two-component mixture consisting of a point-mass "spike" centered at zero and a diffuse "slab" capturing nonzero values. Effectively, such an approach allows researchers to answer questions about particular individuals; specifically, "Who is average?", in the sense of deviating from an average effect, such as the population-averaged slope. We begin with an illustrative example, where the spike-and-slab formulation is used to select random intercepts in logistic regression. This demonstrates the utility of the proposed methodology in a simple setting while also highlighting its flexibility in fitting different kinds of models. We then extend the approach to random slopes that capture experimental effects. In two cognitive tasks, we show that despite there being little variability in the slopes, there were many individual differences in performance. In two simulation studies, we assess the ability of the proposed method to correctly identify (non)average individuals without compromising the mixed-effects estimates. We conclude with future directions for the presented methodology. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

The aim of this study was to propose a procedure for a prediction of the number of fragments generated by fire induced explosions of cylindrical pressure vessels. The prediction is carried out in terms of probabilities of individual fragment numbers. The prevailing numbers of two to four fragments are considered. The fragment number probabilities are estimated by applying data on vessel fragmentations acquired in investigations of past explosion accidents. The pressure vessel explosions known as BLEVEs are considered. The Bayesian analysis is used for the estimation of the fragment number probabilities. This analysis is carried out on the basis of Poisson-gamma model. An approach to developing a gamma prior distribution for the average number of fragments per explosion accident is proposed. The assessment of the fragment number probabilities is carried out by propagating uncertainty related to the average number of fragments to uncertainty in the fragment number probabilities. The stochastic (Monte Carlo) simulation is used for this propagation. Findings of this study are viewed as a possibility to improve the assessment of risk posed by pressure vessel explosions.

Inter-rater agreement measures are used to estimate the degree of agreement between two or more assessors. When the agreement table is ordinal, different weight functions that incorporate row and column scores are used along with the agreement measures. The selection of row and column scores is effectual on the estimated degree of agreement. The weighted measures are prone to the anomalies frequently seen in agreement tables such as unbalanced table structures or grey zones due to the assessment behaviour of the raters. In this study, Bayesian approaches for the estimation of inter-rater agreement measures are proposed. The Bayesian approaches make it possible to include prior information on the assessment behaviour of the raters in the analysis and impose order restrictions on the row and column scores. In this way, we improve the accuracy of the agreement measures and mitigate the impact of the anomalies in the estimation of the strength of agreement between the raters. The elicitation of prior distributions is described theoretically and practically for the Bayesian estimation of five agreement measures with three different weights using an agreement table having two grey zones. A Monte Carlo simulation study is conducted to assess the classification accuracy of the Bayesian and classical approaches for the considered agreement measures for a given level of agreement. Recommendations for the selection of the highest performing agreement measure and weight combination are made in the breakdown of the table structure and sample size.

This article is motivated by the challenge of analysing an agricultural field experiment with observations that are positive on a continuous scale or zero. Such data can be analysed using two-part models, where the distribution is a mixture of a positive distribution and a Bernoulli distribution. However, traditional two-part models do not include any dependencies between the two parts of the model. Since the probability of zero is anticipated to be high when the expected value of the positive part is low, and the other way around, this article introduces dependency-extended two-part models. In addition, these extensions allow for modelling the median instead of the mean, which has advantages when distributions are skewed. The motivating example is an incomplete block trial comparing ten treatments against weed. Gamma and lognormal distributions were used for the positive response, although any density on the support of real numbers can be accommodated. In a cross-validation study, the proposed new models were compared with each other and with a baseline model without dependencies. Model performance and sensitivity to choice of priors were investigated through simulation. A dependency-extended two-part model for the median of the lognormal distribution performed best with regard to mean square error in prediction. Supplementary materials accompanying this paper appear online.

Change-point (CP) VAR models face a dimensionality curse due to the proliferation of parameters that arises when new breaks are detected. We introduce the Sparse CP-VAR model which determines which parameters truly vary when a break is detected. By doing so, the number of new parameters to be estimated at each regime is drastically reduced and the break dynamics becomes easier to be interpreted. The Sparse CP-VAR model disentangles the dynamics of the mean parameters and the covariance matrix. The former uses CP dynamics with shrinkage prior distributions, while the latter is driven by an infinite hidden Markov framework. An extensive simulation study is carried out to compare our approach with existing ones. We provide applications to financial and macroeconomic systems. It turns out that many off-diagonal VAR parameters are zero for the entire sample period and that most break activity is in the covariance matrix. We show that this has important consequences for portfolio optimization, in particular when future instabilities are included in the predictive densities. Forecasting-wise, the Sparse CP-VAR model compares favorably to several time-varying parameter models in terms of density and point forecast metrics.

Bayesian estimations have the advantages of taking into account the uncertainty of all parameter estimates which allows virtually the use of vague priors. This study focused on determining the quantile range at which optimal hyperparameter of normally distributed data with vague information could be obtained in Bayesian estimation of linear regression models. A Monte Carlo simulation approach was used to generate a sample size of 200 data-set. Observation precisions and posterior precisions were estimated from the regression output to determine the posterior means estimate for each model to derive the new dependent variables. The variances were divided into 10 equal parts to obtain the hyperparameters of the prior distribution. Average absolute deviation for model selection was used to validate the adequacy of each model. The study revealed the optimal hyperparameters located at 5th and 7th deciles. The research simplified the process of selecting the hyperparameters of prior distribution from the data with vague information in empirical Bayesian inferences. Keywords: Optimal Hyperparameters; Quantile Ranges; Bayesian Estimation; Vague prior

There are many types of skewed distribution, one of which is the lognormal distribution that is positively skewed and may contain true zero values. The coefficient of quartile variation is a statistical tool used to measure the dispersion of skewed and kurtosis data. The purpose of this study is to establish confidence and credible intervals for the coefficient of quartile variation of a zero-inflated lognormal distribution. The proposed approaches are based on the concepts of the fiducial generalized confidence interval, and the Bayesian method. Coverage probabilities and expected lengths were used to evaluate the performance of the proposed approaches via Monte Carlo simulation. The results of the simulation studies show that the fiducial generalized confidence interval and the Bayesian based on uniform and normal inverse Chi-squared priors were appropriate in terms of the coverage probability and expected length, while the Bayesian approach based on Jeffreys' rule prior can be used as alternatives. In addition, real data based on the red cod density from a trawl survey in New Zealand is used to illustrate the performances of the proposed approaches. Doi: 10.28991/esj-2021-01289 Full Text: PDF

Although Bayesian variable selection methods have been intensively studied, their routine use in practice has not caught up with their non-Bayesian counterparts such as Lasso, likely due to difficu...

Various objective priors have been defined for the common correlation coefficient concerning several bivariate normal populations. In this paper, the proposed approach relies on the asymptotic matching of coverage probabilities corresponding to Bayesian credible intervals considering the corresponding frequentist ones. In the present paper, we focus on several matching criteria including quantile matching, distribution function matching, highest posterior density matching, and matching via inversion of test statistics. In addition, we consider reference priors for different groups of ordering. The proposed methods are investigated and compared between each other in terms of a frequentist coverage probability and then, they are illustrated through a simulation study and two real data examples.

Bayesian regression analysis has great importance in recent years, especially in the Regularization method, Such as ridge, Lasso, adaptive lasso, elastic net methods, where choosing the prior distribution of the interested parameter is the main idea in the Bayesian regression analysis. By penalizing the Bayesian regression model, the variance of the estimators are reduced notable and the bias is getting smaller. The tradeoff between the bias and variance of the penalized Bayesian regression estimator consequently produce more interpretable model with more prediction accuracy. In this paper, we proposed new hierarchical model for the Bayesian quantile regression by employing the scale mixture of normals mixing with truncated gamma distribution that stated by (Li and Lin, 2010) as Laplace prior distribution. Therefore, new Gibbs sampling algorithms are introduced. A comparison has made with classical quantile regression model and with lasso quantile regression model by conducting simulations studies. Our model is comparable and gives better results.

Accelerated Life Testing (ALT) is an effective technique which has been used in different fields to obtain more failures in a shorter period of time. It is more economical than traditional reliability testing. In this article, we propose Bayesian inference approach for planning optimal constant stress ALT with Type I censoring. The lifetime of a test unit follows an exponentiated Lomax distribution. Bayes point estimates of the model parameters and credible intervals under uniform and log-normal priors are obtained. Besides, optimum test plan based on constant stress ALT under Type I censoring is developed by minimizing the pre-posterior variance of a specified low percentile of the lifetime distribution at use condition. Gibbs sampling method is used to find the optimal stress with changing time. The performance of the estimation methods is demonstrated for both simulated and real data sets. Results indicate that both the priors and the sample size affect the optimal Bayesian plans. Further, informative priors provide better results than non-informative priors.

In order to conduct a comparative lifetime experiment in life testing and reliability theory, the joint censoring scheme has received immense popularity in the last decade. Recently, a new improved joint progressive censoring scheme has been introduced in statistical literature, known as balanced joint progressive censoring scheme. The present study deals with the statistical inferences for the balanced jointly progressive type-II censored two Lindley populations. Maximum likelihood estimators of the model parameters are derived and construction of the asymptotic confidence intervals based on the observed Fisher information matrix is discussed. From the Bayesian point of view, the posterior estimates of the unknown model parameters are calculated assuming the informative priors. A numerical study is carried out to evaluate the efficiency and performance of the proposed estimates. A real data set is analyzed to exemplify all the estimation techniques. Lastly, the criteria for an optimum censoring scheme are given.

This article accentuates the estimation of a two-parameter generalized Topp-Leone distribution using dual generalized order statistics (dgos). In the part of estimation, we obtain maximum likelihood (ML) estimates and approximate confidence intervals of the model parameters using dgos, in particular, based on order statistics and lower record values. The Bayes estimate is derived with respect to a squared error loss function using gamma priors. The highest posterior density credible interval is computed based on the MH algorithm. Furthermore, the explicit expressions for single and product moments of dgos from this distribution are also derived. Based on order statistics and lower records, a simulation study is carried out to check the efficiency of these estimators. Two real life data sets, one is for order statistics and another is for lower record values have been analyzed to demonstrate how the proposed methods may work in practice. © 2021 - IOS Press. All rights reserved.

In this paper, we adopt a nonparametric Bayesian approach and investigate the asymptotic behavior of the posterior distribution in continuous-time and general state space semi-Markov processes. In particular, we obtain posterior concentration rates for semi-Markov kernels. For the purposes of this study, we construct robust statistical tests between Hellinger balls around semi-Markov kernels and present some specifications to particular cases, including discrete-time semi-Markov processes and countable state space Markov processes. The objective of this paper is to provide sufficient conditions on priors and semi-Markov kernels that enable us to establish posterior concentration rates.

This paper presents reference priors for non-regular model whose support depends on an unknown parameter. A multi-parameter family which includes both regular and non-regular structures is considered. The resulting priors are obtained by asymptotically maximizing the expected α -divergence between the prior and the corresponding posterior distribution. Some examples of reference priors for typical multi-parameter non-regular distributions such as the location-scale family of distributions and the truncated Weibull distribution are also given.

The paper investigates a mixture of expert models. The mixture of experts is a combination of experts, local approximation model, and a gate function, which weighs these experts and forms their ensemble. In this work, each expert is a linear model. The gate function is a neural network with softmax on the last layer. The paper analyzes various prior distributions for each expert. The authors propose a method that takes into account the relationship between prior distributions of different experts. The EM algorithm optimises both parameters of the local models and parameters of the gate function. As an application problem, the paper solves a problem of shape recognition on images. Each expert fits one circle in an image and recovers its parameters: the coordinates of the center and the radius. The computational experiment uses synthetic and real data to test the proposed method. The real data is a human eye image from the iris detection problem.

This study aims to determine the most appropriate warranty period and policy with the lowest warranty cost from the manufacturer/seller point of view. The warranty policy to be put forward and the warranty period to be offered under this policy should ensure customer satisfaction while at the same time causing a minimum cost to the manufacturer/seller. For this reason, the optimum warranty period within the scope of Free-Replacement Warranty (FRW) policy, Pro-Rata Warranty (PRW) policy, and Combined FRW/PRW policy which was the combination of those two warranty policies were tried to be determined. In the study which was done to determine the most appropriate warranty period, economic benefit and the benefit function obtained from warranty cost and dissatisfaction cost functions were used. While obtaining necessary formulas, exponential distribution, which was widely used in life tests as density function and gamma and inverse-gamma functions as prior distribution of the exponential distribution were used. To demonstrate the applicability and flexibility of the model, some typical sales models and numerical values for exponential lifetime distribution were used, and an algorithm was created to find the optimal solution. When all of the results were analyzed it was seen that Combined FRW/PRW policy was the most appropriate warranty cost as a result of testing the models obtained and it was also found that the warranty cost was almost 3% of the sale price. Within the frame of these obtained results, Combined FRW/PRW policy was suggested for the warranty service to be served with the product to the manufacturer/seller. If the warranty period number of revolutions were chosen almost g1=0.054., g2=0.120. the warranty cost will be in the minimum level and it will be almost 3% of the product sale price. The validity and accuracy of the proposed strategy was verified by a case study with a numerical sample providing a scientific basis. WOS:000665658800001 2-s2.0-85108637834

Number and brightness (N&B) analysis is useful for monitoring the spatial distribution of the concentration and oligomeric state of fluorescently labeled proteins in cells. N&B analysis is based on the statistical analysis of fluorescence images by using the method of moments (MoM). Furthermore, N&B analysis can determine the particle number and particle brightness, which indicate the concentration and oligomeric state, respectively. However, the statistical accuracy and precision are limited in actual experiments with fluorescent proteins, owing to low excitation and the limited number of images. In this study, we applied maximum likelihood (ML) estimation and maximum a posteriori (MAP) estimation coupled with the empirical Bayes (EB) method (referred to as EB-MAP). In EB-MAP, we constructed a simple prior distribution for a pixel to utilize the information of the surrounding pixels. To evaluate the accuracy and precision of our method, we conducted simulations and experiments and compared the results of MoM, ML, and EB-MAP. The results showed that MoM estimated the particle number with many outliers. The outliers hampered the visibility of the spatial distribution and cellular structure. In contrast, EB-MAP suppressed the number of outliers and improved the visibility notably. The precision of EB-MAP was better by an order of magnitude in terms of particle number and 1.5 times better in terms of particle brightness compared with those of MoM. The proposed method (EB-MAP-N&B) is applicable to studies on fluorescence imaging and would aid in accurately recognizing changes in the concentration and oligomeric state in cells. Our results hold significant importance because quantifying the concentration and oligomeric state would contribute to the understanding of dynamic processes in molecular mechanism in cells.

Factor models aim to describe a dependence structure among high-dimensional random variables in terms of a low-dimensional unobserved random vector called a factor. One of the major practical issues of applying the factor model is to determine the factor dimensionality. In this paper, we propose a computationally feasible nonparametric prior distribution which achieves the posterior consistency of the factor dimensionality. We also derive the posterior contraction rate of the covariance matrix which is optimal when the factor dimensionality of the true covariance matrix is bounded. We conduct numerical studies that illustrate our theoretical results.

In this paper, the estimating problems of the model parameters, reliability and hazard functions of an inverted Nadarajah–Haghighi distribution when sample is available from Type-II progressive censoring scheme have been considered. The maximum likelihood and maximum product of spacings estimators have been obtained for any function of the model parameters. The normality property of the classical estimators is used to construct the approximate confidence intervals for the unknown parameters and some related functions of them such as the reliability characteristics. Using independent gamma informative priors, the Bayes estimators of the unknown parameters are derived under squared error loss function. Since the Bayes estimators are obtained in a complex form, so we have been used two approximation techniques, namely: Tierney–Kadane approximation method and Metropolis–Hastings algorithm to carry out the Bayes estimates and also to construct the associate highest posterior density credible intervals. To evaluate the performance of the proposed methods, a Monte Carlo simulation study is carried out. To suggest the optimum censoring scheme among different competing censoring plans, four optimality criteria have been considered. One real-life data set is analyzed to discuss how the applicability of the proposed methods in real phenomenon.

In many applications, variables or features can be naturally partitioned into different groups. In this article, we propose a new Bayesian hierarchical model for group selection problem when the group structure is known. We use spike and slab priors for regression coefficients, and the slab component is assumed to come from the family of nonlocal priors. Contrary to local priors commonly used in Bayesian group selection, nonlocal density priors vanish when a regression coefficient in the model is zero. We use simulation studies to assess the performance of our method and apply it to data collected from individuals undergoing cardiac catheterization at Duke University Medical center between 2001 and 2010.

Adaptive Type-II progressive hybrid censoring scheme has been proposed to increase the efficiency of statistical analysis and save the total test time on a life-testing experiment. This article deals with the problem of estimating the parameters, survival and hazard rate functions of the two-parameter Hjorth distribution under adaptive Type-II progressive hybrid censoring scheme using maximum likelihood and Bayesian approaches. The two-sided approximate confidence intervals of the unknown quantities are constructed. Under the assumption of independent gamma priors, the Bayes estimators are obtained using squared error loss function. Since the Bayes estimators cannot be expressed in closed forms, Lindley’s approximation and Markov chain Monte Carlo methods are considered and the highest posterior density credible intervals are also obtained. To study the behavior of the various estimators, a Monte Carlo simulation study is performed. The performances of the different estimators have been compared on the basis of their average root mean squared error and relative absolute bias. Finally, to show the applicability of the proposed estimators a data set of industrial devices has been analyzed.

Based on progressive Type-II censored samples, we first derive the recurrence relations for the single and product moments of progressively Type-II censored order statistics from two parameter Rayleigh distribution. These recurrence relations enable us to compute the mean and variances of all progressively Type-II censored order statistics for all sample sizes in a simple and efficient manner. Further, an algorithm is discussed which enable us to compute all the means and variances of two parameter Rayleigh progressive Type-II censored order statistics for all sample sizes and all censoring schemes. Next, we obtain the maximum likelihood estimators of the unknown parameters and the approximate confidence intervals of the parameters of the Rayleigh distribution. Finally, we consider Bayes estimation under five different types of loss functions (symmetric and asymmetric loss functions) using independent gamma priors for both the unknown parameters. Monte Carlo simulations are performed to compare the performance of the proposed methods, and one data set has been analyzed for illustrative purposes.

The paper is concerned with the problem of change point for the inter arrival time distribution for the M/M/1 queueing system by considering the number of customers present in the system. Bayesian estimators of traffic intensities, before the change $$(\rho _1)$$ and after the change $$(\rho _2)$$ , and the change point m are derived using the informative as well as non-informative priors under different loss functions. Finally a numerical example along with a practical example is given to illustrate the results.

To study the heterogeneous nature of lifetimes of certain mechanical or engineering processes, a mixture model of some suitable lifetime distributions may be more appropriate and appealing as compared to simple models This paper considers a mixture of the Marshall–Olkin extended Weibull distribution for efficient modeling of failure, survival, and COVID-19 data under classical and Bayesian perspectives based on type-II censored data We derive several properties of the new distribution such as moments, incomplete moments, mean deviation, average lifetime, mean residual lifetime, Renyi entropy, Shannon entropy, and order statistics of the proposed distribution Maximum likelihood and Bayes procedure are used to derive both point and interval estimates of the parameters involved in the model Bayes estimators of the unknown parameters of the model are obtained under symmetric (squared error) and asymmetric (linear exponential (LINEX)) loss functions using gamma priors for both the shape and the scale parameters Furthermore, approximate confidence intervals and Bayes credible intervals (CIs) are also obtained Monte Carlo simulation study is carried out to assess the performance of the maximum likelihood estimators and Bayes estimators with respect to their estimated risk The flexibility and importance of the proposed distribution are illustrated by means of four real datasets [ABSTRACT FROM AUTHOR] Copyright of Mathematical Problems in Engineering is the property of Hindawi Limited and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission However, users may print, download, or email articles for individual use This abstract may be abridged No warranty is given about the accuracy of the copy Users should refer to the original published version of the material for the full abstract (Copyright applies to all Abstracts )