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We consider the Bayesian estimation of the parameters of a finite mixture model from independent order statistics arising from imperfect ranked set sampling designs. As a cost‐effective method, ranked set sampling enables us to incorporate easily attainable characteristics, as ranking information, into data collection and Bayesian estimation. To handle the special structure of the ranked set samples, we develop a Bayesian estimation approach exploiting the Expectation‐Maximization (EM) algorithm in estimating the ranking parameters and Metropolis within Gibbs Sampling to estimate the parameters of the underlying mixture model. Our findings show that the proposed RSS‐based Bayesian estimation method outperforms the commonly used Bayesian counterpart using simple random sampling. The developed method is finally applied to estimate the bone disorder status of women aged 50 and older. [ABSTRACT FROM AUTHOR]

The noterate is a tool for predicting home mortgage rates, it is often skewed and has missing information. The noterate could be affected by incomplete or inaccurate data, thus leading to inaccurate predictions. Financial organizations including mortgage companies or banks need to consider the risk of uncertainty carefully and make a more accurate prediction based on some suitable models. To deal with this situation, in this paper we compared six computational statistical methods, including the ordinary least square model, maximum likelihood estimation, maximum a posterior, bootstrapping, Metropolis-Hastings, and Gibbs sampling method on a mortgage dataset. Based on the k fold cross-validation technique and four metrics including mean absolute error (MAE), mean squared error (MSE), root mean squared error (RMSE), and mean absolute percentage error (MAPE), the bootstrapping method outperforms other methods. In practice, this method is recommended for predicting noterate. [ABSTRACT FROM AUTHOR]

Under mild assumptions, we show that the exact convergence rate in total variation is also exact in weaker Wasserstein distances for the Metropolis–Hastings independence sampler. We develop a new upper and lower bound on the worst-case Wasserstein distance when initialized from points. For an arbitrary point initialization, we show that the convergence rate is the same and matches the convergence rate in total variation. We derive exact convergence expressions for more general Wasserstein distances when initialization is at a specific point. Using optimization, we construct a novel centered independent proposal to develop exact convergence rates in Bayesian quantile regression and many generalized linear model settings. We show that the exact convergence rate can be upper bounded in Bayesian binary response regression (e.g. logistic and probit) when the sample size and dimension grow together. [ABSTRACT FROM AUTHOR]

Multilevel modeling is a modern approach to deal with hierarchical or a nested data structure which can assess the variability between clusters. Bayesian Markov Chain Monte Carlo (MCMC) methods of estimations are advanced methods applicable for estimating multilevel models. However, these estimation methods are not as yet tested to identify its' performances as well as the properties associated with these estimation methods. This study targets to conduct a comparison of Bayesian MCMC methods which are developed for multilevel models where the response is normally distributed. The comparison is based upon extensive simulations and an application to a real-life dataset. The performance of Gibbs sampling (GS) and Metropolis Hastings (MH) methods are compared using a simulation study and additionally the factors which can affect the performance of both MCMC methods are identified. Practicality of these methods in real world scenario is confirmed through the application of MCMC method to a dataset. In the simulations though the Metropolis Hastings (MH) shows slightly better performance than Gibbs, there is no evidence to indicate that significant differences exist between these methods except for small samples where MH is superior. The results from the example are not as clear as from the simulations. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to present a Bayesian analysis of Multivariate GARCH(l, m) (M-GARCH) models including estimation of the coefficient parameters as well as the model order, by combining a set of existing MCMC algorithms in the literature. The proposed algorithm focuses on the BEKK formulation of the multivariate GARCH model. The estimation procedure will be designed as a custom MCMC with embedded Reversible Jump MCMC (RJMCMC) and Delayed Rejection Metropolis-Hastings (DRMH) steps implemented using the statistical software R. The RJMCMC steps allow three variants of BEKK models (constant, diagonal and full) to be indexed and this index included as a parameter to be estimated. The proposed MCMC algorithms are validated using extensive simulation experiments followed by a case study using bivariate data derived from the daily share prices for BHP Group Limited, Rio Tinto Group, and Fortescue Metals Group Limited on the ASX over from September 2013 to December 2021. [ABSTRACT FROM AUTHOR]

This study introduces a unique flexible family of discrete probability distributions for modeling extreme count and zero-inflated count data with different failure rates. Certain significant mathematical properties, such as the cumulant generating function, moment generating function, dispersion index, L-moments, ordinary moments, and central moment are derived. The new failure rate function offers a wide range of flexibility, including "upside down", "monotonically decreasing", "bathtub", "monotonically increasing" and "decreasing-constant failure rate" and "constant". Moreover, the new probability mass function accommodates many useful shapes including the "right skewed function with no peak", "symmetric", "right skewed with one peak" and "left skewed with one peak". To obtain significant characterization findings, the hazard function and the conditional expectation of certain function of the random variable are both employed. Both Bayesian and non-Bayesian estimate methodologies are considered when estimating, assessing, and comparing inferential efficacy. The Bayesian estimation approach for the squared error loss function is suggested, and it is explained. Markov chain Monte Carlo simulation studies are performed using the Metropolis Hastings algorithm and the Gibbs sampler to compare non-Bayesian vs. Bayesian results. Four real-world applications of count data sets are used to evaluate the Bayesian versus non-Bayesian techniques. Four more real count data applications are used to illustrate the significance and versatility of the new discrete class. [ABSTRACT FROM AUTHOR]

Despite its extensive application in practice, the Metropolis-Hastings sampler can suffer from slow mixing and, in turn, statistical inefficiency. We introduce a modification to the Metropolis-Hastings algorithm that, under specified conditions, encourages more efficient movement on general state spaces while preserving the overall quality of convergence, geometric ergodicity in particular. We illustrate the modified algorithm and its properties for the Metropolis-Hastings algorithm for a toy univariate Normal model and for the Gibbs sampling algorithm in a toy bivariate Normal model and a Bayesian dynamic spatiotemporal model. [ABSTRACT FROM AUTHOR]

Data clustering is a fundamental unsupervised learning approach that impacts several domains such as data mining, computer vision, information retrieval, and pattern recognition. In this work, we develop a statistical framework for data clustering which uses Dirichlet processes and asymmetric Gaussian distributions. The parameters of this framework are learned using Markov Chain Monte Carlo inference approaches. We also integrate a feature selection technique to choose the features that are most informative in order to construct an appropriate model in terms of clustering accuracy. This paper reports results based on experiments that concern dynamic textures clustering as well as scene categorization. [ABSTRACT FROM AUTHOR]

Multistage ranking models, including the popular Plackett–Luce distribution (PL), rely on the assumption that the ranking process is performed sequentially, by assigning the positions from the top to the bottom one (forward order). A recent contribution to the ranking literature relaxed this assumption with the addition of the discrete-valued reference order parameter, yielding the novel Extended Plackett–Luce model (EPL). Inference on the EPL and its generalization into a finite mixture framework was originally addressed from the frequentist perspective. In this work, we propose the Bayesian estimation of the EPL in order to address more directly and efficiently the inference on the additional discrete-valued parameter and the assessment of its estimation uncertainty, possibly uncovering potential idiosyncratic drivers in the formation of preferences. We overcome initial difficulties in employing a standard Gibbs sampling strategy to approximate the posterior distribution of the EPL by combining the data augmentation procedure and the conjugacy of the Gamma prior distribution with a tuned joint Metropolis–Hastings algorithm within Gibbs. The effectiveness and usefulness of the proposal is illustrated with applications to simulated and real datasets. [ABSTRACT FROM AUTHOR]

Earlier works on spatial prediction issue often assume that the spatial data are realization of Gaussian random field. However, this assumption is not applicable to the skewed and kurtosis distributed data. The closed skew normal distribution has been used in these circumstances. As another alternative, we apply generalized skew Laplace distributions for defining a skew and heavy tailed random field for Bayesian prediction. Simulation study and a real problem are then applied to evaluate the performance of this model.

Markov jump processes (MJPs) are continuous-time stochastic processes widely used in a variety of applied disciplines. Inference typically proceeds via Markov chain Monte Carlo (MCMC), the state-of-the-art being a uniformization-based auxiliary variable Gibbs sampler. This was designed for situations where the process parameters are known, and Bayesian inference over unknown parameters is typically carried out by incorporating it into a larger Gibbs sampler. This strategy of sampling parameters given path, and path given parameters can result in poor Markov chain mixing. In this work, we propose a simple and efficient algorithm to address this problem. Our scheme brings Metropolis–Hastings (MH) approaches for discrete-time hidden Markov models to the continuous-time setting, resulting in a complete and clean recipe for parameter and path inference in MJPs. In our experiments, we demonstrate superior performance over Gibbs sampling, a more naïve MH algorithm, as well as another popular approach, particle MCMC. We also show our sampler inherits geometric mixing from an "ideal" sampler that is computationally much more expensive. for this article are available online. [ABSTRACT FROM AUTHOR]

In a 1970 Biometrika paper, W. K. Hastings developed a broad class of Markov chain algorithms for sampling from probability distributions that are difficult to sample from directly. The algorithm draws a candidate value from a proposal distribution and accepts the candidate with a probability that can be computed using only the unnormalized density of the target distribution, allowing one to sample from distributions known only up to a constant of proportionality. The stationary distribution of the corresponding Markov chain is the target distribution one is attempting to sample from. The Hastings algorithm generalizes the Metropolis algorithm to allow a much broader class of proposal distributions instead of just symmetric cases. An important class of applications for the Hastings algorithm corresponds to sampling from Bayesian posterior distributions, which have densities given by a prior density multiplied by a likelihood function and divided by a normalizing constant equal to the marginal likelihood. The marginal likelihood is typically intractable, presenting a fundamental barrier to implementation in Bayesian statistics. This barrier can be overcome by Markov chain Monte Carlo sampling algorithms. Amazingly, even after 50 years, the majority of algorithms used in practice today involve the Hastings algorithm. This article provides a brief celebration of the continuing impact of this ingenious algorithm on the 50th anniversary of its publication. [ABSTRACT FROM AUTHOR]

In this paper, we consider a Bayesian mixture model that allows us to integrate out the weights of the mixture in order to obtain a procedure in which the number of clusters is an unknown quantity. To determine clusters and estimate parameters of interest, we develop an MCMC algorithm denominated by sequential data-driven allocation sampler. In this algorithm, a single observation has a non-null probability to create a new cluster and a set of observations may create a new cluster through the split-merge movements. The split-merge movements are developed using a sequential allocation procedure based in allocation probabilities that are calculated according to the Kullback–Leibler divergence between the posterior distribution using the observations previously allocated and the posterior distribution including a 'new' observation. We verified the performance of the proposed algorithm on the simulated data and then we illustrate its use on three publicly available real data sets. [ABSTRACT FROM AUTHOR]

It is commonly asserted that the Gibbs sampler is a special case of the Metropolis–Hastings (MH) algorithm. While this statement is true for certain Gibbs samplers, it is not true in general for the version that is taught and used most often, namely, the deterministic scan Gibbs sampler. In this note, I prove that that there exist deterministic scan Gibbs samplers that do not exhibit detailed balance and hence cannot be considered MH samplers. The nuances of various Gibbs sampling schemes are discussed. [ABSTRACT FROM AUTHOR]

Due to the popularity of social networks, such as microblogs and Twitter, a vast amount of short text data is created every day. Much recent research in short text becomes increasingly significant, such as topic inference for short text. Biterm topic model (BTM) benefits from the word co-occurrence patterns of the corpus, which makes it perform better than conventional topic models in uncovering latent semantic relevance for short text. However, BTM resorts to Gibbs sampling to infer topics, which is very time consuming, especially for large-scale datasets or when the number of topics is extremely large. It requires O ( K ) operations per sample for K topics, where K denotes the number of topics in the corpus. In this paper, we propose an acceleration algorithm of BTM, FastBTM, using an efficient sampling method for BTM, which converges much faster than BTM without degrading topic quality. FastBTM is based on Metropolis-Hastings and alias method, both of which have been widely adopted in Latent Dirichlet Allocation (LDA) model and achieved outstanding speedup. Our FastBTM can effectively reduce the sampling complexity of biterm topic model from O ( K ) to O (1) amortized time. We carry out a number of experiments on three datasets including two short text datasets, Tweets2011 Collection dataset and Yahoo! Answers dataset, and one long document dataset, Enron dataset. Our experimental results show that when the number of topics K increases, the gap in running time speed between FastBTM and BTM gets especially larger. In addition, our FastBTM is effective for both short text datasets and long document datasets. [ABSTRACT FROM AUTHOR]

In this paper we introduce a Bayesian mixture model with an unknown number of components for partitioning gene expression data. Inferences about all the unknown parameters involved are made by using the proposed data-driven Markov chain Monte Carlo. This algorithm is essentially a Metropolis–Hastings within Gibbs sampling. The Metropolis–Hastings is performed to change the number of partitions k in the neighborhood and using a pair of split-merge moves. Our strategy for splitting is based on data in which allocation probabilities are calculated based on marginal likelihood function from the previously allocated observations. Conditional on k, the partitions labels are updated via Gibbs sampling. The two main advantages of the proposed algorithm is that it is easy to be implemented and the acceptance probability for split-merge movements depends only on the observed data. We examine the performance of the proposed algorithm on simulated data and then analyze two publicly available gene expression data sets. [ABSTRACT FROM AUTHOR]

In this article, we present a distributed resource and power allocation scheme for multiple-resource wireless cellular networks. The global optimization of multi-cell multi-link resource allocation problem is known to be NP-hard in the general case. We use Gibbs sampling based algorithms to perform a distributed optimization that would lead to the global optimum of the problem. The objective of this article is to show how to use the Gibbs sampling (GS) algorithm and its variant the Metropolis-Hastings (MH) algorithm. We also propose an enhanced method of the MH algorithm, based on a priori known target state distribution, which improves the convergence speed without increasing the complexity. Also, we study different temperature cooling strategies and investigate their impact on the network optimization and convergence speed. Simulation results have also shown the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

Recovering the origin of an incident after detection of a polluting substance in the environment is crucial to start the remediation procedures. The lack of observations, the measurement errors and the model uncertainties make the problem of source estimation an ill-posed inverse problem that requires regularization to determine a solution. The two most frequent methods of regularization are source parametrization and penalization of undesirable solutions. In this paper, the proposed approach combines both methods in order to obtain a strong regularization that is efficient in case of few and erroneous observations. Point sources with parametric temporal releases and parameter penalizations are incorporated in a Bayesian framework where observations and prior information are combined in a hierarchical probabilistic model and the posterior law is explored with a Markov Chain Monte Carlo sampling algorithm. Estimation of the source parameters is provided by the posterior mean and uncertainties are provided by the posterior variance. To validate the method, several simulated cases with different emission events are considered. Quality of the estimate as well as impact of source model errors are also investigated. Then, a comparison with two existing least squares methods is conducted, in various configurations of sensors and noise level. Finally, the behavior of the method is described on a strongly underdeterminate real case where only one sensor recorded the pollution. [ABSTRACT FROM AUTHOR]

Abstract: Selecting relevant features in multidimensional data is important in several pattern analysis and image processing applications. The goal of this paper is to propose a Bayesian approach for identifying clusters of proportional data based on the selection of relevant features. More specifically, we consider the problem of selecting relevant features in unsupervised settings when generalized Dirichlet mixture models are considered to model and cluster proportional data. The learning of the proposed statistical model, to formulate the unsupervised feature selection problem, is carried out using a powerful reversible jump Markov chain Monte Carlo (RJMCMC) technique. Experiments involving the challenging problems of human action videos categorization, pedestrian detection and face recognition indicate that the proposed approach is efficient. [Copyright &y& Elsevier]

Abstract: The use of mixture models in image and signal processing has proved to be of considerable interest in terms of both theoretical development and in their usefulness in several applications. Researchers have approached the mixture estimation and selection problem, to model complex datasets, with different techniques in the last few years. In theory, it is well-known that full Bayesian approaches, to handle this problem, are fully optimal. The Bayesian learning allows the incorporation of prior knowledge in a formal coherent way that avoids overfitting problems. In this paper, we propose a fully Bayesian approach for finite Beta mixtures learning using a reversible jump Markov chain Monte Carlo (RJMCMC) technique which simultaneously allows cluster assignments, parameters estimation, and the selection of the optimal number of clusters. The adverb “fully” is justified by the fact that all parameters of interest in our model including number of clusters and missing values are considered as random variables for which priors are specified and posteriors are approximated using RJMCMC. Our work is motivated by the fact that Beta mixtures are able to fit any unknown distributional shape and then can be considered as a useful class of flexible models to address several problems and applications involving measurements and features having well-known marked deviation from the Gaussian shape. The usefulness of the proposed approach is confirmed using synthetic mixture data, real data, and through an interesting application namely texture classification and retrieval. [Copyright &y& Elsevier]

Abstract: This paper presents a fully Bayesian approach to analyze finite generalized Gaussian mixture models which incorporate several standard mixtures, widely used in signal and image processing applications, such as Laplace and Gaussian. Our work is motivated by the fact that the generalized Gaussian distribution (GGD) can be applied on a wide range of data due to its shape flexibility which justifies its usefulness to model the statistical behavior of multimedia signals . We present a method to evaluate the posterior distribution and Bayes estimators using a Gibbs sampling algorithm. For the selection of number of components in the mixture, we use the integrated likelihood and Bayesian information criteria. We validate the proposed method by applying it to: synthetic data, real datasets, texture classification and retrieval, and image segmentation; while comparing it to different other approaches. [ABSTRACT FROM AUTHOR]

In this paper, we examine deterministic and Bayesian methods for analyzing finite Dirichlet mixtures. The deterministic method is based on the likelihood approach, and the Bayesian approach is implemented using the Gibbs sampler. The selection of the number of clusters for both approaches is based on the Bayesian information criterion, which is equivalent to the minimum description length. Experimental results are presented using simulated data, and a real application for software modules classification is also included. [ABSTRACT FROM AUTHOR]

In this work we propose Bayesian measures to quantify the influence of observations on the structural parameters of the simple measurement error model (MEM). Different influence measures, like those based on q-divergence between posterior distributions and Bayes risk, are studied to evaluate the influence. A strategy based on the perturbation function and MCMC samples is used to compute these measures. The samples from the posterior distributions are obtained by using the Metropolis-Hastings algorithm and assuming specific proper prior distributions. The results are illustrated with an application to a real example modeled with MEM in the literature. [ABSTRACT FROM AUTHOR]

Multilevel factor analysis models are widely used in the social sciences to account for heterogeneity in mean structures. In this paper we extend previous work on multilevel models to account for general forms of heterogeneity in confirmatory factor analysis models. We specify various models of mean and covariance heterogeneity in confirmatory factor analysis and develop Markov Chain Monte Carlo (MCMC) procedures to perform Bayesian inference, model checking, and model comparison. We test our methodology using synthetic data and data from a consumption emotion study. The results from synthetic data show that our Bayesian model perform well in recovering the true parameters and selecting the appropriate model. More importantly, the results clearly illustrate the consequences of ignoring heterogeneity. Specifically, we find that ignoring heterogeneity can lead to sign reversals of the factor covariances, inflation of factor variances and underappreciation of uncertainty in parameter estimates. The results from the emotion study show that subjects vary both in means and covariances. Thus traditional psychometric methods cannot fully capture the heterogeneity in our data. [ABSTRACT FROM AUTHOR]

Multilevel covariance structure models have become increasingly popular in the psychometric literature in the past few years to account for population heterogeneity and complex study designs. We develop practical simulation based procedures for Bayesian inference of multilevel binary factor analysis models. We illustrate how Markov Chain Monte Carlo procedures such as Gibbs sampling and Metropolis-Hastings methods can be used to perform Bayesian inference, model checking and model comparison without the need for multidimensional numerical integration. We illustrate the proposed estimation methods using three simulation studies and an application involving student's achievement results in different areas of mathematics. [ABSTRACT FROM AUTHOR]

In this work, we propose and study a new family of discrete distributions. Many useful mathematical properties, such as ordinary moments, moment generating function, cumulant generating function, probability generating function, central moment, and dispersion index are derived. Some special discrete versions are presented. A certain special case is discussed graphically and numerically. The hazard rate function of the new class can be "decreasing", "upside down", "increasing", and "decreasing-constant-increasing (U-shape)". Some useful characterization results based on the conditional expectation of certain function of the random variable and in terms of the hazard function are derived and presented. Bayesian and non-Bayesian methods of estimation are considered. The Bayesian estimation procedure under the squared error loss function is discussed. Markov chain Monte Carlo simulation studies for comparing non-Bayesian and Bayesian estimations are performed using the Gibbs sampler and Metropolis–Hastings algorithm. Four applications to real data sets are employed for comparing the Bayesian and non-Bayesian methods. The importance and flexibility of the new discrete class is illustrated by means of four real data applications. [ABSTRACT FROM AUTHOR]

In this paper, the problem of estimating parameters of the inverted exponentiated Rayleigh distribution under adaptive Type II progressive hybrid censored sample is discussed. The maximum likelihood estimators (MLEs) are developed for estimating the unknown parameters. The asymptotic normality of the MLEs is used to construct the approximate confidence intervals for the parameters. By applying the Bayesian approach, the estimators of the unknown parameters are derived under symmetric and asymmetric loss functions. The Bayesian estimates are evaluated by using the Lindley's approximation as well as the Monte Carlo Markov chain (MCMC) technique together with Metropolis–Hastings algorithm. The MCMC samples are further utilized to construct the Bayesian intervals for the unknown parameters. Monte Carlo simulations are implemented and observations are given. Finally, the data of the maximum spreading diameter of nano-droplet impact on hydrophobic surfaces is analyzed to illustrative purposes. [ABSTRACT FROM AUTHOR]