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The number of modes in a probability density function is representative of the complexity of a model and can also be viewed as the number of subpopulations. Despite its relevance, there has been limited research in this area. A novel approach to estimating the number of modes in the univariate setting is presented, focusing on prediction accuracy and inspired by some overlooked aspects of the problem: the need for structure in the solutions, the subjective and uncertain nature of modes, and the convenience of a holistic view that blends local and global density properties. The technique combines flexible kernel estimators and parsimonious compositional splines in the Bayesian inference paradigm, providing soft solutions and incorporating expert judgment. The procedure includes feature exploration, model selection, and mode testing, illustrated in a sports analytics case study showcasing multiple companion visualisation tools. A thorough simulation study also demonstrates that traditional modality-driven approaches paradoxically struggle to provide accurate results. In this context, the new method emerges as a top-tier alternative, offering innovative solutions for analysts. • Combining kernel estimators and compositional splines benefits mode exploration. • Dimensionality reduction with one principal component captures the essential modes. • Bayesian inference admits expert knowledge regarding modality in soft solutions. • The new proposal and other generic methods outperform classic modality approaches. [ABSTRACT FROM AUTHOR]

In multiple instance learning (MIL), a bag represents a sample that has a set of instances, each of which is described by a vector of explanatory variables, but the entire bag only has one label/response. Though many methods for MIL have been developed to date, few have paid attention to interpretability of models and results. The proposed Bayesian regression model stands on two levels of hierarchy, which transparently show how explanatory variables explain and instances contribute to bag responses. Moreover, two selection problems are simultaneously addressed; the instance selection to find out the instances in each bag responsible for the bag response, and the variable selection to search for the important covariates. To explore a joint discrete space of indicator variables created for selection of both explanatory variables and instances, the shotgun stochastic search algorithm is modified to fit in the MIL context. Also, the proposed model offers a natural and rigorous way to quantify uncertainty in coefficient estimation and outcome prediction, which many modern MIL applications call for. The simulation study shows the proposed regression model can select variables and instances with high performance (AUC greater than 0.86), thus predicting responses well. The proposed method is applied to the musk data for prediction of binding strengths (labels) between molecules (bags) with different conformations (instances) and target receptors. It outperforms all existing methods, and can identify variables relevant in modeling responses. [ABSTRACT FROM AUTHOR]

For numerous applications, it is of interest to provide full probabilistic forecasts, which are able to assign plausibilities to each predicted outcome. Therefore, attention is shifting constantly from conditional mean models to probabilistic distributional models capturing location, scale, shape and other aspects of the response distribution. One of the most established models for distributional regression is the generalized additive model for location, scale and shape (GAMLSS). In high-dimensional data set-ups, classical fitting procedures for GAMLSS often become rather unstable and methods for variable selection are desirable. Therefore, a regularization approach for high-dimensional data set-ups in the framework of GAMLSS is proposed. It is designed for linear covariate effects and is based on L 1 -type penalties. The following three penalization options are provided: the conventional least absolute shrinkage and selection operator (LASSO) for metric covariates, and both group and fused LASSO for categorical predictors. The methods are investigated both for simulated data and for two real data examples, namely Munich rent data and data on extreme operational losses from the Italian bank UniCredit. [ABSTRACT FROM AUTHOR]

Abstract Hypothesis testing for finite mixture model has long been a challenging problem. The standard likelihood ratio test (LRT) does not have the usual asymptotic χ 2 distribution partly because the mixture model is not identifiable under null hypothesis. A simple class of hypothesis test procedures for finite mixture models based on goodness of fit (GOF) test statistics is investigated. The suggested hypothesis test procedure is easy to understand and use and can be applied to many mixture models with continuous data. Five commonly used goodness of fit test statistics are considered and compared. The limit distribution of test statistics is simulated based on the bootstrap method. It is demonstrated that a simple application of GOF test statistics to finite mixture models can provide comparable or even superior hypothesis test performance compared to the existing cutting edge EM test method through extensive simulation studies. The effectiveness of GOF test to choose the number components is also demonstrated based on limited empirical studies and a real data application. [ABSTRACT FROM AUTHOR]

Abstract Multidimensional scaling methods are frequently used by researchers and practitioners to project high dimensional data into a low dimensional space. However, it is a challenge to integrate side information which is available along with the dissimilarities to perform such dimension reduction analysis. A novel Bayesian integrative multidimensional scaling procedure, namely Bayesian multidimensional scaling with variable selection, is proposed to incorporate external information on the objects into the analysis through the use of a latent multivariate regression structure. The proposed Bayesian procedure allows the incorporation of covariate information into the dimension reduction analysis through the use of a variable selection strategy. An efficient computational algorithm to implement the procedure is also developed. A series of simulation experiments and a real data analysis are conducted, and the proposed model is shown to outperform several benchmark models based on some measures commonly used in the literature. [ABSTRACT FROM AUTHOR]

Abstract A loss-based approach to change point analysis is proposed. In particular, the problem is looked from two perspectives. The first focuses on the definition of a prior when the number of change points is known a priori. The second contribution aims to estimate the number of change points by using a loss-based approach recently introduced in the literature. The latter considers change point estimation as a model selection exercise. The performance of the proposed approach is shown on simulated data and real data sets. [ABSTRACT FROM AUTHOR]

Abstract Max-stable processes are a common choice for modelling spatial extreme data as they arise naturally as the infinite-dimensional generalisation of multivariate extreme value theory. Statistical inference for such models is complicated by the intractability of the multivariate density function. Nonparametric, composite likelihood-based, and Bayesian approaches have been proposed to address this difficulty. More recently, a simulation-based approach using approximate Bayesian computation (ABC) has been employed for estimating parameters of max-stable models. ABC algorithms rely on the evaluation of discrepancies between model simulations and the observed data rather than explicit evaluations of computationally expensive or intractable likelihood functions. The use of an ABC method to perform model selection for max-stable models is explored. Three max-stable models are regarded: the extremal- t model with either a Whittle–Matérn or a powered exponential covariance function, and the Brown–Resnick model with power variogram. In addition, the non-extremal Student- t copula model with a Whittle–Matérn or a powered exponential covariance function is also considered. The method is applied to annual maximum temperature data from 25 weather stations dispersed around South Australia. [ABSTRACT FROM AUTHOR]

Abstract Several statistical approaches based on reproducing kernels have been proposed to detect abrupt changes arising in the full distribution of the observations and not only in the mean or variance. Some of these approaches enjoy good statistical properties (oracle inequality, consistency). Nonetheless, they have a high computational cost both in terms of time and memory. This makes their application difficult even for small and medium sample sizes (n < 1 0 4). This computational issue is addressed by first describing a new efficient procedure for kernel multiple change-point detection with an improved worst-case complexity that is quadratic in time and linear in space. It is based on an exact optimization algorithm and deals with medium size signals (up to n ≈ 1 0 5). Second, a faster procedure (based on an approximate optimization algorithm) is described. It relies on a low-rank approximation to the Gram matrix and is linear in time and space. The resulting procedure can be applied to large-scale signals (n ≥ 1 0 6). These two procedures (based on the exact or approximate optimization algorithms) have been implemented in R and C for various kernels. The computational and statistical performances of these new algorithms have been assessed through empirical experiments. The runtime of the new algorithms is observed to be faster than that of other considered procedures. Finally, simulations confirmed the higher statistical accuracy of kernel-based approaches to detect changes that are not only in the mean. These simulations also illustrate the flexibility of kernel-based approaches to analyze complex biological profiles made of DNA copy number and allele B frequencies. [ABSTRACT FROM AUTHOR]

Effective and accurate model selection is an important problem in modern data analysis. One of the major challenges is the computational burden required to handle large datasets that cannot be stored or processed on one machine. Another challenge one may encounter is the presence of outliers and contaminations that damage the inference quality. The parallel “divide and conquer” model selection strategy divides the observations of the full dataset into roughly equal subsets and perform inference and model selection independently on each subset. After local subset inference, this method aggregates the posterior model probabilities or other model/variable selection criteria to obtain a final model by using the notion of geometric median. This approach leads to improved concentration in finding the “correct” model and model parameters and also is provably robust to outliers and data contamination. [ABSTRACT FROM AUTHOR]

Noisy and missing data are often encountered in real applications such that the observed covariates contain measurement errors. Despite the rapid progress of model selection with contaminated covariates in high dimensions, methodology that enjoys virtues in all aspects of prediction, variable selection, and computation remains largely unexplored. In this paper, we propose a new method called as the balanced estimation for high-dimensional error-in-variables regression to achieve an ideal balance between prediction and variable selection under both additive and multiplicative measurement errors. It combines the strengths of the nearest positive semi-definite projection and the combined L 1 and concave regularization, and thus can be efficiently solved through the coordinate optimization algorithm. We also provide theoretical guarantees for the proposed methodology by establishing the oracle prediction and estimation error bounds equivalent to those for Lasso with the clean data set, as well as an explicit and asymptotically vanishing bound on the false sign rate that controls overfitting, a serious problem under measurement errors. Our numerical studies show that the amelioration of variable selection will in turn improve the prediction and estimation performance under measurement errors. [ABSTRACT FROM AUTHOR]

This paper is concerned with learning of mixture regression models for individuals that are measured repeatedly. The adjective “unsupervised” implies that the number of mixing components is unknown and has to be determined, ideally by data driven tools. For this purpose, a novel penalized method is proposed to simultaneously select the number of mixing components and to estimate the mixture proportions and unknown parameters in the models. The proposed method is capable of handling both continuous and discrete responses by only requiring the first two moment conditions of the model distribution. It is shown to be consistent in both selecting the number of components and estimating the mixture proportions and unknown regression parameters. Further, a modified EM algorithm is developed to seamlessly integrate model selection and estimation. Simulation studies are conducted to evaluate the finite sample performance of the proposed procedure. And it is further illustrated via an analysis of a primary biliary cirrhosis data set. [ABSTRACT FROM AUTHOR]

The risk of the phi-divergence of a statistical model for categorical data is defined using two independent sets of data. The asymptotic bias of the phi-divergence based on current data as an estimator of the risk is shown to be equal to the negative penalty term of the Akaike information criterion (AIC). Though the higher-order asymptotic bias is derived, the higher-order bias depends on the form of the phi-divergence and the estimation method of parameters using a possible different form of the phi-divergence. An approximation to the higher-order bias is obtained based on the simple result of the saturated model. The information criteria using this approximation yield improved results in simulations for model selection. Some cases of the phi-divergences show advantages over the AIC in simulations. [ABSTRACT FROM AUTHOR]

Sparsity in features presents a big technical challenge to existing clustering methods for categorical data. Hierarchical Bayesian Bernoulli mixture model (HBBMM) incorporates constrained empirical Bayes priors for model parameters, so the resulting Expectation Maximization (EM) algorithm of estimator searching is confined in a proper region. The EM algorithm enables to obtain the maximum a posterior (MAP) estimation, in which cluster labels are simultaneously assigned. Three criteria are proposed to identify defining features of individual clusters, leading to understanding of the underlying data structures. Information based model selection criterion is applied to determine the number of clusters. Estimation consistency and performance of model selection criteria are investigated. Two real-world sparse categorical datasets are analyzed with the proposed method. [ABSTRACT FROM AUTHOR]

Determining the number of clusters in a dataset is a fundamental issue in data clustering. Many methods have been proposed to solve the problem of selecting the number of clusters, considering it to be a problem with regard to model selection. This paper proposes an efficient algorithm that automatically selects a suitable number of clusters based on a probability distribution model framework. The algorithm includes the following two components. First, a generalization of Kohonen's self-organizing map (SOM) is introduced. In Kohonen's SOM, clusters are modeled as mean vectors. In the generalized SOM, each cluster is modeled as a probabilistic distribution and constructed by samples classified based on the likelihood. Second, the dynamically updating method of the SOM structure is introduced. In Kohonen's SOM, each cluster is tied to a node of a fixed two-dimensional lattice space and learned using neighborhood relations between nodes based on Euclidean distance. The extended SOM defines a graph with clusters as vertices and neighborhood relations as links and updates the graph structure by cutting weakly connected and unnecessary vertex deletions. The weakness of a link is measured using the Kullback–Leibler divergence, and the redundancy of a vertex is measured using the minimum description length. Those extensions make it efficient to determine the appropriate number of clusters. Compared with existing methods, the proposed method is computationally efficient and can accurately select the number of clusters. [ABSTRACT FROM AUTHOR]

A new family of one-factor distributions for modeling high-dimensional binary data is introduced. The model provides an explicit probability for each event, thus avoiding the numeric approximations often made by existing methods. Model interpretation is easy, because each variable is described by two continuous parameters (corresponding to the marginal probability and to the strength of dependency with the other variables) and by one binary parameter (defining if the dependencies are positive or negative). This model is extended by splitting the variables into independent blocks, where each block follows the new one-factor distribution. Finally, a parsimonious version of the model, forcing some equality constraints between the dependency parameters, is proposed. Parameter estimation is carried out by an inference margin procedure, where the second step is achieved by an expectation–maximization algorithm. Model selection is performed by a deterministic approach, which strongly reduces the number of competing models. This consistent approach uses a hierarchical ascendant classification of the variables which selects a narrow subset of models. This selection is based on the empirical version of Cramer’s V. The new model is evaluated on numerical experiments and on a real data set. The procedure is implemented in the R package MvBinary. [ABSTRACT FROM AUTHOR]

Discrete vine copulas provide a flexible modeling framework for high-dimensional data and have significant computational advantages over competing methods. A vine-based multivariate probability mass function is constructed from bivariate copula building blocks and univariate marginal distributions. However, even for a moderate number of variables, the number of alternative vine decompositions is very large and additionally there is a large set of candidate bivariate copula families that can be used as building blocks in any given decomposition. Together, these two issues ensure that it is infeasible to evaluate all possible vine copula models. Instead, two greedy algorithms for automatically selecting vine structures and component pair-copula building blocks are introduced. The algorithms are tested in a simulation study that is itself driven by real world data from online retail. Both algorithms select vines that provide accurate estimates of the joint probabilities. Using three different f-divergences as criteria, the proposed algorithms outperform a Gaussian copula benchmark, especially for data with high dependence. Finally, the selection algorithm is applied to data from the General Social Survey and outperforms a Gaussian copula benchmark using both in-sample and out-of-sample criteria. [ABSTRACT FROM AUTHOR]

G-Enum histograms are a new fast and fully automated method for irregular histogram construction. By framing histogram construction as a density estimation problem and its automation as a model selection task, these histograms leverage the Minimum Description Length principle (MDL) to derive two different model selection criteria. Several proven theoretical results about these criteria give insights about their asymptotic behaviour and are used to speed up their optimisation. These insights, combined to a greedy search heuristic, are used to construct histograms in linearithmic time rather than the polynomial time incurred by previous works. The capabilities of the proposed MDL density estimation method are illustrated with reference to other fully automated methods in the literature, both on synthetic and large real-world data sets. [ABSTRACT FROM AUTHOR]

A basis expansion with regularization methods is much appealing to the flexible or robust nonlinear regression models for data with complex structures. When the underlying function has inhomogeneous smoothness, it does not perform well when one tries to estimate it with regularization methods that do not require intensive computational load. Specifically, when the underlying function has both smooth and non-smooth parts, the conventional regularization methods tend to over-fit in the smooth part or under-fit in the non-smooth part. Therefore, a new efficient basis expansion is considered by proposing a smoothly varying regularization method which is constructed by some special penalties. These should be called adaptive penalties. In the modeling, adaptive-type penalties play key roles and it has been successful in giving good estimation for inhomogeneous smoothness functions. A crucial issue in the modeling process is the choice of a suitable model among candidates. To select the suitable model, an approximated generalized information criterion (GIC) is derived. The proposed method is investigated through Monte Carlo simulations and real data analysis. Numerical results suggest that the proposed method performs well in various situations. • A method which smoothly varies regularization by coefficients is proposed. • The method can handle inhomogeneous smoothness in regression functions. • The regularizations and the coefficients are simply and simultaneously given. • A theoretically guaranteed model selection criterion is given. • Simulation studies show that the method avoids both over-fitting and under-fitting. [ABSTRACT FROM AUTHOR]

Robust procedures in high-dimensional regression are important because outliers are often present in data. For data with heavy-tailed errors, quantile regression and least absolute deviation regression methods have been widely used with great success. Some interesting Huber-loss-based and robust M-type regularized estimators have also been developed. However, high-dimensional regression estimation under L q -loss functions (1 ≤ q < 2) has not been fully studied in the literature. A lack of smoothness of these loss functions near the origin makes the regularized optimization problems computationally challenging. Robust sparse regression estimation under the L q -loss functions (1 ≤ q < 2) is investigated. A regularized estimator under the L q -loss combined with a weighted penalty function is proposed and its properties, such as the model-selection oracle property and asymptotic normality, are studied. The l 1 and l 2 estimation error bounds of the proposed estimator are also obtained. A novel computational algorithm is also proposed. Monte Carlo studies are conducted to compare the finite-sample and robustness properties of the proposed procedure with some existing regularized robust methods. The methods are also compared using two real data examples. The numerical studies show the satisfactory finite-sample performance of our procedure. [ABSTRACT FROM AUTHOR]

This paper deals with Bayesian linear quantile regression models based on a recently developed Expectation–Maximization Variable Selection (EMVS) method. By using additional latent variables, the proposed approach enjoys enormous computational savings compared to commonly used Markov Chain Monte Carlo (MCMC) algorithm. Using location-scale mixture representation of asymmetric Laplace distribution (ALD), we develop a rapid and efficient Expectation–Maximization (EM) algorithm, which is illustrated with several carefully designed simulation examples. We further apply the proposed method to construct financial index tracking portfolios. [ABSTRACT FROM AUTHOR]

The performances of fit indices used for model selection in cross-sectional mixture modeling with nonnormally distributed indicators were examined in two studies using Monte Carlo methods. Simulation conditions were selected to mirror conditions found in educational and psychological research. The design factors under investigation were: indicator distribution, number of indicators, sample size, and profile prevalence. All models contained five, ten, or 15 continuous indicators with varying departures from normality. The fit indices examined were Akaike’s information criterion (AIC), corrected Akaike’s information criterion (AICc), consistent Akaike’s information criterion (CAIC), Bayesian information criterion (BIC), sample size-adjusted Bayesian information criterion (SSBIC), Draper’s information criterion (DIC), integrated classification likelihood criterion with Bayesian-type approximation (ICL), entropy, and the adjusted Lo–Mendell–Rubin likelihood ratio test (LMR). In the first study, nonnormally distributed data were used to estimate the mixture models. No fit index uniformly identified the simulated number of profiles using nonnormal indicators. The fit indices that tended to identify the simulated number of profiles more frequently than others were BIC, SSBIC, CAIC, and LMR although the condition(s) in which this was observed varied. In the second study, the raw data were transformed using van der Waerden quantile normal scores. Despite deflating the indicator variances, the use of normal scores increased the frequency with which fit indices identified the simulated number of profiles across most conditions. [ABSTRACT FROM AUTHOR]

Modeling time series that present non-Gaussian features plays as central role in many fields, including finance, seismology, psychological, and life course studies. The Hidden Mixture Transition Distribution model is an answer to the complexity of such series. The observed heterogeneity can be induced by one or several latent factors, and each level of these factors is related to a different component of the observed process. The time series is then treated as a mixture and the relation between the components is governed by a Markovian latent transition process. This framework generalizes several specifications that appear separately in related literature. Both the expectation and the standard deviation of each component are allowed to be functions of the past of the process. The latent process can be of any order, and can be modeled using a discrete Mixture Transition Distribution. The effects of covariates at the visible and hidden levels are also investigated. One of the main difficulties lies in correctly specifying the structure of the model. Therefore, we propose a hierarchical model selection procedure that exploits the multilevel structure of our approach. Finally, we illustrate the model and the model selection procedure through a real application in social science. [ABSTRACT FROM AUTHOR]

Navigation patterns expressed by sequences of visited web-sites or categories can characterize the behavior and habits of users. Such web-page routes taken by individuals are commonly called clickstreams. Clustering clickstream sequences is a recent yet challenging problem with many applications. The main difficulty is related to the fact that one needs to group categorical data sequences rather than vectors and the majority of traditional clustering algorithms are not applicable in this setting. The time-related character of data suggests that dynamic models have a better promise than static ones. Model-based clustering relying on the mixture of first order Markov models will be considered. Since the number of distinct web-pages, and therefore the number of states in a Markov process, can be very high, such a mixture model involves a large number of parameters. Thus, grouping states by their similarity to reduce the number of parameters in the model is also proposed. Then, states are clustered along with users providing a biclustering framework. The developed methodology is illustrated on synthetic and real datasets with good results. [ABSTRACT FROM AUTHOR]

Many regression problems exhibit a natural grouping among predictor variables. Examples are groups of dummy variables representing categorical variables, or present and lagged values of time series data. Since model selection in such cases typically aims for selecting groups of variables rather than individual covariates, an extension of the popular least angle regression (LARS) procedure to groupwise variable selection is considered. Data sets occurring in applied statistics frequently contain outliers that do not follow the model or the majority of the data. Therefore a modification of the groupwise LARS algorithm is introduced that reduces the influence of outlying data points. Simulation studies and a real data example demonstrate the excellent performance of groupwise LARS and, when outliers are present, its robustification. [ABSTRACT FROM AUTHOR]

Motivated by the analysis of spectrometric data, a Gaussian graphical model for learning the dependence structure among frequency bands of the infrared absorbance spectrum is introduced. The spectra are modeled as continuous functional data through a B-spline basis expansion and a Gaussian graphical model is assumed as a prior specification for the smoothing coefficients to induce sparsity in their precision matrix. Bayesian inference is carried out to simultaneously smooth the curves and to estimate the conditional independence structure between portions of the functional domain. The proposed model is applied to the analysis of infrared absorbance spectra of strawberry purees. [ABSTRACT FROM AUTHOR]

We consider regression models with a group structure in explanatory variables. This structure is commonly seen in practice, but it is only recently realized that taking the information into account in the modeling process may improve both the interpretability and accuracy of the model. In this paper, we study a new approach to group variable selection using random-effect models. Specific distributional assumptions on random effects pertaining to a given structure lead to a new class of penalties that include some existing penalties. We also develop an efficient computational algorithm. Numerical studies are provided to demonstrate better sensitivity and specificity properties without sacrificing the prediction accuracy. Finally, we present some real-data applications of the proposed approach. [ABSTRACT FROM AUTHOR]

The Bayesian information criterion (BIC) is one of the most popular criteria for model selection in finite mixture models. However, it implausibly penalizes the complexity of each component using the whole sample size and completely ignores the clustered structure inherent in the data, resulting in over-penalization. To overcome this problem, a novel criterion called hierarchical BIC (HBIC) is proposed which penalizes the component complexity only using its local sample size and matches the clustered data structure well. Theoretically, HBIC is an approximation of the variational Bayesian (VB) lower bound when sample size is large and the widely used BIC is a less accurate approximation. An empirical study is conducted to verify this theoretical result and a series of experiments is performed on simulated and real data sets to compare HBIC and BIC. The results show that HBIC outperforms BIC substantially and BIC suffers from underestimation. [ABSTRACT FROM AUTHOR]

A new methodological approach that enables the use of the maximum likelihood method in the Generalized Pareto Distribution is presented. Thus several models for the same data can be compared under Akaike and Bayesian information criteria. The view is based on a detailed theoretical study of the Generalized Pareto Distribution submodels with compact support. [ABSTRACT FROM AUTHOR]

The problem of covariate selection for regression models with right censored data is considered. It is approached from a default Bayesian point of view with Bayes factors (BFs) and in particular with Intrinsic BF (IBF) that depends on the minimal training samples (MTSs). In the presence of censored data, the number of possible MTSs increases, due to the fact that uncensored data, relevant for training the improper prior into a proper posterior, must be combined with censored data. For this purpose, the sequential minimal training sample scheme (SMTS) accounts for such requirements but generally leads to IBF correction factors that do not have an analytical form and thus require numerical approximation. In order to obtain an analytical expression of the correction terms, a different TS scheme is introduced based on the Kaplan–Meier (KM) estimator, termed the KM minimal training sample scheme. This new tool works extremely well in the analyzed simulation setting and also in the applications; it produces results which are similar, if not better, than the IBF calculated using MTSs. The resulting new IBF, being based on analytical expressions, is much faster to compute. Evidence of these results comes from a large simulation study, theoretical arguments, and an application to a real data set. [ABSTRACT FROM AUTHOR]

This article develops a mean field variational Bayes approximation algorithm for posterior inferences of the recently proposed partially linear additive models with simultaneous and automatic variable selection and linear/nonlinear component identification abilities. To solve the problem induced by some complicated expectation evaluations, we proposed two approximations based on Monte Carlo method and Laplace approximation respectively. With high accuracy, the algorithm we derived is much more computationally efficient than the existing Markov Chain Monte Carlo (MCMC) method. The simulation examples are used to demonstrate the performance of our new algorithm versus MCMC. The proposed approach is further illustrated on a real dataset. [ABSTRACT FROM AUTHOR]