A Fully Bayesian Framework for Positive Data Clustering

In the context of high-dimensional multivariate linear regression, sparse reduced-rank regression (SRRR) provides a way to handle both variable selection and low-rank estimation problems. Although there has been extensive research on SRRR, statistical inference procedures that deal with the uncertainty due to variable selection and rank reduction are still limited. To fill this research gap, we develop a fully Bayesian approach to SRRR. A major difficulty that occurs in a fully Bayesian framework is that the dimension of parameter space varies with the selected variables and the reduced-rank. Due to the varying-dimensional problems, traditional Markov chain Monte Carlo (MCMC) methods such as Gibbs sampler and Metropolis-Hastings algorithm are inapplicable in our Bayesian framework. To address this issue, we propose a new posterior computation procedure based on the Laplace approximation within the collapsed Gibbs sampler. A key feature of our fully Bayesian method is that the model uncertainty is automatically integrated out by the proposed MCMC computation. The proposed method is examined via simulation study and real data analysis.

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Bayesian Learning of Shifted-Scaled Dirichlet Mixture Models and Its Application to Early COVID-19 Detection in Chest X-ray Images

Journal of Imaging ◽

10.3390/jimaging7010007 ◽

2021 ◽

Vol 7 (1) ◽

pp. 7

Author(s):

Sami Bourouis ◽

Abdullah Alharbi ◽

Nizar Bouguila

Keyword(s):

Mixture Models ◽

Bayesian Learning ◽

Bayesian Framework ◽

Model Parameters ◽

X Ray ◽

Therapeutic Implications ◽

Biomedical Image ◽

Dirichlet Mixture ◽

Chest X Ray ◽

Fully Bayesian

Early diagnosis and assessment of fatal diseases and acute infections on chest X-ray (CXR) imaging may have important therapeutic implications and reduce mortality. In fact, many respiratory diseases have a serious impact on the health and lives of people. However, certain types of infections may include high variations in terms of contrast, size and shape which impose a real challenge on classification process. This paper introduces a new statistical framework to discriminate patients who are either negative or positive for certain kinds of virus and pneumonia. We tackle the current problem via a fully Bayesian approach based on a flexible statistical model named shifted-scaled Dirichlet mixture models (SSDMM). This mixture model is encouraged by its effectiveness and robustness recently obtained in various image processing applications. Unlike frequentist learning methods, our developed Bayesian framework has the advantage of taking into account the uncertainty to accurately estimate the model parameters as well as the ability to solve the problem of overfitting. We investigate here a Markov Chain Monte Carlo (MCMC) estimator, which is a computer–driven sampling method, for learning the developed model. The current work shows excellent results when dealing with the challenging problem of biomedical image classification. Indeed, extensive experiments have been carried out on real datasets and the results prove the merits of our Bayesian framework.

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Framework to Analyze Construction Labor Productivity Using Fuzzy Data Clustering and Multi-Criteria Decision-Making

Construction Research Congress 2020 ◽

10.1061/9780784482865.006 ◽

2020 ◽

Author(s):

Matin Kazerooni ◽

Mohammad Raoufi ◽

Aminah Robinson Fayek

Keyword(s):

Decision Making ◽

Labor Productivity ◽

Data Clustering ◽

Fuzzy Data ◽

Multi Criteria Decision Making

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Modeling Interstation Travel Speed of Hybrid Bus Rapid Transit within A Bayesian Framework

智能城市应用 ◽

10.33142/sca.v2i5.817 ◽

2019 ◽

Vol 2 (5) ◽

Author(s):

Ji-hua Hu ◽

Jia-xian Liang

Keyword(s):

Road Traffic ◽

Travel Speed ◽

Bayesian Framework ◽

Bus Rapid Transit ◽

Rapid Transit ◽

Important Indicator ◽

Main Road ◽

Traffic Lights ◽

Speed Distribution ◽

Hybrid Bus

Interstation travel speed is an important indicator of the running state of hybrid Bus Rapid Transit and passenger experience. Due to the influence of road traffic, traffic lights and other factors, the interstation travel speeds are often some kind of multi-peak and it is difficult to use a single distribution to model them. In this paper, a Gaussian mixture model charactizing the interstation travel speed of hybrid BRT under a Bayesian framework is established. The parameters of the model are inferred using the Reversible-Jump Markov Chain Monte Carlo approach (RJMCMC), including the number of model components and the weight, mean and variance of each component. Then the model is applied to Guangzhou BRT, a kind of hybrid BRT. From the results, it can be observed that the model can very effectively describe the heterogeneous speed data among different inter-stations, and provide richer information usually not available from the traditional models, and the model also produces an excellent fit to each multimodal speed distribution curve of the inter-stations. The causes of different speed distribution can be identified through investigating the Internet map of GBRT, they are big road traffic and long traffic lights respectively, which always contribute to a main road crossing. So, the BRT lane should be elevated through the main road to decrease the complexity of the running state.

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