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Creators/Authors contains: "Mallick, Bani K."

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  1. Abstract

    Survival models are used to analyze time-to-event data in a variety of disciplines. Proportional hazard models provide interpretable parameter estimates, but proportional hazard assumptions are not always appropriate. Non-parametric models are more flexible but often lack a clear inferential framework. We propose a Bayesian treed hazards partition model that is both flexible and inferential. Inference is obtained through the posterior tree structure and flexibility is preserved by modeling the log-hazard function in each partition using a latent Gaussian process. An efficient reversible jump Markov chain Monte Carlo algorithm is accomplished by marginalizing the parameters in each partition element via a Laplace approximation. Consistency properties for the estimator are established. The method can be used to help determine subgroups as well as prognostic and/or predictive biomarkers in time-to-event data. The method is compared with some existing methods on simulated data and a liver cirrhosis dataset.

     
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  2. Abstract

    Bayesian optimization (BO) is an indispensable tool to optimize objective functions that either do not have known functional forms or are expensive to evaluate. Currently, optimal experimental design is always conducted within the workflow of BO leading to more efficient exploration of the design space compared to traditional strategies. This can have a significant impact on modern scientific discovery, in particular autonomous materials discovery, which can be viewed as an optimization problem aimed at looking for the maximum (or minimum) point for the desired materials properties. The performance of BO-based experimental design depends not only on the adopted acquisition function but also on the surrogate models that help to approximate underlying objective functions. In this paper, we propose a fully autonomous experimental design framework that uses more adaptive and flexible Bayesian surrogate models in a BO procedure, namely Bayesian multivariate adaptive regression splines and Bayesian additive regression trees. They can overcome the weaknesses of widely used Gaussian process-based methods when faced with relatively high-dimensional design space or non-smooth patterns of objective functions. Both simulation studies and real-world materials science case studies demonstrate their enhanced search efficiency and robustness.

     
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  3. null (Ed.)
  4. Abstract Motivation It is well known that the integration among different data-sources is reliable because of its potential of unveiling new functionalities of the genomic expressions, which might be dormant in a single-source analysis. Moreover, different studies have justified the more powerful analyses of multi-platform data. Toward this, in this study, we consider the circadian genes’ omics profile, such as copy number changes and RNA-sequence data along with their survival response. We develop a Bayesian structural equation modeling coupled with linear regressions and log normal accelerated failure-time regression to integrate the information between these two platforms to predict the survival of the subjects. We place conjugate priors on the regression parameters and derive the Gibbs sampler using the conditional distributions of them. Results Our extensive simulation study shows that the integrative model provides a better fit to the data than its closest competitor. The analyses of glioblastoma cancer data and the breast cancer data from TCGA, the largest genomics and transcriptomics database, support our findings. Availability and implementation The developed method is wrapped in R package available at https://github.com/MAITYA02/semmcmc. Supplementary information Supplementary data are available at Bioinformatics online. 
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  5. Summary We develop a Bayesian methodology aimed at simultaneously estimating low-rank and row-sparse matrices in a high-dimensional multiple-response linear regression model. We consider a carefully devised shrinkage prior on the matrix of regression coefficients which obviates the need to specify a prior on the rank, and shrinks the regression matrix towards low-rank and row-sparse structures. We provide theoretical support to the proposed methodology by proving minimax optimality of the posterior mean under the prediction risk in ultra-high-dimensional settings where the number of predictors can grow subexponentially relative to the sample size. A one-step post-processing scheme induced by group lasso penalties on the rows of the estimated coefficient matrix is proposed for variable selection, with default choices of tuning parameters. We additionally provide an estimate of the rank using a novel optimization function achieving dimension reduction in the covariate space. We exhibit the performance of the proposed methodology in an extensive simulation study and a real data example. 
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  6. Summary

    Precise classification of tumours is critical for the diagnosis and treatment of cancer. Diagnostic pathology has traditionally relied on macroscopic and microscopic histology and tumour morphology as the basis for the classification of tumours. Current classification frameworks, however, cannot discriminate between tumours with similar histopathologic features, which vary in clinical course and in response to treatment. In recent years, there has been a move towards the use of complementary deoxyribonucleic acid microarrays for the classi-fication of tumours. These high throughput assays provide relative messenger ribonucleic acid expression measurements simultaneously for thousands of genes. A key statistical task is to perform classification via different expression patterns. Gene expression profiles may offer more information than classical morphology and may provide an alternative to classical tumour diagnosis schemes. The paper considers several Bayesian classification methods based on reproducing kernel Hilbert spaces for the analysis of microarray data. We consider the logistic likelihood as well as likelihoods related to support vector machine models. It is shown through simulation and examples that support vector machine models with multiple shrinkage parameters produce fewer misclassification errors than several existing classical methods as well as Bayesian methods based on the logistic likelihood or those involving only one shrinkage parameter.

     
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