Zeitschriftenartikel: „Spike-and-slab priors“

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Ročková, Veronika, und Edward I. George. „Negotiating multicollinearity with spike-and-slab priors“. METRON 72, Nr. 2 (11.06.2014): 217–29. http://dx.doi.org/10.1007/s40300-014-0047-y.

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Rockova, Veronika, und Kenichiro McAlinn. „Dynamic Variable Selection with Spike-and-Slab Process Priors“. Bayesian Analysis 16, Nr. 1 (2021): 233–69. http://dx.doi.org/10.1214/20-ba1199.

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Antonelli, Joseph, Giovanni Parmigiani und Francesca Dominici. „High-Dimensional Confounding Adjustment Using Continuous Spike and Slab Priors“. Bayesian Analysis 14, Nr. 3 (September 2019): 805–28. http://dx.doi.org/10.1214/18-ba1131.

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4

Hernández-Lobato, José Miguel, Daniel Hernández-Lobato und Alberto Suárez. „Expectation propagation in linear regression models with spike-and-slab priors“. Machine Learning 99, Nr. 3 (10.12.2014): 437–87. http://dx.doi.org/10.1007/s10994-014-5475-7.

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5

Scheipl, Fabian, Ludwig Fahrmeir und Thomas Kneib. „Spike-and-Slab Priors for Function Selection in Structured Additive Regression Models“. Journal of the American Statistical Association 107, Nr. 500 (17.10.2012): 1518–32. http://dx.doi.org/10.1080/01621459.2012.737742.

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6

Yen, Tso-Jung. „A majorization–minimization approach to variable selection using spike and slab priors“. Annals of Statistics 39, Nr. 3 (Juni 2011): 1748–75. http://dx.doi.org/10.1214/11-aos884.

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7

Koch, Brandon, David M. Vock, Julian Wolfson und Laura Boehm Vock. „Variable selection and estimation in causal inference using Bayesian spike and slab priors“. Statistical Methods in Medical Research 29, Nr. 9 (15.01.2020): 2445–69. http://dx.doi.org/10.1177/0962280219898497.

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Unbiased estimation of causal effects with observational data requires adjustment for confounding variables that are related to both the outcome and treatment assignment. Standard variable selection techniques aim to maximize predictive ability of the outcome model, but they ignore covariate associations with treatment and may not adjust for important confounders weakly associated to outcome. We propose a novel method for estimating causal effects that simultaneously considers models for both outcome and treatment, which we call the bilevel spike and slab causal estimator (BSSCE). By using a Bayesian formulation, BSSCE estimates the posterior distribution of all model parameters and provides straightforward and reliable inference. Spike and slab priors are used on each covariate coefficient which aim to minimize the mean squared error of the treatment effect estimator. Theoretical properties of the treatment effect estimator are derived justifying the prior used in BSSCE. Simulations show that BSSCE can substantially reduce mean squared error over numerous methods and performs especially well with large numbers of covariates, including situations where the number of covariates is greater than the sample size. We illustrate BSSCE by estimating the causal effect of vasoactive therapy vs. fluid resuscitation on hypotensive episode length for patients in the Multiparameter Intelligent Monitoring in Intensive Care III critical care database.

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Xi, Ruibin, Yunxiao Li und Yiming Hu. „Bayesian Quantile Regression Based on the Empirical Likelihood with Spike and Slab Priors“. Bayesian Analysis 11, Nr. 3 (September 2016): 821–55. http://dx.doi.org/10.1214/15-ba975.

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Legramanti, Sirio, Daniele Durante und David B. Dunson. „Bayesian cumulative shrinkage for infinite factorizations“. Biometrika 107, Nr. 3 (27.05.2020): 745–52. http://dx.doi.org/10.1093/biomet/asaa008.

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Summary The dimension of the parameter space is typically unknown in a variety of models that rely on factorizations. For example, in factor analysis the number of latent factors is not known and has to be inferred from the data. Although classical shrinkage priors are useful in such contexts, increasing shrinkage priors can provide a more effective approach that progressively penalizes expansions with growing complexity. In this article we propose a novel increasing shrinkage prior, called the cumulative shrinkage process, for the parameters that control the dimension in overcomplete formulations. Our construction has broad applicability and is based on an interpretable sequence of spike-and-slab distributions which assign increasing mass to the spike as the model complexity grows. Using factor analysis as an illustrative example, we show that this formulation has theoretical and practical advantages relative to current competitors, including an improved ability to recover the model dimension. An adaptive Markov chain Monte Carlo algorithm is proposed, and the performance gains are outlined in simulations and in an application to personality data.

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Yi, Jieyi, und Niansheng Tang. „Variational Bayesian Inference in High-Dimensional Linear Mixed Models“. Mathematics 10, Nr. 3 (31.01.2022): 463. http://dx.doi.org/10.3390/math10030463.

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In high-dimensional regression models, the Bayesian lasso with the Gaussian spike and slab priors is widely adopted to select variables and estimate unknown parameters. However, it involves large matrix computations in a standard Gibbs sampler. To solve this issue, the Skinny Gibbs sampler is employed to draw observations required for Bayesian variable selection. However, when the sample size is much smaller than the number of variables, the computation is rather time-consuming. As an alternative to the Skinny Gibbs sampler, we develop a variational Bayesian approach to simultaneously select variables and estimate parameters in high-dimensional linear mixed models under the Gaussian spike and slab priors of population-specific fixed-effects regression coefficients, which are reformulated as a mixture of a normal distribution and an exponential distribution. The coordinate ascent algorithm, which can be implemented efficiently, is proposed to optimize the evidence lower bound. The Bayes factor, which can be computed with the path sampling technique, is presented to compare two competing models in the variational Bayesian framework. Simulation studies are conducted to assess the performance of the proposed variational Bayesian method. An empirical example is analyzed by the proposed methodologies.

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Chen, Su, und Stephen G. Walker. „Fast Bayesian variable selection for high dimensional linear models: Marginal solo spike and slab priors“. Electronic Journal of Statistics 13, Nr. 1 (2019): 284–309. http://dx.doi.org/10.1214/18-ejs1529.

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Leach, Justin M., Lloyd J. Edwards, Rajesh Kana, Kristina Visscher, Nengjun Yi und Inmaculada Aban. „The spike-and-slab elastic net as a classification tool in Alzheimer’s disease“. PLOS ONE 17, Nr. 2 (03.02.2022): e0262367. http://dx.doi.org/10.1371/journal.pone.0262367.

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Alzheimer’s disease (AD) is the leading cause of dementia and has received considerable research attention, including using neuroimaging biomarkers to classify patients and/or predict disease progression. Generalized linear models, e.g., logistic regression, can be used as classifiers, but since the spatial measurements are correlated and often outnumber subjects, penalized and/or Bayesian models will be identifiable, while classical models often will not. Many useful models, e.g., the elastic net and spike-and-slab lasso, perform automatic variable selection, which removes extraneous predictors and reduces model variance, but neither model exploits spatial information in selecting variables. Spatial information can be incorporated into variable selection by placing intrinsic autoregressive priors on the logit probabilities of inclusion within a spike-and-slab elastic net framework. We demonstrate the ability of this framework to improve classification performance by using cortical thickness and tau-PET images from the Alzheimer’s Disease Neuroimaging Initiative (ADNI) to classify subjects as cognitively normal or having dementia, and by using a simulation study to examine model performance using finer resolution images.

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Nayek, R., R. Fuentes, K. Worden und E. J. Cross. „On spike-and-slab priors for Bayesian equation discovery of nonlinear dynamical systems via sparse linear regression“. Mechanical Systems and Signal Processing 161 (Dezember 2021): 107986. http://dx.doi.org/10.1016/j.ymssp.2021.107986.

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Fan, Yue, Xiao Wang und Qinke Peng. „Inference of Gene Regulatory Networks Using Bayesian Nonparametric Regression and Topology Information“. Computational and Mathematical Methods in Medicine 2017 (2017): 1–8. http://dx.doi.org/10.1155/2017/8307530.

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Gene regulatory networks (GRNs) play an important role in cellular systems and are important for understanding biological processes. Many algorithms have been developed to infer the GRNs. However, most algorithms only pay attention to the gene expression data but do not consider the topology information in their inference process, while incorporating this information can partially compensate for the lack of reliable expression data. Here we develop a Bayesian group lasso with spike and slab priors to perform gene selection and estimation for nonparametric models. B-spline basis functions are used to capture the nonlinear relationships flexibly and penalties are used to avoid overfitting. Further, we incorporate the topology information into the Bayesian method as a prior. We present the application of our method on DREAM3 and DREAM4 datasets and two real biological datasets. The results show that our method performs better than existing methods and the topology information prior can improve the result.

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Mohammed, Shariq, Dipak K. Dey und Yuping Zhang. „Bayesian variable selection using spike‐and‐slab priors with application to high dimensional electroencephalography data by local modelling“. Journal of the Royal Statistical Society: Series C (Applied Statistics) 68, Nr. 5 (26.07.2019): 1305–26. http://dx.doi.org/10.1111/rssc.12369.

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Liu, Yunli, und Xin Tong. „A Tutorial on Bayesian Linear Regression with Compositional Predictors Using JAGS“. Journal of Behavioral Data Science 4, Nr. 1 (28.01.2024): 1–24. http://dx.doi.org/10.35566/jbds/tongliu.

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This tutorial offers an exploration of advanced Bayesian methodologies for compositional data analysis, specifically the Bayesian Lasso and Bayesian Spike-and-Slab Lasso (SSL) techniques. Our focus is on a novel Bayesian methodology that integrates Lasso and SSL priors, enhancing both parameter estimation and variable selection for linear regression with compositional predictors. The tutorial is structured to streamline the learning process, breaking down complex analyses into a series of straightforward steps. We demonstrate these methods using R and JAGS, employing simulated datasets to illustrate key concepts. Our objective is to provide a clear and comprehensive understanding of these sophisticated Bayesian techniques, preparing readers to adeptly navigate and apply these methods in their own compositional data analysis endeavors.

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Brandt, Holger, Jenna Cambria und Augustin Kelava. „An Adaptive Bayesian Lasso Approach with Spike-and-Slab Priors to Identify Multiple Linear and Nonlinear Effects in Structural Equation Models“. Structural Equation Modeling: A Multidisciplinary Journal 25, Nr. 6 (12.06.2018): 946–60. http://dx.doi.org/10.1080/10705511.2018.1474114.

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Bassetti, Federico, und Lucia Ladelli. „Mixture of Species Sampling Models“. Mathematics 9, Nr. 23 (04.12.2021): 3127. http://dx.doi.org/10.3390/math9233127.

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We introduce mixtures of species sampling sequences (mSSS) and discuss how these sequences are related to various types of Bayesian models. As a particular case, we recover species sampling sequences with general (not necessarily diffuse) base measures. These models include some “spike-and-slab” non-parametric priors recently introduced to provide sparsity. Furthermore, we show how mSSS arise while considering hierarchical species sampling random probabilities (e.g., the hierarchical Dirichlet process). Extending previous results, we prove that mSSS are obtained by assigning the values of an exchangeable sequence to the classes of a latent exchangeable random partition. Using this representation, we give an explicit expression of the Exchangeable Partition Probability Function of the partition generated by an mSSS. Some special cases are discussed in detail—in particular, species sampling sequences with general base measures and a mixture of species sampling sequences with Gibbs-type latent partition. Finally, we give explicit expressions of the predictive distributions of an mSSS.

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Martínez, Carlos Alberto, Kshitij Khare, Arunava Banerjee und Mauricio A. Elzo. „Joint genome-wide prediction in several populations accounting for randomness of genotypes: A hierarchical Bayes approach. II: Multivariate spike and slab priors for marker effects and derivation of approximate Bayes and fractional Bayes factors for the complete family of models“. Journal of Theoretical Biology 417 (März 2017): 131–41. http://dx.doi.org/10.1016/j.jtbi.2016.12.022.

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Lu, Xiaoqiang, Yuan Yuan und Pingkun Yan. „Sparse coding for image denoising using spike and slab prior“. Neurocomputing 106 (April 2013): 12–20. http://dx.doi.org/10.1016/j.neucom.2012.09.014.

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Haller, Olivia C., Tricia Z. King, Xin Ma, Negar Fani und Suprateek Kundu. „5 White Matter Tract Shape as a Predictor of PTSD Symptom Severity in Trauma-Exposed Black American Women“. Journal of the International Neuropsychological Society 29, s1 (November 2023): 519–20. http://dx.doi.org/10.1017/s1355617723006690.

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Objective:Machine learning studies of PTSD show promise for identifying neurobiological signatures of this disorder, but studies to date have largely excluded Black American women, who experience disproportionately greater trauma and have relatively higher rates of PTSD. PTSD is characterized by four symptom clusters: trauma reexperiencing, trauma avoidance, hyperarousal, and anhedonia. A prior machine learning study reported successful PTSD symptom cluster severity prediction using functional MRI data but did not examine white matter predictors. White matter microstructural integrity has been related to PTSD presence and symptoms, and unexplored metrics such as estimates of tract shape may provide unique predictive utility. Therefore, this study examines the relationship between white matter tract shape and PTSD symptom cluster severity amongst trauma-exposed Black American women using multiple machine learning models.Participants and Methods:Participants included 45 Black American women with PTSD (Mage=40.4(12.9)) and 89 trauma-exposed controls (Mage=39.8(11.6)). Shape and diffusion metrics for the cingulum, corpus callosum, fornix, inferior longitudinal fasciculus, superior longitudinal fasciculus, and uncinate fasciculus were calculated using deterministic tractography. Current symptom severity was calculated using the PTSD Symptom Scales. Input features included tract metrics, questionnaire responses, and age. The following regression models were generated: least absolute shrinkage and selection operator (LASSO), ridge, elastic net, and gaussian process (GPR). Additionally, two forms of latent-scale GPR, one without (lsGPR) and with (sp-lsGPR) node selection via spike and slab priors, were calculated. The performance of regression models was estimated using mean square error (MSE) and R2.Results:sp-lsGPR performed at or above other models across all symptom clusters. LASSO models were comparable to sp-lsGPR for avoidance and hyperarousal clusters. Ridge regression and GPR had the weakest performance across clusters. Scores for sp-lsGPR by cluster are as follows: reexperiencing Mmse=0.70(0.17), Mr2=0.56(0.13); avoidance Mmse=0.75(0.17), Mr2= 0.51(0.13); hyperarousal Mmse=0.57(0.18), Mr2=0.66(0.12); anhedonia Mmse=0.74(0.27), Mr2=0.57(0.13). The top three ranked posterior inclusion probabilities for white matter tracts across sp-lsGPR models include four sections of the cingulum, three sections of the corpus callosum, the right fornix, the left inferior longitudinal fasciculus, the first segment of the right superior longitudinal fasciculus, and the right uncincate fasciculus. The greatest posterior inclusion probability value for the sp-lsGPR models was the left frontal parahippocampal cingulum for the hyperarousal cluster.Conclusions:Results support the combined predictive utility of white matter metrics for brain imaging regression models of PTSD. Results also support the use of sp-lsGPR models, which are designed to balance interpretable linear models and highly-flexible non-linear models. The sp-lsGPR model performance was similar across clusters but was relatively better for the hyperarousal cluster. This finding contrasts with prior machine learning work using functional data which was unable to predict hyperarousal scores above chance (MR2=0.06). These diverging findings highlight the importance of examining both functional and structural data in PTSD populations. Differing findings may also be related to sample characteristics as the prior study was conducted in China. Black American women and Chinese individuals have unique lived experiences that may differentially impact brain structure and function. Future work should continue to include diverse research samples to account for such experiences.

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Ročková, Veronika. „Bayesian estimation of sparse signals with a continuous spike-and-slab prior“. Annals of Statistics 46, Nr. 1 (Februar 2018): 401–37. http://dx.doi.org/10.1214/17-aos1554.

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Canale, A., A. Lijoi, B. Nipoti und I. Prünster. „On the Pitman–Yor process with spike and slab base measure“. Biometrika 104, Nr. 3 (03.08.2017): 681–97. http://dx.doi.org/10.1093/biomet/asx041.

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Summary For the most popular discrete nonparametric models, beyond the Dirichlet process, the prior guess at the shape of the data-generating distribution, also known as the base measure, is assumed to be diffuse. Such a specification greatly simplifies the derivation of analytical results, allowing for a straightforward implementation of Bayesian nonparametric inferential procedures. However, in several applied problems the available prior information leads naturally to the incorporation of an atom into the base measure, and then the Dirichlet process is essentially the only tractable choice for the prior. In this paper we fill this gap by considering the Pitman–Yor process with an atom in its base measure. We derive computable expressions for the distribution of the induced random partitions and for the predictive distributions. These findings allow us to devise an effective generalized Pólya urn Gibbs sampler. Applications to density estimation, clustering and curve estimation, with both simulated and real data, serve as an illustration of our results and allow comparisons with existing methodology. In particular, we tackle a functional data analysis problem concerning basal body temperature curves.

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Serra, Juan G., Javier Mateos, Rafael Molina und Aggelos K. Katsaggelos. „Variational EM method for blur estimation using the spike-and-slab image prior“. Digital Signal Processing 88 (Mai 2019): 116–29. http://dx.doi.org/10.1016/j.dsp.2019.01.004.

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Zhang, Qi, Yihui Zhang und Yemao Xia. „Bayesian Feature Extraction for Two-Part Latent Variable Model with Polytomous Manifestations“. Mathematics 12, Nr. 5 (06.03.2024): 783. http://dx.doi.org/10.3390/math12050783.

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Semi-continuous data are very common in social sciences and economics. In this paper, a Bayesian variable selection procedure is developed to assess the influence of observed and/or unobserved exogenous factors on semi-continuous data. Our formulation is based on a two-part latent variable model with polytomous responses. We consider two schemes for the penalties of regression coefficients and factor loadings: a Bayesian spike and slab bimodal prior and a Bayesian lasso prior. Within the Bayesian framework, we implement a Markov chain Monte Carlo sampling method to conduct posterior inference. To facilitate posterior sampling, we recast the logistic model from Part One as a norm-type mixture model. A Gibbs sampler is designed to draw observations from the posterior. Our empirical results show that with suitable values of hyperparameters, the spike and slab bimodal method slightly outperforms Bayesian lasso in the current analysis. Finally, a real example related to the Chinese Household Financial Survey is analyzed to illustrate application of the methodology.

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Mohammed, Shariq, Dipak K. Dey und Yuping Zhang. „Classification of high‐dimensional electroencephalography data with location selection using structured spike‐and‐slab prior“. Statistical Analysis and Data Mining: The ASA Data Science Journal 13, Nr. 5 (28.07.2020): 465–81. http://dx.doi.org/10.1002/sam.11477.

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Meng, Xiangming, Sheng Wu, Michael Riis Andersen, Jiang Zhu und Zuyao Ni. „Efficient recovery of structured sparse signals via approximate message passing with structured spike and slab prior“. China Communications 15, Nr. 6 (Juni 2018): 1–17. http://dx.doi.org/10.1109/cc.2018.8398220.

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Thomson, W., S. Jabbari, A. E. Taylor, W. Arlt und D. J. Smith. „Simultaneous parameter estimation and variable selection via the logit-normal continuous analogue of the spike-and-slab prior“. Journal of The Royal Society Interface 16, Nr. 150 (Januar 2019): 20180572. http://dx.doi.org/10.1098/rsif.2018.0572.

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We introduce a Bayesian prior distribution, the logit-normal continuous analogue of the spike-and-slab, which enables flexible parameter estimation and variable/model selection in a variety of settings. We demonstrate its use and efficacy in three case studies—a simulation study and two studies on real biological data from the fields of metabolomics and genomics. The prior allows the use of classical statistical models, which are easily interpretable and well known to applied scientists, but performs comparably to common machine learning methods in terms of generalizability to previously unseen data.

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Zhu, Xiaowei, Yu Han, Shichong Li und Xinyin Wang. „A spatial-temporal topic model with sparse prior and RNN prior for bursty topic discovering in social networks“. Journal of Intelligent & Fuzzy Systems 42, Nr. 4 (04.03.2022): 3909–22. http://dx.doi.org/10.3233/jifs-212135.

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With the rapid growth of social network users, the social network has accumulated massive social network topics. However, due to the randomness of content, it becomes sparse and noisy, accompanied by many daily chats and meaningless topics, which brings challenges to bursty topics discovery. To deal with these problems, this paper proposes the spatial-temporal topic model with sparse prior and recurrent neural networks (RNN) prior for bursty topic discovering (ST-SRTM). The semantic relationship of words is learned through RNN to alleviate the sparsity. The spatial-temporal areas information is introduced to focus on bursty topics for further weakening the semantic sparsity of social network context. Besides, we introduced the “Spike and Slab” prior to decouple the sparseness and smoothness. Simultaneously, we realized the automatic discovery of social network bursts by introducing the burstiness of words as the prior and binary switching variables. We constructed multiple sets of comparative experiments to verify the performance of ST-SRTM by leveraging different evaluation indicators on real Sina Weibo data sets. The experimental results confirm the superiority of our ST-SRTM.

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Marnissi, Yosra, Yasmine Hawwari, Amadou Assoumane, Dany Abboud und Mohamed El-Badaoui. „On the Use of Structured Prior Models for Bayesian Compressive Sensing of Modulated Signals“. Applied Sciences 11, Nr. 6 (16.03.2021): 2626. http://dx.doi.org/10.3390/app11062626.

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The compressive sensing (CS) of mechanical signals is an emerging research topic for remote condition monitoring. The signals generated by machines are mostly periodic due to the rotating nature of its components. Often, these vibrations witness strong interactions among two or multiple rotating sources, leading to modulation phenomena. This paper is specifically concerned with the CS of this particular class of signals using a Bayesian approach. The main contribution of this paper is to consider the particular spectral structure of these signals through two families of hierarchical models. The first one adopts a block-sparse model that jointly estimates the sparse coefficients at identical or symmetrical positions around the carrier frequencies. The second is a spike-and-slab model where the spike component takes into account the symmetrical properties of the support of non-zero-coefficients in the spectrum. The resulting posterior distribution is approximated using a Gibbs sampler. Simulations show that considering the structure in the prior model yields better noise shrinkage and better reconstruction of small side-bands. Application to condition monitoring of a gearbox through CS of vibration signals highlights the good performance of the proposed models in reconstructing the signal, offering an accurate fault detection with relatively high compression rate.

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Chen, Xian Bo, Xing Hao Ding und Hui Liu. „MRI Denoising Based on a Non-Parametric Bayesian Image Sparse Representation Method“. Advanced Materials Research 219-220 (März 2011): 1354–58. http://dx.doi.org/10.4028/www.scientific.net/amr.219-220.1354.

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Magnetic Resonance images are often corrupted by Gaussian noise which highly affects the quality of MR images. In this paper, a Non-Parametric hierarchical Bayesian image sparse representation method is proposed to wipe out Gaussian distribution noise coupling in MR images. In this method a spike-slab prior is imposed on sparse coefficients, and a redundant dictionary is learned from the corrupted image. Experimental results show that the method not only improves the effect of MRI denoising, but also can obtain good estimation of the noise variance. Compared to non-local filter method, this model shows better visual quality as well as higher PSNR.

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Xu, Chendong, und Qisong Wu. „High-Resolution Through-the-Wall Radar Imaging with Exploitation of Target Structure“. Applied Sciences 12, Nr. 22 (17.11.2022): 11684. http://dx.doi.org/10.3390/app122211684.

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It is quite challenging for through-the-wall radar imaging (TWRI) to achieve high-resolution ghost-free imaging with limited measurements in an indoor multipath scenario. In this paper, a novel high-resolution TWRI algorithm with the exploitation of the target clustered structure in a hierarchical Bayesian framework is proposed. More specifically, an extended spike-and-slab clustered prior is imposed to statistically encourage the cluster formations in both downrange and crossrange domains of the target region, and a generative model of the proposed approach is provided. Then, a Markov Chain Monte Carol (MCMC) sampler is used to implement the posterior inference. Compared to other state-of-the-art algorithms, the proposed nonparametric Bayesian algorithm can preserve underlying target clustered properties and effectively suppress these isolated spurious scatterers without any prior information on targets themselves, such as sizes, shapes, and numbers.

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Zhao, Yuanying, und Dengke Xu. „A Bayesian Variable Selection Method for Spatial Autoregressive Quantile Models“. Mathematics 11, Nr. 4 (15.02.2023): 987. http://dx.doi.org/10.3390/math11040987.

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In this paper, a Bayesian variable selection method for spatial autoregressive (SAR) quantile models is proposed on the basis of spike and slab prior for regression parameters. The SAR quantile models, which are more generalized than SAR models and quantile regression models, are specified by adopting the asymmetric Laplace distribution for the error term in the classical SAR models. The proposed approach could perform simultaneously robust parametric estimation and variable selection in the context of SAR quantile models. Bayesian statistical inferences are implemented by a detailed Markov chain Monte Carlo (MCMC) procedure that combines Gibbs samplers with a probability integral transformation (PIT) algorithm. In the end, empirical numerical examples including several simulation studies and a Boston housing price data analysis are employed to demonstrate the newly developed methodologies.

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Ding, Xing Hao, und Xian Bo Chen. „Image Sparse Representation Based on a Nonparametric Bayesian Model“. Applied Mechanics and Materials 103 (September 2011): 109–14. http://dx.doi.org/10.4028/www.scientific.net/amm.103.109.

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In recent years there has been a growing interest in the research of image sparse representation. Sparse representation based on over-complete dictionary become another hot topic in the field of image processing. In this paper a Nonparametric Bayesian model based on hierarchical Bayesian theory is proposed. In this model a sparse spike-slab prior is imposed on sparse coefficients and the Non-parametric Bayesian techniques based on sparse image representation are considering for learning dictionary. Proposed model can learn an over-complete dictionary from original image. Furthermore, the unknown noise variance can be estimated from noisy image. As regards to the image sparse representation, proposed model obtains good sparse solution. Comparing to other state-of-the-art image sparse representation method, this model obtains better reconstruction effects.

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Culpepper, Steven Andrew, und Yinghan Chen. „Development and Application of an Exploratory Reduced Reparameterized Unified Model“. Journal of Educational and Behavioral Statistics 44, Nr. 1 (13.08.2018): 3–24. http://dx.doi.org/10.3102/1076998618791306.

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Exploratory cognitive diagnosis models (CDMs) estimate the Q matrix, which is a binary matrix that indicates the attributes needed for affirmative responses to each item. Estimation of Q is an important next step for improving classifications and broadening application of CDMs. Prior research primarily focused on an exploratory version of the restrictive deterministic-input, noisy-and-gate model, and research is needed to develop exploratory methods for more flexible CDMs. We consider Bayesian methods for estimating an exploratory version of the more flexible reduced reparameterized unified model (rRUM). We show that estimating the rRUM Q matrix is complicated by a confound between elements of Q and the rRUM item parameters. A Bayesian framework is presented that accurately recovers Q using a spike–slab prior for item parameters to select the required attributes for each item. We present Monte Carlo simulation studies, demonstrating the developed algorithm improves upon prior Bayesian methods for estimating the rRUM Q matrix. We apply the developed method to the Examination for the Certificate of Proficiency in English data set. The results provide evidence of five attributes with a partially ordered attribute hierarchy.

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Shi, Lei, Junping Du und Feifei Kou. „A Sparse Topic Model for Bursty Topic Discovery in Social Networks“. International Arab Journal of Information Technology 17, Nr. 5 (01.09.2020): 816–24. http://dx.doi.org/10.34028/iajit/17/5/15.

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Bursty topic discovery aims to automatically identify bursty events and continuously keep track of known events. The existing methods focus on the topic model. However, the sparsity of short text brings the challenge to the traditional topic models because the words are too few to learn from the original corpus. To tackle this problem, we propose a Sparse Topic Model (STM) for bursty topic discovery. First, we distinguish the modeling between the bursty topic and the common topic to detect the change of the words in time and discover the bursty words. Second, we introduce “Spike and Slab” prior to decouple the sparsity and smoothness of a distribution. The bursty words are leveraged to achieve automatic discovery of the bursty topics. Finally, to evaluate the effectiveness of our proposed algorithm, we collect Sina weibo dataset to conduct various experiments. Both qualitative and quantitative evaluations demonstrate that the proposed STM algorithm outperforms favorably against several state-of-the-art methods

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Shaddox, Elin, Christine B. Peterson, Francesco C. Stingo, Nicola A. Hanania, Charmion Cruickshank-Quinn, Katerina Kechris, Russell Bowler und Marina Vannucci. „Bayesian inference of networks across multiple sample groups and data types“. Biostatistics 21, Nr. 3 (26.12.2018): 561–76. http://dx.doi.org/10.1093/biostatistics/kxy078.

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Summary In this article, we develop a graphical modeling framework for the inference of networks across multiple sample groups and data types. In medical studies, this setting arises whenever a set of subjects, which may be heterogeneous due to differing disease stage or subtype, is profiled across multiple platforms, such as metabolomics, proteomics, or transcriptomics data. Our proposed Bayesian hierarchical model first links the network structures within each platform using a Markov random field prior to relate edge selection across sample groups, and then links the network similarity parameters across platforms. This enables joint estimation in a flexible manner, as we make no assumptions on the directionality of influence across the data types or the extent of network similarity across the sample groups and platforms. In addition, our model formulation allows the number of variables and number of subjects to differ across the data types, and only requires that we have data for the same set of groups. We illustrate the proposed approach through both simulation studies and an application to gene expression levels and metabolite abundances on subjects with varying severity levels of chronic obstructive pulmonary disease. Bayesian inference; Chronic obstructive pulmonary disease (COPD); Data integration; Gaussian graphical model; Markov random field prior; Spike and slab prior.

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Kalinina, Irina A., und Aleksandr P. Gozhyj. „Modeling and forecasting of nonlinear nonstationary processes based on the Bayesian structural time series“. Applied Aspects of Information Technology 5, Nr. 3 (25.10.2022): 240–55. http://dx.doi.org/10.15276/aait.05.2022.17.

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The article describes an approach to modelling and forecasting non-linear non-stationary time series for various purposes using Bayesian structural time series. The concepts of non-linearity and non-stationarity, as well as methods for processing non-linearity’sand non-stationarity in the construction of forecasting models are considered. The features of the Bayesian approach in the processing of nonlinearities and nonstationaryare presented. An approach to the construction of probabilistic-statistical models based on Bayesian structural models of time series has been studied. Parametric and non-parametric methods for forecasting non-linear and non-stationary time series are considered. Parametric methods include methods: classical autoregressive models, neural networks, models of support vector machines, hidden Markov models. Non-parametric methods include methods: state-space models, functional decomposition models, Bayesian non-parametric models. One of the types of non-parametric models isBayesian structural time series. The main features of constructing structural time series are considered. Models of structural time series are presented. The process of learning the Bayesianstructural model of time series is described. Training is performed in four stages: setting the structure of the model and a priori probabilities; applying a Kalman filter to update state estimates based on observed data;application of the “spike-and-slab”method to select variables in a structural model; Bayesian averaging to combine the results to make a prediction. An algorithm for constructing a Bayesian structural time seriesmodel is presented. Various components of the BSTS model are considered andanalysed, with the help of which the structures of alternative predictive models are formed. As an example of the application of Bayesian structural time series, the problem of predicting Amazon stock prices is considered. The base dataset is amzn_share. After loading, the structure and data types were analysed, and missing values were processed. The data are characterized by irregular registration of observations, which leads to a large number of missing values and “masking” possible seasonal fluctuations. This makes the task of forecasting rather difficult. To restore gaps in the amzn_sharetime series, the linear interpolation method was used. Using a set of statistical tests (ADF, KPSS, PP), the series was tested for stationarity. The data set is divided into two parts: training and testing. The fitting of structural models of time series was performed using the Kalman filterand the Monte Carlo method according to the Markov chain scheme. To estimate and simultaneously regularize the regression coefficients, the spike-and-slab method was applied. The quality of predictive models was assessed.

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Qin, Si, Yimin D. Zhang, Qisong Wu und Moeness G. Amin. „Structure-Aware Bayesian Compressive Sensing for Near-Field Source Localization Based on Sensor-Angle Distributions“. International Journal of Antennas and Propagation 2015 (2015): 1–15. http://dx.doi.org/10.1155/2015/783467.

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A novel technique for localization of narrowband near-field sources is presented. The technique utilizes the sensor-angle distribution (SAD) that treats the source range and direction-of-arrival (DOA) information as sensor-dependent phase progression. The SAD draws parallel to quadratic time-frequency distributions and, as such, is able to reveal the changes in the spatial frequency over sensor positions. For a moderate source range, the SAD signature is of a polynomial shape, thus simplifying the parameter estimation. Both uniform and sparse linear arrays are considered in this work. To exploit the sparsity and continuity of the SAD signature in the joint space and spatial frequency domain, a modified Bayesian compressive sensing algorithm is exploited to estimate the SAD signature. In this method, a spike-and-slab prior is used to statistically encourage sparsity of the SAD across each segmented SAD region, and a patterned prior is imposed to enforce the continuous structure of the SAD. The results are then mapped back to source range and DOA estimation for source localization. The effectiveness of the proposed technique is verified using simulation results with uniform and sparse linear arrays where the array sensors are located on a grid but with consecutive and missing positions.

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Xu, Yuanyuan, Jun Wang und Jinmao Wei. „To Avoid the Pitfall of Missing Labels in Feature Selection: A Generative Model Gives the Answer“. Proceedings of the AAAI Conference on Artificial Intelligence 34, Nr. 04 (03.04.2020): 6534–41. http://dx.doi.org/10.1609/aaai.v34i04.6127.

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In multi-label learning, instances have a large number of noisy and irrelevant features, and each instance is associated with a set of class labels wherein label information is generally incomplete. These missing labels possess two sides like a coin; people cannot predict whether their provided information for feature selection is favorable (relevant) or not (irrelevant) during tossing. Existing approaches either superficially consider the missing labels as negative or indiscreetly impute them with some predicted values, which may either overestimate unobserved labels or introduce new noises in selecting discriminative features. To avoid the pitfall of missing labels, a novel unified framework of selecting discriminative features and modeling incomplete label matrix is proposed from a generative point of view in this paper. Concretely, we relax Smoothness Assumption to infer the label observability, which can reveal the positions of unobserved labels, and employ the spike-and-slab prior to perform feature selection by excluding unobserved labels. Using a data-augmentation strategy leads to full local conjugacy in our model, facilitating simple and efficient Expectation Maximization (EM) algorithm for inference. Quantitative and qualitative experimental results demonstrate the superiority of the proposed approach under various evaluation metrics.

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Liu, Qi, Louis J. Muglia und Lei Frank Huang. „Network as a Biomarker: A Novel Network-Based Sparse Bayesian Machine for Pathway-Driven Drug Response Prediction“. Genes 10, Nr. 8 (09.08.2019): 602. http://dx.doi.org/10.3390/genes10080602.

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With the advances in different biological networks including gene regulation, gene co-expression, protein–protein interaction networks, and advanced approaches for network reconstruction, analysis, and interpretation, it is possible to discover reliable and accurate molecular network-based biomarkers for monitoring cancer treatment. Such efforts will also pave the way toward the realization of biomarker-driven personalized medicine against cancer. Previously, we have reconstructed disease-specific driver signaling networks using multi-omics profiles and cancer signaling pathway data. In this study, we developed a network-based sparse Bayesian machine (NBSBM) approach, using previously derived disease-specific driver signaling networks to predict cancer cell responses to drugs. NBSBM made use of the information encoded in a disease-specific (differentially expressed) network to improve its prediction performance in problems with a reduced amount of training data and a very high-dimensional feature space. Sparsity in NBSBM is favored by a spike and slab prior distribution, which is combined with a Markov random field prior that encodes the network of feature dependencies. Gene features that are connected in the network are assumed to be both relevant and irrelevant to drug responses. We compared the proposed method with network-based support vector machine (NBSVM) approaches and found that the NBSBM approach could achieve much better accuracy than the other two NBSVM methods. The gene modules selected from the disease-specific driver networks for predicting drug sensitivity might be directly involved in drug sensitivity or resistance. This work provides a disease-specific network-based drug sensitivity prediction approach and can uncover the potential mechanisms of the action of drugs by selecting the most predictive sub-networks from the disease-specific network.

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Dong, Xianlei, Jian Xu, Ying Ding, Chenwei Zhang, Kunpeng Zhang und Min Song. „Understanding the Correlations between Social Attention and Topic Trends of Scientific Publications“. Journal of Data and Information Science 1, Nr. 1 (01.09.2017): 28–49. http://dx.doi.org/10.20309/jdis.201604.

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AbstractPurposeWe propose and apply a simplified nowcasting model to understand the correlations between social attention and topic trends of scientific publications.Design/methodology/approachFirst, topics are generated from the obesity corpus by using the latent Dirichlet allocation (LDA) algorithm and time series of keyword search trends in Google Trends are obtained. We then establish the structural time series model using data from January 2004 to December 2012, and evaluate the model using data from January 2013. We employ a state-space model to separate different non-regression components in an observational time series (i.e. the tendency and the seasonality) and apply the “spike and slab prior” and stepwise regression to analyze the correlations between the regression component and the social media attention. The two parts are combined using Markov-chain Monte Carlo sampling techniques to obtain our results.FindingsThe results of our study show that (1) the number of publications on child obesity increases at a lower rate than that of diabetes publications; (2) the number of publication on a given topic may exhibit a relationship with the season or time of year; and (3) there exists a correlation between the number of publications on a given topic and its social media attention, i.e. the search frequency related to that topic as identified by Google Trends. We found that our model is also able to predict the number of publications related to a given topic.Research limitationsFirst, we study a correlation rather than causality between topics’ trends and social media. As a result, the relationships might not be robust, so we cannot predict the future in the long run. Second, we cannot identify the reasons or conditions that are driving obesity topics to present such tendencies and seasonal patterns, so we might need to do “field” study in the future. Third, we need to improve the efficiency of our model by finding more efficient variable selection models, because the stepwise regression method is time consuming, especially for a large number of variables.Practical implicationsThis paper analyzes publication topic trends from three perspectives: tendency, seasonality, and correlation with social media attention, providing a new perspective for identifying and understanding topical themes in academic publications.Originality/valueTo the best of our knowledge, we are the first to apply the state-space model to examine the relationships between healthcare-related publications and social media to investigate the relationships between a topic’s evolvement and people’s search behavior in social media. This paper thus provides a new viewpoint in the correlation analysis area, and demonstrates the value of considering social media attention in the analysis of publication topic trends.

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Frühwirth-Schnatter, Sylvia. „Generalized cumulative shrinkage process priors with applications to sparse Bayesian factor analysis“. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 381, Nr. 2247 (27.03.2023). http://dx.doi.org/10.1098/rsta.2022.0148.

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The paper discusses shrinkage priors which impose increasing shrinkage in a sequence of parameters. We review the cumulative shrinkage process (CUSP) prior of Legramanti et al. (Legramanti et al . 2020 Biometrika 107 , 745–752. ( doi:10.1093/biomet/asaa008 )), which is a spike-and-slab shrinkage prior where the spike probability is stochastically increasing and constructed from the stick-breaking representation of a Dirichlet process prior. As a first contribution, this CUSP prior is extended by involving arbitrary stick-breaking representations arising from beta distributions. As a second contribution, we prove that exchangeable spike-and-slab priors, which are popular and widely used in sparse Bayesian factor analysis, can be represented as a finite generalized CUSP prior, which is easily obtained from the decreasing order statistics of the slab probabilities. Hence, exchangeable spike-and-slab shrinkage priors imply increasing shrinkage as the column index in the loading matrix increases, without imposing explicit order constraints on the slab probabilities. An application to sparse Bayesian factor analysis illustrates the usefulness of the findings of this paper. A new exchangeable spike-and-slab shrinkage prior based on the triple gamma prior of Cadonna et al. (Cadonna et al . 2020 Econometrics 8 , 20. ( doi:10.3390/econometrics8020020 )) is introduced and shown to be helpful for estimating the unknown number of factors in a simulation study. This article is part of the theme issue ‘Bayesian inference: challenges, perspectives, and prospects’.

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Malsiner-Walli, Gertraud, und Helga Wagner. „Comparing Spike and Slab Priors for Bayesian Variable Selection“. Austrian Journal of Statistics 40, Nr. 4 (24.02.2016). http://dx.doi.org/10.17713/ajs.v40i4.215.

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An important task in building regression models is to decide which regressors should be included in the final model. In a Bayesian approach, variable selection can be performed using mixture priors with a spike and a slab component for the effects subject to selection. As the spike is concentrated at zero, variable selection is based on the probability of assigning the corresponding regression effect to the slab component. These posterior inclusion probabilities can be determined by MCMC sampling. In this paper we compare the MCMC implementations for several spike and slab priors with regard to posterior inclusion probabilities and their sampling efficiency for simulated data. Further, we investigate posterior inclusion probabilities analytically for different slabs in two simple settings. Application of variable selection with spike and slab priors is illustrated on a data set of psychiatric patients where the goal is to identify covariates affecting metabolism.

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Samorodnitsky, Sarah, Katherine A. Hoadley und Eric F. Lock. „A hierarchical spike-and-slab model for pan-cancer survival using pan-omic data“. BMC Bioinformatics 23, Nr. 1 (17.06.2022). http://dx.doi.org/10.1186/s12859-022-04770-3.

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Abstract Background Pan-omics, pan-cancer analysis has advanced our understanding of the molecular heterogeneity of cancer. However, such analyses have been limited in their ability to use information from multiple sources of data (e.g., omics platforms) and multiple sample sets (e.g., cancer types) to predict clinical outcomes. We address the issue of prediction across multiple high-dimensional sources of data and sample sets by using molecular patterns identified by BIDIFAC+, a method for integrative dimension reduction of bidimensionally-linked matrices, in a Bayesian hierarchical model. Our model performs variable selection through spike-and-slab priors that borrow information across clustered data. We use this model to predict overall patient survival from the Cancer Genome Atlas with data from 29 cancer types and 4 omics sources and use simulations to characterize the performance of the hierarchical spike-and-slab prior. Results We found that molecular patterns shared across all or most cancers were largely not predictive of survival. However, our model selected patterns unique to subsets of cancers that differentiate clinical tumor subtypes with markedly different survival outcomes. Some of these subtypes were previously established, such as subtypes of uterine corpus endometrial carcinoma, while others may be novel, such as subtypes within a set of kidney carcinomas. Through simulations, we found that the hierarchical spike-and-slab prior performs best in terms of variable selection accuracy and predictive power when borrowing information is advantageous, but also offers competitive performance when it is not. Conclusions We address the issue of prediction across multiple sources of data by using results from BIDIFAC+ in a Bayesian hierarchical model for overall patient survival. By incorporating spike-and-slab priors that borrow information across cancers, we identified molecular patterns that distinguish clinical tumor subtypes within a single cancer and within a group of cancers. We also corroborate the flexibility and performance of using spike-and-slab priors as a Bayesian variable selection approach.

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Cappello, Lorenzo, Oscar Hernan Madrid Padilla und Julia A. Palacios. „Bayesian change point detection with spike and slab priors“. Journal of Computational and Graphical Statistics, 21.02.2023, 1–24. http://dx.doi.org/10.1080/10618600.2023.2182312.

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Antonelli, Joseph, Ander Wilson und Brent Coull. „Bayesian distributed lag interaction models using spike and slab priors“. ISEE Conference Abstracts 2021, Nr. 1 (23.08.2021). http://dx.doi.org/10.1289/isee.2021.o-sy-069.

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Tendeiro, Jorge N., und Henk A. L. Kiers. „With Bayesian estimation one can get all that Bayes factors offer, and more“. Psychonomic Bulletin & Review, 09.09.2022. http://dx.doi.org/10.3758/s13423-022-02164-3.

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AbstractIn classical statistics, there is a close link between null hypothesis significance testing (NHST) and parameter estimation via confidence intervals. However, for the Bayesian counterpart, a link between null hypothesis Bayesian testing (NHBT) and Bayesian estimation via a posterior distribution is less straightforward, but does exist, and has recently been reiterated by Rouder, Haaf, and Vandekerckhove (2018). It hinges on a combination of a point mass probability and a probability density function as prior (denoted as the spike-and-slab prior). In the present paper, it is first carefully explained how the spike-and-slab prior is defined, and how results can be derived for which proofs were not given in Rouder, Haaf, and Vandekerckhove (2018). Next, it is shown that this spike-and-slab prior can be approximated by a pure probability density function with a rectangular peak around the center towering highly above the remainder of the density function. Finally, we will indicate how this ‘hill-and-chimney’ prior may in turn be approximated by fully continuous priors. In this way, it is shown that NHBT results can be approximated well by results from estimation using a strongly peaked prior, and it is noted that the estimation itself offers more than merely the posterior odds on which NHBT is based. Thus, it complies with the strong APA requirement of not just mentioning testing results but also offering effect size information. It also offers a transparent perspective on the NHBT approach employing a prior with a strong peak around the chosen point null hypothesis value.

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Zhu, Rui, Sufang Chen, Dong Jiang, Shitao Xie, Lei Ma, Stefano Marchesiello und Dario Anastasio. „Enhancing Nonlinear Subspace Identification Using Sparse Bayesian Learning with Spike and Slab Priors“. Journal of Vibration Engineering & Technologies, 07.06.2023. http://dx.doi.org/10.1007/s42417-023-01030-3.

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Yang, Cheng‐Han, Evan Kwiatkowski, J. Jack Lee und Ruitao Lin. „REDOMA: Bayesian random‐effects dose‐optimization meta‐analysis using spike‐and‐slab priors“. Statistics in Medicine, 10.06.2024. http://dx.doi.org/10.1002/sim.10107.

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The rise of cutting‐edge precision cancer treatments has led to a growing significance of the optimal biological dose (OBD) in modern oncology trials. These trials now prioritize the consideration of both toxicity and efficacy simultaneously when determining the most desirable dosage for treatment. Traditional approaches in early‐phase oncology trials have conventionally relied on the assumption of a monotone relationship between treatment efficacy and dosage. However, this assumption may not hold valid for novel oncology therapies. In reality, the dose‐efficacy curve of such treatments may reach a plateau at a specific dose, posing challenges for conventional methods in accurately identifying the OBD. Furthermore, achieving reliable identification of the OBD is typically not possible based on a single small‐sample trial. With data from multiple phase I and phase I/II trials, we propose a novel Bayesian random‐effects dose‐optimization meta‐analysis (REDOMA) approach to identify the OBD by synthesizing toxicity and efficacy data from each trial. The REDOMA method can address trials with heterogeneous characteristics. We adopt a curve‐free approach based on a Gamma process prior to model the average dose‐toxicity relationship. In addition, we utilize a Bayesian model selection framework that uses the spike‐and‐slab prior as an automatic variable selection technique to eliminate monotonic constraints on the dose‐efficacy curve. The good performance of the REDOMA method is confirmed by extensive simulation studies.

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