Bayesian Analysis最新文献_第6页

Deep Gaussian Processes for Calibration of Computer Models 校正计算机模型的深度高斯过程

IF 4.4 2区数学

Bayesian Analysis Pub Date : 2022-01-01 DOI: 10.1214/21-ba1293

Sébastien Marmin, M. Filippone

{"title":"Deep Gaussian Processes for Calibration of Computer Models","authors":"Sébastien Marmin, M. Filippone","doi":"10.1214/21-ba1293","DOIUrl":"https://doi.org/10.1214/21-ba1293","url":null,"abstract":". Bayesian calibration of black-box computer models oﬀers an estab-lished framework for quantiﬁcation of uncertainty of model parameters and predictions. Traditional Bayesian calibration involves the emulation of the computer model and an additive model discrepancy term using Gaussian processes; inference is then carried out using Markov chain Monte Carlo. This calibration approach is limited by the poor scalability of Gaussian processes and by the need to specify a sensible covariance function to deal with the complexity of the computer model and the discrepancy. In this work, we propose a novel calibration framework, where these challenges are addressed by means of compositions of Gaussian processes into Deep Gaussian processes and scalable variational inference techniques. Thanks to this formulation, it is possible to obtain a ﬂexible calibration approach, which is easy to implement in development environments featuring automatic dif-ferentiation and exploiting GPU-type hardware. We show how our proposal yields a powerful alternative to the state-of-the-art by means of experimental validations on various calibration problems. We conclude the paper by showing how we can carry out adaptive experimental design, and by discussing the identiﬁability properties of the proposed calibration model.","PeriodicalId":55398,"journal":{"name":"Bayesian Analysis","volume":null,"pages":null},"PeriodicalIF":4.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45174347","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 8

Bayesian Image-on-Scalar Regression with a Spatial Global-Local Spike-and-Slab Prior 具有空间全局局部Spike和Slab先验的标量回归的Bayes图像

IF 4.4 2区数学

Bayesian Analysis Pub Date : 2022-01-01 DOI: 10.1214/22-ba1352

Zijian Zeng, Meng Li, M. Vannucci

{"title":"Bayesian Image-on-Scalar Regression with a Spatial Global-Local Spike-and-Slab Prior","authors":"Zijian Zeng, Meng Li, M. Vannucci","doi":"10.1214/22-ba1352","DOIUrl":"https://doi.org/10.1214/22-ba1352","url":null,"abstract":"In this article, we propose a novel spatial global-local spike-and-slab selection prior for image-on-scalar regression. We consider a Bayesian hierarchical Gaussian process model for image smoothing, that uses a flexible Inverse-Wishart process prior to handle within-image dependency, and propose a general global-local spatial selection prior that extends a rich class of well-studied selection priors. Unlike existing constructions, we achieve simultaneous global (i.e, at covariate-level) and local (i.e., at pixel/voxel-level) selection by introducing `participation rate' parameters that measure the probability for the individual covariates to affect the observed images. This along with a hard-thresholding strategy leads to dependency between selections at the two levels, introduces extra sparsity at the local level, and allows the global selection to be informed by the local selection, all in a model-based manner. We design an efficient Gibbs sampler that allows inference for large image data. We show on simulated data that parameters are interpretable and lead to efficient selection. Finally, we demonstrate performance of the proposed model by using data from the Autism Brain Imaging Data Exchange (ABIDE) study. To the best of our knowledge, the proposed model construction is the first in the Bayesian literature to simultaneously achieve image smoothing, parameter estimation and a two-level variable selection for image-on-scalar regression.","PeriodicalId":55398,"journal":{"name":"Bayesian Analysis","volume":null,"pages":null},"PeriodicalIF":4.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41986886","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 2

Informative Priors for the Consensus Ranking in the Bayesian Mallows Model 贝叶斯Mallows模型中一致性排序的信息先验

IF 4.4 2区数学

Bayesian Analysis Pub Date : 2022-01-01 DOI: 10.1214/22-ba1307

Marta Crispino, Isadora Antoniano-Villalobos

引用次数: 1

Bayesian Sparse Spiked Covariance Model with a Continuous Matrix Shrinkage Prior 具有连续矩阵收缩先验的贝叶斯稀疏尖刺协方差模型

IF 4.4 2区数学

Bayesian Analysis Pub Date : 2022-01-01 DOI: 10.1214/21-ba1292

Fangzheng Xie, J. Cape, C. Priebe, Yanxun Xu

{"title":"Bayesian Sparse Spiked Covariance Model with a Continuous Matrix Shrinkage Prior","authors":"Fangzheng Xie, J. Cape, C. Priebe, Yanxun Xu","doi":"10.1214/21-ba1292","DOIUrl":"https://doi.org/10.1214/21-ba1292","url":null,"abstract":". We propose a Bayesian methodology for estimating spiked covariance matrices with a jointly sparse structure in high dimensions. The spiked covariance matrix is reparameterized in terms of the latent factor model, where the loading matrix is equipped with a novel matrix spike-and-slab LASSO prior, which is a continuous shrinkage prior for modeling jointly sparse matrices. We establish the rate-optimal posterior contraction for the covariance matrix with respect to the spectral norm as well as that for the principal subspace with respect to the projection spectral norm loss. We also study the posterior contraction rate of the principal subspace with respect to the two-to-inﬁnity norm loss, a novel loss function measuring the distance between subspaces that is able to capture entrywise eigenvector perturbations. We show that the posterior contraction rate with respect to the two-to-inﬁnity norm loss is tighter than that with respect to the routinely used projection spectral norm loss under certain low-rank and bounded coherence conditions. In addition, a point estimator for the principal subspace is proposed with the rate-optimal risk bound with respect to the projection spectral norm loss. The numerical performance of the proposed methodology is assessed through synthetic examples and the analysis of a real-world face data example. 62H25, 62C10; secondary 62H12.","PeriodicalId":55398,"journal":{"name":"Bayesian Analysis","volume":null,"pages":null},"PeriodicalIF":4.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46683181","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 3

Causal Inference Under Mis-Specification: Adjustment Based on the Propensity Score 不规范条件下的因果推理：基于倾向得分的调整

IF 4.4 2区数学

Bayesian Analysis Pub Date : 2022-01-01 DOI: 10.1214/22-ba1322

D. Stephens, Widemberg S. Nobre, E. Moodie, A. M. Schmidt

引用次数: 18

Controlling the Flexibility of Non-Gaussian Processes Through Shrinkage Priors 通过收缩先验控制非高斯过程的灵活性

IF 4.4 2区数学

Bayesian Analysis Pub Date : 2022-01-01 DOI: 10.1214/22-ba1342

Rafael Cabral, D. Bolin, H. Rue

{"title":"Controlling the Flexibility of Non-Gaussian Processes Through Shrinkage Priors","authors":"Rafael Cabral, D. Bolin, H. Rue","doi":"10.1214/22-ba1342","DOIUrl":"https://doi.org/10.1214/22-ba1342","url":null,"abstract":"The normal inverse Gaussian (NIG) and generalized asymmetric Laplace (GAL) distributions can be seen as skewed and semi-heavy-tailed extensions of the Gaussian distribution. Models driven by these more ﬂexible noise distributions are then re-garded as ﬂexible extensions of simpler Gaussian models. Inferential procedures tend to overestimate the degree of non-Gaussianity in the data and therefore we propose controlling the ﬂexibility of these non-Gaussian models by adding sensible priors in the inferential framework that contract the model towards Gaussianity. In our venture to derive sensible priors, we also propose a new intuitive parameterization of the non-Gaussian models and discuss how to implement them eﬃciently in Stan . The methods are derived for a generic class of non-Gaussian models that include spatial Mat´ern ﬁelds, autoregressive models for time series, and simultaneous autoregressive models for aerial data. The results are illustrated with a simulation study and geostatistics application, where priors that penalize model complexity were shown to lead to more robust estimation and give preference to the Gaussian model, while at the same time allowing for non-Gaussianity if there is suﬃcient evidence in the data.","PeriodicalId":55398,"journal":{"name":"Bayesian Analysis","volume":null,"pages":null},"PeriodicalIF":4.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44689926","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 2

A General Scheme for Deriving Conditional Reference Priors 一种推导条件参考先验的一般方案

IF 4.4 2区数学

Bayesian Analysis Pub Date : 2022-01-01 DOI: 10.1214/22-ba1345

Chetkar Jha, Dongchu Sun

引用次数: 1

Bayes Linear Bayes Networks with an Application to Prognostic Indices Bayes线性Bayes网络及其在预测指标中的应用

IF 4.4 2区数学

Bayesian Analysis Pub Date : 2022-01-01 DOI: 10.1214/22-ba1314

W. A. J. Al-Taie, M. Farrow

引用次数: 0

Sparse Bayesian Inference on Gamma-Distributed Observations Using Shape-Scale Inverse-Gamma Mixtures 利用形状尺度逆伽马混合对伽马分布观测的稀疏贝叶斯推断

IF 4.4 2区数学

Bayesian Analysis Pub Date : 2022-01-01 DOI: 10.1214/22-ba1348

Y. Hamura, T. Onizuka, Shintaro Hashimoto, S. Sugasawa

引用次数: 0

The Posterior Predictive Null 后验预测零

IF 4.4 2区数学

Bayesian Analysis Pub Date : 2021-12-06 DOI: 10.1214/22-BA1313

Gemma E. Moran, J. Cunningham, D. Blei

{"title":"The Posterior Predictive Null","authors":"Gemma E. Moran, J. Cunningham, D. Blei","doi":"10.1214/22-BA1313","DOIUrl":"https://doi.org/10.1214/22-BA1313","url":null,"abstract":". Bayesian model criticism is an important part of the practice of Bayesian statistics. Traditionally, model criticism methods have been based on the predictive check, an adaptation of goodness-of-ﬁt testing to Bayesian modeling and an eﬀective method to understand how well a model captures the distribution of the data. In modern practice, however, researchers iteratively build and develop many models, exploring a space of models to help solve the problem at hand. While classical predictive checks can help assess each one, they cannot help the researcher understand how the models relate to each other. This paper introduces the posterior predictive null check (PPN), a method for Bayesian model criticism that helps characterize the relationships between models. The idea behind the PPN is to check whether data from one model’s predictive distribution can pass a predictive check designed for another model. This form of criticism complements the classical predictive check by providing a comparative tool. A collection of PPNs, which we call a PPN study, can help us understand which models are equivalent and which models provide diﬀerent perspectives on the data. With mixture models, we demonstrate how a PPN study, along with traditional predictive checks, can help select the number of components by the principle of parsimony. With probabilistic factor models, we demonstrate how a PPN study can help understand relationships between diﬀerent classes of models, such as linear models and models based on neural networks. Finally, we analyze data from the literature on predictive checks to show how a PPN study can improve the practice of Bayesian model criticism. Code to replicate the results in this paper is available at https://github.com/gemoran/ppn-code .","PeriodicalId":55398,"journal":{"name":"Bayesian Analysis","volume":null,"pages":null},"PeriodicalIF":4.4,"publicationDate":"2021-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44348645","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0