Bayesian Analysis最新文献_第9页

Biclustering via Semiparametric Bayesian Inference 基于半参数贝叶斯推理的双聚类

IF 4.4 2区数学

Bayesian Analysis Pub Date : 2021-01-01 DOI: 10.1214/21-ba1284

Alejandro Murua, F. Quintana

引用次数: 2

Error Control of the Numerical Posterior with Bayes Factors in Bayesian Uncertainty Quantification 贝叶斯不确定性量化中贝叶斯因子的数值后验误差控制

IF 4.4 2区数学

Bayesian Analysis Pub Date : 2021-01-01 DOI: 10.1214/20-ba1255

Marcos A. Capistrán, J. Christen, M. Daza-Torres, Hugo Flores-Arguedas, J. Montesinos-López

{"title":"Error Control of the Numerical Posterior with Bayes Factors in Bayesian Uncertainty Quantification","authors":"Marcos A. Capistrán, J. Christen, M. Daza-Torres, Hugo Flores-Arguedas, J. Montesinos-López","doi":"10.1214/20-ba1255","DOIUrl":"https://doi.org/10.1214/20-ba1255","url":null,"abstract":". In this paper, we address the numerical posterior error control problem for the Bayesian approach to inverse problems or recently known as Bayesian Uncertainty Quantiﬁcation (UQ). We generalize the results of Capistr´an et al. (2016) to (a priori) expected Bayes factors (BF) and in a more general, inﬁnite-dimensional setting. In this inverse problem, the unavoidable numerical approximation of the Forward Map (FM, i.e., the regressor function), arising from the numerical solution of a system of diﬀerential equations, demands error estimates of the corresponding approximate numerical posterior distribution. Our approach is to make such comparisons in the setting of Bayesian model selection and BFs. The main result of this paper is a bound on the absolute global error tolerated by the numerical solver of the FM in order to keep the BF of the numerical versus the theoretical posterior near one. For two examples, we provide a detailed analysis of the computation and implementation of the introduced bound. Furthermore, we show that the resulting numerical posterior turns out to be nearly identical from the theoretical posterior, given the control of the BF near one.","PeriodicalId":55398,"journal":{"name":"Bayesian Analysis","volume":" ","pages":""},"PeriodicalIF":4.4,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42140508","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

Optimal Shrinkage Estimation of Predictive Densities Under α-Divergences α-散度下预测密度的最优收缩估计

IF 4.4 2区数学

Bayesian Analysis Pub Date : 2021-01-01 DOI: 10.1214/21-BA1264

E. George, Gourab Mukherjee, Keisuke Yano

引用次数: 1

Perfect Sampling of the Posterior in the Hierarchical Pitman-Yor Process. 分层Pitman-Yor过程中后验的完美抽样。

IF 4.4 2区数学

Bayesian Analysis Pub Date : 2021-01-01 DOI: 10.1214/21-BA1269

S. Bacallado, S. Favaro, Samuel Power, L. Trippa

引用次数: 1

On a Dirichlet Process Mixture Representation of Phase-Type Distributions 相型分布的Dirichlet过程混合表示

IF 4.4 2区数学

Bayesian Analysis Pub Date : 2021-01-01 DOI: 10.1214/21-BA1272

Daniel Ayala, Leonardo Jofré, Luis Gutiérrez, R. H. Mena

引用次数: 0

Bayesian Nonstationary and Nonparametric Covariance Estimation for Large Spatial Data 大空间数据的贝叶斯非平稳和非参数协方差估计

IF 4.4 2区数学

Bayesian Analysis Pub Date : 2020-12-10 DOI: 10.1214/21-ba1273

Brian Kidd, M. Katzfuss

引用次数: 8

A Dirichlet Process Mixture Model for Non-Ignorable Dropout 不可忽略衰减的Dirichlet过程混合模型

IF 4.4 2区数学

Bayesian Analysis Pub Date : 2020-12-01 DOI: 10.1214/19-ba1181

Camille M. Moore, N. Carlson, S. MaWhinney, S. Kreidler

{"title":"A Dirichlet Process Mixture Model for Non-Ignorable Dropout","authors":"Camille M. Moore, N. Carlson, S. MaWhinney, S. Kreidler","doi":"10.1214/19-ba1181","DOIUrl":"https://doi.org/10.1214/19-ba1181","url":null,"abstract":". Longitudinal cohorts are a valuable resource for studying HIV disease progression; however, dropout is common in these studies. Subjects often fail to re-turn for visits due to disease progression, loss to follow-up, or death. When dropout depends on unobserved outcomes, data are missing not at random, and results from standard longitudinal data analyses can be biased. Several methods have been proposed to adjust for non-ignorable dropout; however, many of these approaches rely on parametric assumptions about the distribution of dropout times and the functional form of the relationship between the outcome and dropout time. More ﬂexible approaches may be needed when the distribution of dropout times does not follow a known distribution or violates proportional hazards assumptions, or when the relationship between the outcome and dropout times does not have a simple polynomial form. We propose a Bayesian semi-parametric Dirichlet process mixture model to ﬂexibly model the relationship between dropout time and the outcome and show that more accurate inference can be obtained by non-parametrically modeling the distribution of subject-speciﬁc eﬀects as well as the distribution of dropout times. Results from simulation studies as well as an application to a longitudinal HIV cohort study database illustrate the strengths of our Bayesian semi-parametric approach.","PeriodicalId":55398,"journal":{"name":"Bayesian Analysis","volume":" ","pages":""},"PeriodicalIF":4.4,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49479134","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: 1

Calibrating Expert Assessments Using Hierarchical Gaussian Process Models 使用层次高斯过程模型校准专家评估

IF 4.4 2区数学

Bayesian Analysis Pub Date : 2020-12-01 DOI: 10.1214/19-ba1180

T. Perälä, J. Vanhatalo, A. Chrysafi

{"title":"Calibrating Expert Assessments Using Hierarchical Gaussian Process Models","authors":"T. Perälä, J. Vanhatalo, A. Chrysafi","doi":"10.1214/19-ba1180","DOIUrl":"https://doi.org/10.1214/19-ba1180","url":null,"abstract":". Expert assessments are routinely used to inform management and other decision making. However, often these assessments contain considerable biases and uncertainties for which reason they should be calibrated if possible. More-over, coherently combining multiple expert assessments into one estimate poses a long-standing problem in statistics since modeling expert knowledge is often dif-ﬁcult. Here, we present a hierarchical Bayesian model for expert calibration in a task of estimating a continuous univariate parameter. The model allows experts’ biases to vary as a function of the true value of the parameter and according to the expert’s background. We follow the fully Bayesian approach (the so-called supra-Bayesian approach) and model experts’ bias functions explicitly using hierarchical Gaussian processes. We show how to use calibration data to infer the experts’ observation models with the use of bias functions and to calculate the bias corrected posterior distributions for an unknown system parameter of interest. We demonstrate and test our model and methods with simulated data and a real case study on data-limited ﬁsheries stock assessment. The case study results show that experts’ biases vary with respect to the true system parameter value and that the calibration of the expert assessments improves the inference compared to using uncalibrated expert assessments or a vague uniform guess. Moreover, the bias functions in the real case study show important diﬀerences between the reliability of alternative experts. The model and methods presented here can be also straightforwardly applied to other applications than our case study.","PeriodicalId":55398,"journal":{"name":"Bayesian Analysis","volume":" ","pages":""},"PeriodicalIF":4.4,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46512597","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: 6

Nested Adaptation of MCMC Algorithms MCMC算法的嵌套自适应

IF 4.4 2区数学

Bayesian Analysis Pub Date : 2020-12-01 DOI: 10.1214/19-ba1190

D. Nguyen, P. Valpine, Y. Atchadé, Daniel Turek, Nick Michaud, C. Paciorek

引用次数: 2

Flexible Bayesian Dynamic Modeling of Correlation and Covariance Matrices. 相关矩阵和协方差矩阵的灵活贝叶斯动态建模

IF 4.4 2区数学

Bayesian Analysis Pub Date : 2020-12-01 Epub Date: 2019-11-04 DOI: 10.1214/19-ba1173

Shiwei Lan, Andrew Holbrook, Gabriel A Elias, Norbert J Fortin, Hernando Ombao, Babak Shahbaba

{"title":"Flexible Bayesian Dynamic Modeling of Correlation and Covariance Matrices.","authors":"Shiwei Lan, Andrew Holbrook, Gabriel A Elias, Norbert J Fortin, Hernando Ombao, Babak Shahbaba","doi":"10.1214/19-ba1173","DOIUrl":"10.1214/19-ba1173","url":null,"abstract":"<p><p>Modeling correlation (and covariance) matrices can be challenging due to the positive-definiteness constraint and potential high-dimensionality. Our approach is to decompose the covariance matrix into the correlation and variance matrices and propose a novel Bayesian framework based on modeling the correlations as products of unit vectors. By specifying a wide range of distributions on a sphere (e.g. the squared-Dirichlet distribution), the proposed approach induces flexible prior distributions for covariance matrices (that go beyond the commonly used inverse-Wishart prior). For modeling real-life spatio-temporal processes with complex dependence structures, we extend our method to dynamic cases and introduce unit-vector Gaussian process priors in order to capture the evolution of correlation among components of a multivariate time series. To handle the intractability of the resulting posterior, we introduce the adaptive Δ-Spherical Hamiltonian Monte Carlo. We demonstrate the validity and flexibility of our proposed framework in a simulation study of periodic processes and an analysis of rat's local field potential activity in a complex sequence memory task.</p>","PeriodicalId":55398,"journal":{"name":"Bayesian Analysis","volume":"15 4","pages":"1199-1228"},"PeriodicalIF":4.4,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8048134/pdf/nihms-1059273.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"38884999","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0