Bayesian Analysis最新文献_第10页

An Explanatory Rationale for Priors Sharpened Into Occam’s Razors 奥卡姆剃刀上的先验理论解释

IF 4.4 2区数学

Bayesian Analysis Pub Date : 2020-12-01 DOI: 10.1214/19-ba1189

D. Bickel

引用次数: 6

Post-Processed Posteriors for Banded Covariances 带协方差的后处理后验算子

IF 4.4 2区数学

Bayesian Analysis Pub Date : 2020-11-25 DOI: 10.1214/22-ba1333

Kwangmin Lee, Kyoungjae Lee, Jaeyong Lee

{"title":"Post-Processed Posteriors for Banded Covariances","authors":"Kwangmin Lee, Kyoungjae Lee, Jaeyong Lee","doi":"10.1214/22-ba1333","DOIUrl":"https://doi.org/10.1214/22-ba1333","url":null,"abstract":"We consider Bayesian inference of banded covariance matrices and propose a post-processed posterior. The post-processing of the posterior consists of two steps. In the first step, posterior samples are obtained from the conjugate inverse-Wishart posterior which does not satisfy any structural restrictions. In the second step, the posterior samples are transformed to satisfy the structural restriction through a post-processing function. The conceptually straightforward procedure of the post-processed posterior makes its computation efficient and can render interval estimators of functionals of covariance matrices. We show that it has nearly optimal minimax rates for banded covariances among all possible pairs of priors and post-processing functions. Furthermore, we prove that the expected coverage probability of the $(1-alpha)100%$ highest posterior density region of the post-processed posterior is asymptotically $1-alpha$ with respect to a conventional posterior distribution. It implies that the highest posterior density region of the post-processed posterior is, on average, a credible set of a conventional posterior. The advantages of the post-processed posterior are demonstrated by a simulation study and a real data analysis.","PeriodicalId":55398,"journal":{"name":"Bayesian Analysis","volume":" ","pages":""},"PeriodicalIF":4.4,"publicationDate":"2020-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43532988","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: 4

Gaussian Orthogonal Latent Factor Processes for Large Incomplete Matrices of Correlated Data 相关数据大不完全矩阵的高斯正交潜在因子处理

IF 4.4 2区数学

Bayesian Analysis Pub Date : 2020-11-21 DOI: 10.1214/21-ba1295

Mengyang Gu, Hanmo Li

引用次数: 5

Functional Central Limit Theorems for Stick-Breaking Priors 断棒先验的泛函中心极限定理

IF 4.4 2区数学

Bayesian Analysis Pub Date : 2020-11-19 DOI: 10.1214/21-ba1290

Yaozhong Hu, Junxi Zhang

引用次数: 1

R ∗ : A Robust MCMC Convergence Diagnostic with Uncertainty Using Decision Tree Classifiers R *:基于决策树分类器的鲁棒不确定性MCMC收敛诊断

IF 4.4 2区数学

Bayesian Analysis Pub Date : 2020-11-19 DOI: 10.1214/20-ba1252

Ben Lambert, Aki Vehtari

{"title":"R ∗ : A Robust MCMC Convergence Diagnostic with Uncertainty Using Decision Tree Classifiers","authors":"Ben Lambert, Aki Vehtari","doi":"10.1214/20-ba1252","DOIUrl":"https://doi.org/10.1214/20-ba1252","url":null,"abstract":"Markov chain Monte Carlo (MCMC) has transformed Bayesian model inference over the past three decades: mainly because of this, Bayesian inference is now a workhorse of applied scientists. Under general conditions, MCMC sampling converges asymptotically to the posterior distribution, but this provides no guarantees about its performance in finite time. The predominant method for monitoring convergence is to run multiple chains and monitor individual chains' characteristics and compare these to the population as a whole: if within-chain and between-chain summaries are comparable, then this is taken to indicate that the chains have converged to a common stationary distribution. Here, we introduce a new method for diagnosing convergence based on how well a machine learning classifier model can successfully discriminate the individual chains. We call this convergence measure $R^*$. In contrast to the predominant $widehat{R}$, $R^*$ is a single statistic across all parameters that indicates lack of mixing, although individual variables' importance for this metric can also be determined. Additionally, $R^*$ is not based on any single characteristic of the sampling distribution; instead it uses all the information in the chain, including that given by the joint sampling distribution, which is currently largely overlooked by existing approaches. We recommend calculating $R^*$ using two different machine learning classifiers - gradient-boosted regression trees and random forests - which each work well in models of different dimensions. Because each of these methods outputs a classification probability, as a byproduct, we obtain uncertainty in $R^*$. The method is straightforward to implement and could be a complementary additional check on MCMC convergence for applied analyses.","PeriodicalId":55398,"journal":{"name":"Bayesian Analysis","volume":" ","pages":""},"PeriodicalIF":4.4,"publicationDate":"2020-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46532990","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: 14

Joint Bayesian Analysis of Multiple Response-Types Using the Hierarchical Generalized Transformation Model 基于层次广义变换模型的多响应类型联合贝叶斯分析

IF 4.4 2区数学

Bayesian Analysis Pub Date : 2020-11-01 DOI: 10.1214/20-ba1246

J. Bradley

{"title":"Joint Bayesian Analysis of Multiple Response-Types Using the Hierarchical Generalized Transformation Model","authors":"J. Bradley","doi":"10.1214/20-ba1246","DOIUrl":"https://doi.org/10.1214/20-ba1246","url":null,"abstract":"Consider the situation where an analyst has a Bayesian statistical model that performs well for continuous data. However, suppose the observed dataset consists of multiple response-types (e.g., continuous, count-valued, Bernoulli trials, etc.), which are distributed from more than one class of distributions. We refer to these types of data as “multiple response-type” datasets. The goal of this article is to introduce a reasonable easy-to-implement all-purpose method that “converts” a Bayesian statistical model for continuous responses (call this the preferred model) into a Bayesian model for multiple response-type datasets. To do this, we consider a transformation of the multiple response-type data, such that the transformed data can be reasonably modeled using the preferred model. What is unique with our strategy is that we treat the transformations as unknown and use a Bayesian approach to model this uncertainty. The implementation of our Bayesian approach to unknown transformations is straightforward, and involves two steps. The first step produces posterior replicates of the transformed multiple responsetype data from a latent conjugate multivariate (LCM) model. The second step involves generating values from the posterior distribution implied by the preferred model. We demonstrate the flexibility of our model through an application to Bayesian additive regression trees (BART) and a spatio-temporal mixed effects (SME) model.We provide a thorough joint multiple response-type spatio-temporal analysis of coronavirus disease 2019 (COVID-19) cases, the adjusted closing price of the Dow Jones Industrial (DJI), and Google Trends data. © 2022 International Society for Bayesian Analysis","PeriodicalId":55398,"journal":{"name":"Bayesian Analysis","volume":"1 1","pages":""},"PeriodicalIF":4.4,"publicationDate":"2020-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66080991","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: 10

High-Dimensional Bayesian Network Classification with Network Global-Local Shrinkage Priors 具有全局局部收缩先验的高维贝叶斯网络分类

IF 4.4 2区数学

Bayesian Analysis Pub Date : 2020-09-23 DOI: 10.1214/23-ba1378

Sharmistha Guha, Abel Rodríguez

{"title":"High-Dimensional Bayesian Network Classification with Network Global-Local Shrinkage Priors","authors":"Sharmistha Guha, Abel Rodríguez","doi":"10.1214/23-ba1378","DOIUrl":"https://doi.org/10.1214/23-ba1378","url":null,"abstract":"This article proposes a novel Bayesian classification framework for networks with labeled nodes. While literature on statistical modeling of network data typically involves analysis of a single network, the recent emergence of complex data in several biological applications, including brain imaging studies, presents a need to devise a network classifier for subjects. This article considers an application from a brain connectome study, where the overarching goal is to classify subjects into two separate groups based on their brain network data, along with identifying influential regions of interest (ROIs) (referred to as nodes). Existing approaches either treat all edge weights as a long vector or summarize the network information with a few summary measures. Both these approaches ignore the full network structure, may lead to less desirable inference in small samples and are not designed to identify significant network nodes. We propose a novel binary logistic regression framework with the network as the predictor and a binary response, the network predictor coefficient being modeled using a novel class global-local shrinkage priors. The framework is able to accurately detect nodes and edges in the network influencing the classification. Our framework is implemented using an efficient Markov Chain Monte Carlo algorithm. Theoretically, we show asymptotically optimal classification for the proposed framework when the number of network edges grows faster than the sample size. The framework is empirically validated by extensive simulation studies and analysis of a brain connectome data.","PeriodicalId":55398,"journal":{"name":"Bayesian Analysis","volume":" ","pages":""},"PeriodicalIF":4.4,"publicationDate":"2020-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43499599","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

Independent Finite Approximations for Bayesian Nonparametric Inference 贝叶斯非参数推理的独立有限逼近

IF 4.4 2区数学

Bayesian Analysis Pub Date : 2020-09-22 DOI: 10.1214/23-ba1385

Tin D. Nguyen, Jonathan Huggins, L. Masoero, Lester W. Mackey, Tamara Broderick

{"title":"Independent Finite Approximations for Bayesian Nonparametric Inference","authors":"Tin D. Nguyen, Jonathan Huggins, L. Masoero, Lester W. Mackey, Tamara Broderick","doi":"10.1214/23-ba1385","DOIUrl":"https://doi.org/10.1214/23-ba1385","url":null,"abstract":"Bayesian nonparametric priors based on completely random measures (CRMs) offer a flexible modeling approach when the number of latent components in a dataset is unknown. However, managing the infinite dimensionality of CRMs typically requires practitioners to derive ad-hoc algorithms, preventing the use of general-purpose inference methods and often leading to long compute times. We propose a general but explicit recipe to construct a simple finite-dimensional approximation that can replace the infinite-dimensional CRMs. Our independent finite approximation (IFA) is a generalization of important cases that are used in practice. The independence of atom weights in our approximation (i) makes the construction well-suited for parallel and distributed computation and (ii) facilitates more convenient inference schemes. We quantify the approximation error between IFAs and the target nonparametric prior. We compare IFAs with an alternative approximation scheme -- truncated finite approximations (TFAs), where the atom weights are constructed sequentially. We prove that, for worst-case choices of observation likelihoods, TFAs are a more efficient approximation than IFAs. However, in real-data experiments with image denoising and topic modeling, we find that IFAs perform very similarly to TFAs in terms of task-specific accuracy metrics.","PeriodicalId":55398,"journal":{"name":"Bayesian Analysis","volume":" ","pages":""},"PeriodicalIF":4.4,"publicationDate":"2020-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43520200","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

Bayesian Nonparametric Bivariate Survival Regression for Current Status Data 现状数据的贝叶斯非参数双变量生存回归

IF 4.4 2区数学

Bayesian Analysis Pub Date : 2020-09-14 DOI: 10.1214/22-ba1346

Giorgio Paulon, Peter Muller, V. S. Y. Rosas

引用次数: 1

Bayesian Modelling of Time-Varying Conditional Heteroscedasticity 时变条件异方差的贝叶斯模型

IF 4.4 2区数学

Bayesian Analysis Pub Date : 2020-09-13 DOI: 10.1214/21-BA1267

Sayar Karmakar, Arkaprava Roy

引用次数: 10