Bayesian Analysis最新文献

How Trustworthy Is Your Tree? Bayesian Phylogenetic Effective Sample Size Through the Lens of Monte Carlo Error. 你的圣诞树有多值得信赖?蒙特卡罗误差下的贝叶斯系统发育有效样本量

IF 4.4 2区数学

Bayesian Analysis Pub Date : 2024-06-01 Epub Date: 2024-04-09 DOI: 10.1214/22-ba1339

Andrew Magee, Michael Karcher, Frederick A Matsen, Volodymyr M Minin

{"title":"How Trustworthy Is Your Tree? Bayesian Phylogenetic Effective Sample Size Through the Lens of Monte Carlo Error.","authors":"Andrew Magee, Michael Karcher, Frederick A Matsen, Volodymyr M Minin","doi":"10.1214/22-ba1339","DOIUrl":"10.1214/22-ba1339","url":null,"abstract":"Bayesian inference is a popular and widely-used approach to infer phylogenies (evolutionary trees). However, despite decades of widespread application, it remains difficult to judge how well a given Bayesian Markov chain Monte Carlo (MCMC) run explores the space of phylogenetic trees. In this paper, we investigate the Monte Carlo error of phylogenies, focusing on high-dimensional summaries of the posterior distribution, including variability in estimated edge/branch (known in phylogenetics as \"split\") probabilities and tree probabilities, and variability in the estimated summary tree. Specifically, we ask if there is any measure of effective sample size (ESS) applicable to phylogenetic trees which is capable of capturing the Monte Carlo error of these three summary measures. We find that there are some ESS measures capable of capturing the error inherent in using MCMC samples to approximate the posterior distributions on phylogenies. We term these tree ESS measures, and identify a set of three which are useful in practice for assessing the Monte Carlo error. Lastly, we present visualization tools that can improve comparisons between multiple independent MCMC runs by accounting for the Monte Carlo error present in each chain. Our results indicate that common post-MCMC workflows are insufficient to capture the inherent Monte Carlo error of the tree, and highlight the need for both within-chain mixing and between-chain convergence assessments.","PeriodicalId":55398,"journal":{"name":"Bayesian Analysis","volume":null,"pages":null},"PeriodicalIF":4.4,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11042687/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42960044","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

A General Bayesian Functional Spatial Partitioning Method for Multiple Region Discovery Applied to Prostate Cancer MRI. 一种用于前列腺癌症MRI多区域发现的通用Bayesian函数空间划分方法

IF 4.9 2区数学

Bayesian Analysis Pub Date : 2024-06-01 Epub Date: 2024-06-28 DOI: 10.1214/23-ba1366

Maria Masotti, Lin Zhang, Gregory J Metzger, Joseph S Koopmeiners

{"title":"A General Bayesian Functional Spatial Partitioning Method for Multiple Region Discovery Applied to Prostate Cancer MRI.","authors":"Maria Masotti, Lin Zhang, Gregory J Metzger, Joseph S Koopmeiners","doi":"10.1214/23-ba1366","DOIUrl":"10.1214/23-ba1366","url":null,"abstract":"Current protocols to estimate the number, size, and location of cancerous lesions in the prostate using multiparametric magnetic resonance imaging (mpMRI) are highly dependent on reader experience and expertise. Automatic voxel-wise cancer classifiers do not directly provide estimates of number, location, and size of cancerous lesions that are clinically important. Existing spatial partitioning methods estimate linear or piecewise-linear boundaries separating regions of local stationarity in spatially registered data and are inadequate for the application of lesion detection. Frequentist segmentation and clustering methods often require pre-specification of the number of clusters and do not quantify uncertainty. Previously, we developed a novel Bayesian functional spatial partitioning method to estimate the boundary surrounding a single cancerous lesion using data derived from mpMRI. We propose a Bayesian functional spatial partitioning method for multiple lesion detection with an unknown number of lesions. Our method utilizes functional estimation to model the smooth boundary curves surrounding each cancerous lesion. In a Reversible Jump Markov Chain Monte Carlo (RJ-MCMC) framework, we develop novel jump steps to jointly estimate and quantify uncertainty in the number of lesions, their boundaries, and the spatial parameters in each lesion. Through simulation we show that our method is robust to the shape of the lesions, number of lesions, and region-specific spatial processes. We illustrate our method through the detection of prostate cancer lesions using MRI.","PeriodicalId":55398,"journal":{"name":"Bayesian Analysis","volume":null,"pages":null},"PeriodicalIF":4.9,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11343089/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44759667","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

Heavy-Tailed NGG-Mixture Models 重尾 NGG 混合物模型

IF 4.4 2区数学

Bayesian Analysis Pub Date : 2024-01-01 DOI: 10.1214/24-ba1420

Vianey Palacios Ramírez, Miguel de Carvalho, Luis Gutiérrez

引用次数: 0

Posterior Sampling From Truncated Ferguson-Klass Representation of Normalised Completely Random Measure Mixtures 从归一化完全随机测量混合物的截断弗格森-类表示进行后验取样

IF 4.4 2区数学

Bayesian Analysis Pub Date : 2024-01-01 DOI: 10.1214/24-ba1421

Junyi Zhang, A. Dassios

引用次数: 0

Posterior Shrinkage Towards Linear Subspaces 后向线性子空间收缩

IF 4.4 2区数学

Bayesian Analysis Pub Date : 2024-01-01 DOI: 10.1214/24-ba1414

Daniel K. Sewell

{"title":"Posterior Shrinkage Towards Linear Subspaces","authors":"Daniel K. Sewell","doi":"10.1214/24-ba1414","DOIUrl":"https://doi.org/10.1214/24-ba1414","url":null,"abstract":"It is common to hold prior beliefs that are not characterized by points in the parameter space but instead are relational in nature and can be described by a linear subspace. While some previous work has been done to account for such prior beliefs, the focus has primarily been on point estimators within a regression framework. We argue, however, that prior beliefs about parameters ought to be encoded into the prior distribution rather than in the formation of a point estimator. In this way, the prior beliefs help shape textit{all} inference. Through exponential tilting, we propose a fully generalizable method of taking existing prior information from, e.g., a pilot study, and combining it with additional prior beliefs represented by parameters lying on a linear subspace. We provide computationally efficient algorithms for posterior inference that, once inference is made using a non-tilted prior, does not depend on the sample size. We illustrate our proposed approach on an antihypertensive clinical trial dataset where we shrink towards a power law dose-response relationship, and on monthly influenza and pneumonia data where we shrink moving average lag parameters towards smoothness. Software to implement the proposed approach is provided in the R package verb+SUBSET+ available on GitHub.","PeriodicalId":55398,"journal":{"name":"Bayesian Analysis","volume":null,"pages":null},"PeriodicalIF":4.4,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140518466","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

Dynamic Functional Variable Selection for Multimodal mHealth Data 多模态移动医疗数据的动态功能变量选择

IF 4.4 2区数学

Bayesian Analysis Pub Date : 2024-01-01 DOI: 10.1214/24-ba1413

Matthew D. Koslovsky, Kelley Pettee Gabriel, Michael Businelle, David W. Wetter, Darla E. Kendzor

引用次数: 0

Shrinkage with shrunken shoulders: Gibbs sampling shrinkage model posteriors with guaranteed convergence rates. 收缩肩部:Gibbs抽样收缩模型后验与保证收敛率

IF 4.4 2区数学

Bayesian Analysis Pub Date : 2023-06-01 Epub Date: 2022-04-05 DOI: 10.1214/22-ba1308

Akihiko Nishimura, Marc A Suchard

{"title":"Shrinkage with shrunken shoulders: Gibbs sampling shrinkage model posteriors with guaranteed convergence rates.","authors":"Akihiko Nishimura, Marc A Suchard","doi":"10.1214/22-ba1308","DOIUrl":"10.1214/22-ba1308","url":null,"abstract":"Use of continuous shrinkage priors - with a \"spike\" near zero and heavy-tails towards infinity - is an increasingly popular approach to induce sparsity in parameter estimates. When the parameters are only weakly identified by the likelihood, however, the posterior may end up with tails as heavy as the prior, jeopardizing robustness of inference. A natural solution is to \"shrink the shoulders\" of a shrinkage prior by lightening up its tails beyond a reasonable parameter range, yielding a regularized version of the prior. We develop a regularization approach which, unlike previous proposals, preserves computationally attractive structures of original shrinkage priors. We study theoretical properties of the Gibbs sampler on resulting posterior distributions, with emphasis on convergence rates of the Pólya-Gamma Gibbs sampler for sparse logistic regression. Our analysis shows that the proposed regularization leads to geometric ergodicity under a broad range of global-local shrinkage priors. Essentially, the only requirement is for the prior <math><msub><mrow><mi>π</mi></mrow><mrow><mtext>local</mtext></mrow></msub><mo>(</mo><mo>⋅</mo><mo>)</mo></math> on the local scale <math><mi>λ</mi></math> to satisfy <math><msub><mrow><mi>π</mi></mrow><mrow><mtext>local</mtext></mrow></msub><mo>(</mo><mn>0</mn><mo>)</mo><mo><</mo><mo>∞</mo></math>. If <math><msub><mrow><mi>π</mi></mrow><mrow><mtext>local</mtext></mrow></msub><mo>(</mo><mo>⋅</mo><mo>)</mo></math> further satisfies <math><msub><mrow><mtext>lim</mtext></mrow><mrow><mi>λ</mi><mo>→</mo><mn>0</mn></mrow></msub><msub><mrow><mi>π</mi></mrow><mrow><mtext>local</mtext></mrow></msub><mo>(</mo><mi>λ</mi><mo>)</mo><mo>/</mo><msup><mrow><mi>λ</mi></mrow><mrow><mi>a</mi></mrow></msup><mo><</mo><mo>∞</mo></math> for <math><mi>a</mi><mo>></mo><mn>0</mn></math>, as in the case of Bayesian bridge priors, we show the sampler to be uniformly ergodic.","PeriodicalId":55398,"journal":{"name":"Bayesian Analysis","volume":null,"pages":null},"PeriodicalIF":4.4,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11105165/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47795793","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

Reproducible Model Selection Using Bagged Posteriors. 利用袋装后验进行可重复性模型选择。

IF 4.4 2区数学

Bayesian Analysis Pub Date : 2023-03-01 DOI: 10.1214/21-ba1301

Jonathan H Huggins, Jeffrey W Miller

{"title":"Reproducible Model Selection Using Bagged Posteriors.","authors":"Jonathan H Huggins, Jeffrey W Miller","doi":"10.1214/21-ba1301","DOIUrl":"https://doi.org/10.1214/21-ba1301","url":null,"abstract":"Bayesian model selection is premised on the assumption that the data are generated from one of the postulated models. However, in many applications, all of these models are incorrect (that is, there is misspecification). When the models are misspecified, two or more models can provide a nearly equally good fit to the data, in which case Bayesian model selection can be highly unstable, potentially leading to self-contradictory findings. To remedy this instability, we propose to use bagging on the posterior distribution (\"BayesBag\") - that is, to average the posterior model probabilities over many bootstrapped datasets. We provide theoretical results characterizing the asymptotic behavior of the posterior and the bagged posterior in the (misspecified) model selection setting. We empirically assess the BayesBag approach on synthetic and real-world data in (i) feature selection for linear regression and (ii) phylogenetic tree reconstruction. Our theory and experiments show that, when all models are misspecified, BayesBag (a) provides greater reproducibility and (b) places posterior mass on optimal models more reliably, compared to the usual Bayesian posterior; on the other hand, under correct specification, BayesBag is slightly more conservative than the usual posterior, in the sense that BayesBag posterior probabilities tend to be slightly farther from the extremes of zero and one. Overall, our results demonstrate that BayesBag provides an easy-to-use and widely applicable approach that improves upon Bayesian model selection by making it more stable and reproducible.","PeriodicalId":55398,"journal":{"name":"Bayesian Analysis","volume":null,"pages":null},"PeriodicalIF":4.4,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9838736/pdf/nihms-1796997.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"9229540","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: 10

A Bayesian Nonparametric Latent Space Approach to Modeling Evolving Communities in Dynamic Networks 动态网络中演化群体建模的贝叶斯非参数隐空间方法

2区数学

Bayesian Analysis Pub Date : 2023-03-01 DOI: 10.1214/21-ba1300

Joshua Daniel Loyal, Yuguo Chen

{"title":"A Bayesian Nonparametric Latent Space Approach to Modeling Evolving Communities in Dynamic Networks","authors":"Joshua Daniel Loyal, Yuguo Chen","doi":"10.1214/21-ba1300","DOIUrl":"https://doi.org/10.1214/21-ba1300","url":null,"abstract":"The evolution of communities in dynamic (time-varying) network data is a prominent topic of interest. A popular approach to understanding these dynamic networks is to embed the dyadic relations into a latent metric space. While methods for clustering with this approach exist for dynamic networks, they all assume a static community structure. This paper presents a Bayesian nonparametric model for dynamic networks that can model networks with evolving community structures. Our model extends existing latent space approaches by explicitly modeling the additions, deletions, splits, and mergers of groups with a hierarchical Dirichlet process hidden Markov model. Our proposed approach, the hierarchical Dirichlet process latent position cluster model (HDP-LPCM), incorporates transitivity, models both individual and group level aspects of the data, and avoids the computationally expensive selection of the number of groups required by most popular methods. We provide a Markov chain Monte Carlo estimation algorithm and demonstrate its ability to detect evolving community structure in a network of military alliances during the Cold War and a narrative network constructed from the Game of Thrones television series.","PeriodicalId":55398,"journal":{"name":"Bayesian Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135643392","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

Fast Bayesian Functional Regression for Non-Gaussian Spatial Data 非高斯空间数据的快速贝叶斯函数回归

IF 4.4 2区数学

Bayesian Analysis Pub Date : 2023-01-01 DOI: 10.1214/22-ba1354

Hyun Bin Kang, Yeo Jin Jung, Jaewoo Park

引用次数: 2