贝叶斯非参数推断——为何及如何进行
Bayesian Nonparametric Inference - Why and How.
作者信息
Müller Peter, Mitra Riten
机构信息
Department of Mathematics, University of Texas,
ICES, University of Texas,
出版信息
Bayesian Anal. 2013;8(2). doi: 10.1214/13-BA811.
Abstract
We review inference under models with nonparametric Bayesian (BNP) priors. The discussion follows a set of examples for some common inference problems. The examples are chosen to highlight problems that are challenging for standard parametric inference. We discuss inference for density estimation, clustering, regression and for mixed effects models with random effects distributions. While we focus on arguing for the need for the flexibility of BNP models, we also review some of the more commonly used BNP models, thus hopefully answering a bit of both questions, why and how to use BNP.
摘要
我们回顾了具有非参数贝叶斯（BNP）先验的模型下的推断。讨论围绕一些常见推断问题的一系列示例展开。选择这些示例是为了突出对标准参数推断具有挑战性的问题。我们讨论了密度估计、聚类、回归以及具有随机效应分布的混合效应模型的推断。虽然我们着重论证BNP模型灵活性的必要性，但我们也回顾了一些更常用的BNP模型，从而有望在一定程度上回答两个问题：为什么以及如何使用BNP。
相似文献
1
Bayesian Nonparametric Inference - Why and How.
Bayesian Anal. 2013;8(2). doi: 10.1214/13-BA811.
2
A menu-driven software package of Bayesian nonparametric (and parametric) mixed models for regression analysis and density estimation.
Behav Res Methods. 2017 Feb;49(1):335-362. doi: 10.3758/s13428-016-0711-7.
3
Fast Bayesian Inference in Dirichlet Process Mixture Models.
J Comput Graph Stat. 2011 Jan 1;20(1). doi: 10.1198/jcgs.2010.07081.
4
A practical introduction to Bayesian estimation of causal effects: Parametric and nonparametric approaches.
Stat Med. 2021 Jan 30;40(2):518-551. doi: 10.1002/sim.8761. Epub 2020 Oct 5.
5
Spiked Dirichlet Process Prior for Bayesian Multiple Hypothesis Testing in Random Effects Models.
Bayesian Anal. 2009;4(4):707-732. doi: 10.1214/09-BA426.
6
Are Gibbs-Type Priors the Most Natural Generalization of the Dirichlet Process?
IEEE Trans Pattern Anal Mach Intell. 2015 Feb;37(2):212-29. doi: 10.1109/TPAMI.2013.217.
7
A framework for Bayesian nonparametric inference for causal effects of mediation.
Biometrics. 2017 Jun;73(2):401-409. doi: 10.1111/biom.12575. Epub 2016 Aug 1.
8
Marginally specified priors for non-parametric Bayesian estimation.
J R Stat Soc Series B Stat Methodol. 2015 Jan 1;77(1):35-58. doi: 10.1111/rssb.12059.
9
Bayesian nonparametric inference on stochastic ordering.
Biometrika. 2008 Dec;95(4):859-874. doi: 10.1093/biomet/asn043. Epub 2008 Nov 3.
10
Scalable Bayesian nonparametric regression via a Plackett-Luce model for conditional ranks.
Electron J Stat. 2016 Jul 18;10(2):1807-1828. doi: 10.1214/15-EJS1032.
引用本文的文献
1
Bayesian Estimation of Propensity Scores for Integrating Multiple Cohorts with High-Dimensional Covariates.
Stat Biosci. 2024 Dec 9. doi: 10.1007/s12561-024-09470-5.
2
Nonparametric Bayes Differential Analysis of Multigroup DNA Methylation Data.
Bayesian Anal. 2025 Jun;20(2):489-518. doi: 10.1214/23-ba1407. Epub 2023 Nov 23.
3
VICatMix: variational Bayesian clustering and variable selection for discrete biomedical data.
Bioinform Adv. 2025 Mar 17;5(1):vbaf055. doi: 10.1093/bioadv/vbaf055. eCollection 2025.
4
Covering Hierarchical Dirichlet Mixture Models on binary data to enhance genomic stratifications in onco-hematology.
PLoS Comput Biol. 2024 Feb 2;20(2):e1011299. doi: 10.1371/journal.pcbi.1011299. eCollection 2024 Feb.
5
Utility-based Bayesian personalized treatment selection for advanced breast cancer.
J R Stat Soc Ser C Appl Stat. 2022 Nov;71(5):1605-1622. doi: 10.1111/rssc.12582. Epub 2022 Sep 9.
6
A Causal Framework for Making Individualized Treatment Decisions in Oncology.
Cancers (Basel). 2022 Aug 14;14(16):3923. doi: 10.3390/cancers14163923.
7
Assessing the Impact of Precision Parameter Prior in Bayesian Non-parametric Growth Curve Modeling.
Front Psychol. 2021 Mar 31;12:624588. doi: 10.3389/fpsyg.2021.624588. eCollection 2021.
8
Effect-Size Estimation Using Semiparametric Hierarchical Mixture Models in Disease-Association Studies with Neuroimaging Data.
Comput Math Methods Med. 2020 Dec 9;2020:7482403. doi: 10.1155/2020/7482403. eCollection 2020.
9
Bayesian credible subgroup identification for treatment effectiveness in time-to-event data.
PLoS One. 2020 Feb 26;15(2):e0229336. doi: 10.1371/journal.pone.0229336. eCollection 2020.
10
Bayesian non-parametric survival regression for optimizing precision dosing of intravenous busulfan in allogeneic stem cell transplantation.
J R Stat Soc Ser C Appl Stat. 2019 Apr;68(3):809-828. doi: 10.1111/rssc.12331. Epub 2018 Dec 16.
本文引用的文献
1
A Bayesian Semi-parametric Approach for the Differential Analysis of Sequence Counts Data.
J R Stat Soc Ser C Appl Stat. 2014 Apr;63(3):385-404. doi: 10.1111/rssc.12041.
2
CENTER-ADJUSTED INFERENCE FOR A NONPARAMETRIC BAYESIAN RANDOM EFFECT DISTRIBUTION.
Stat Sin. 2011;21. doi: 10.5705/ss.2009.180.
3
Defining Predictive Probability Functions for Species Sampling Models.
Stat Sci. 2013;28(2):209-222. doi: 10.1214/12-sts407.
4
Semiparametric Bayesian classification with longitudinal markers.
J R Stat Soc Ser C Appl Stat. 2007 Mar;56(2):119-37. doi: 10.1111/j.1467-9876.2007.00569.x.
5
The multivariate beta process and an extension of the Polya tree model.
Biometrika. 2011 Mar;98(1):17-34. doi: 10.1093/biomet/asq072. Epub 2011 Feb 2.
6
Semiparametric Bayesian inference for phage display data.
Biometrics. 2013 Mar;69(1):174-83. doi: 10.1111/j.1541-0420.2012.01817.x. Epub 2013 Jan 22.
7
A class of mixtures of dependent tail-free processes.
Biometrika. 2011 Sep;98(3):553-566. doi: 10.1093/biomet/asq082.
8
Borrowing strength with nonexchangeable priors over subpopulations.
Biometrics. 2012 Jun;68(2):550-8. doi: 10.1111/j.1541-0420.2011.01693.x. Epub 2011 Oct 31.
9
DPpackage: Bayesian Non- and Semi-parametric Modelling in R.
J Stat Softw. 2011 Apr 1;40(5):1-30.
10
A Product Partition Model With Regression on Covariates.
J Comput Graph Stat. 2011 Mar 1;20(1):260-278. doi: 10.1198/jcgs.2011.09066.
Zotero 插件