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序贯 Gibbs 后验及其主成分分析应用AI 解读

Summary Gibbs posteriors are proportional to a prior distribution multiplied by an exponentiated loss function, with a key tuning parameter that weights the information in the loss relative to the prior and provides control of posterior uncertainty. Gibbs posteriors provide a principled framework for likelihood-free Bayesian inference; however, in many situations, the inclusion of a single tuning parameter inevitably leads to poor uncertainty quantification. In particular,…

利用高斯过程推断流形AI 解读

Abstract It is often of interest to infer lower-dimensional structure underlying complex data. As a flexible class of nonlinear structures, it is common to focus on Riemannian manifolds. Most existing manifold-learning algorithms replace the original data with lower-dimensional coordinates without providing an estimate of the manifold or using it to denoise the original data. This article proposes a new methodology to address these issues, allowing interpolation of the…

用于贝叶斯多视图聚类的乘积中心狄利克雷过程AI 解读

Abstract While there is an immense literature on Bayesian methods for clustering, the multiview case has received little attention. This problem focuses on obtaining distinct but statistically dependent clusterings in a common set of entities for different data types. For example, clustering patients into subgroups with subgroup membership varying according to the domain of the patient variables. A challenge is how to model the across-view dependence between the partitions…

利用快进随机游走精确抽样生成树AI 解读

Summary Tree graphs are used routinely in statistics. When estimating a Bayesian model with a tree component, sampling the posterior remains a core difficulty. Existing Markov chain Monte Carlo methods tend to rely on local moves, often leading to poor mixing. A promising approach is to instead directly sample spanning trees on an auxiliary graph. Current spanning tree samplers, such as the celebrated Aldous–Broder algorithm, rely predominantly on simulating random walks…

概率聚类的广义贝叶斯框架AI 解读

Summary Loss-based clustering methods, such as k-means clustering and its variants, are standard tools for finding groups in data. However, the lack of quantification of uncertainty in the estimated clusters is a disadvantage. Model-based clustering based on mixture models provides an alternative approach, but such methods face computational problems and are highly sensitive to the choice of kernel. In this article we propose a generalized Bayes framework that bridges…

贝叶斯金字塔：离散数据的可识别多层离散潜结构模型AI 解读

Abstract High-dimensional categorical data are routinely collected in biomedical and social sciences. It is of great importance to build interpretable parsimonious models that perform dimension reduction and uncover meaningful latent structures from such discrete data. Identifiability is a fundamental requirement for valid modeling and inference in such scenarios, yet is challenging to address when there are complex latent structures. In this article, we propose a class of…

高维不平衡逻辑回归的高效后验抽样AI 解读

Summary Classification with high-dimensional data is of widespread interest and often involves dealing with imbalanced data. Bayesian classification approaches are hampered by the fact that current Markov chain Monte Carlo algorithms for posterior computation become inefficient as the number $p$ of predictors or the number $n$ of subjects to classify gets large, because of the increasing computational time per step and worsening mixing rates. One strategy is to employ a…

无限分解的贝叶斯累积收缩AI 解读

Summary The dimension of the parameter space is typically unknown in a variety of models that rely on factorizations. For example, in factor analysis the number of latent factors is not known and has to be inferred from the data. Although classical shrinkage priors are useful in such contexts, increasing shrinkage priors can provide a more effective approach that progressively penalizes expansions with growing complexity. In this article we propose a novel increasing…

用于离散参数与不连续似然的非连续哈密顿蒙特卡洛AI 解读

Summary Hamiltonian Monte Carlo has emerged as a standard tool for posterior computation. In this article we present an extension that can efficiently explore target distributions with discontinuous densities. Our extension in particular enables efficient sampling from ordinal parameters through the embedding of probability mass functions into continuous spaces. We motivate our approach through a theory of discontinuous Hamiltonian dynamics and develop a corresponding…

贝叶斯约束松弛AI 解读

Summary Prior information often takes the form of parameter constraints. Bayesian methods include such information through prior distributions having constrained support. By using posterior sampling algorithms, one can quantify uncertainty without relying on asymptotic approximations. However, sharply constrained priors are not necessary in some settings and tend to limit modelling scope to a narrow set of distributions that are tractable computationally. We propose to…

嵌套狄利克雷过程AI 解读

In multicenter studies, subjects in different centers may have different outcome distributions. This article is motivated by the problem of nonparametric modeling of these distributions, borrowing information across centers while also allowing centers to be clustered. Starting with a stick-breaking representation of the Dirichlet process (DP), we replace the random atoms with random probability measures drawn from a DP. This results in a nested DP prior, which can be placed…

功能相关基因中多态性的贝叶斯选择与聚类AI 解读

In epidemiologic studies, there is often interest in assessing the relationship between polymorphisms in functionally related genes and a health outcome. For each candidate gene, single nucleotide polymorphism (SNP) data are collected at a number of locations, resulting in a large number of possible genotypes. Because instabilities can result in analyses that include all the SNPs, dimensionality is typically reduced by conducting single SNP analyses or attempting to identify…

矩阵折棒过程AI 解读

In analyzing data from multiple related studies, it often is of interest to borrow information across studies and to cluster similar studies. Although parametric hierarchical models are commonly used, of concern is sensitivity to the form chosen for the random-effects distribution. A Dirichlet process (DP) prior can allow the distribution to be unknown, while clustering studies; however, the DP does not allow local clustering of studies with respect to a subset of the…

贝叶斯多元保序回归样条AI 解读

In many applications, interest focuses on assessing the relationship between a predictor and a multivariate outcome variable, and there may be prior knowledge about the shape of the regression curves. For example, regression functions that relate dose of a possible risk factor to different adverse outcomes can often be assumed to be nondecreasing. In such cases, interest focuses on (1) assessing evidence of an overall adverse effect, (2) determining which outcomes are most…

计数数据的贝叶斯半参数保序回归AI 解读

This article proposes a semiparametric Bayesian approach for inference on an unknown isotonic regression function, f(x), characterizing the relationship between a continuous predictor, X, and a count response variable, Y, adjusting for covariates, Z. A Dirichlet process mixture of Poisson distributions is used to avoid parametric assumptions on the conditional distribution of Y given X and Z. Then, to also avoid parametric assumptions on f(x), a novel prior formulation is…

多维纵向数据的动态潜在特质模型AI 解读

This article presents a new approach for analysis of multidimensional longitudinal data, motivated by studies using an item response battery to measure traits of an individual repeatedly over time. A general modeling framework is proposed that allows mixtures of count, categorical, and continuous response variables. Each response is related to age-specific latent traits through a generalized linear model that accommodates item-specific measurement errors. A transition model…

每日生育力标记的贝叶斯建模AI 解读

Cervical mucus hydration increases during the fertile interval before ovulation. Because sperm can only penetrate mucus having a high water content, cervical secretions provide a reliable marker of the fertile days of the menstrual cycle. This article develops a Bayesian approach for modeling of daily observations of cervical mucus and applies the approach to assess heterogeneity among women and cycles from a given woman with respect to the increase in mucus hydration during…