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高维混杂模型同时推断的去相关与去偏方法AI 解读

Motivated by the simultaneous association analysis with the presence of latent confounders, this article studies the large-scale hypothesis testing problem for the high-dimensional confounded linear models with both non-asymptotic and asymptotic false discovery control. Such model covers a wide range of practical settings where both the response and the predictors may be confounded. In the presence of the high-dimensional predictors and the unobservable confounders, the…

用于高维分布的隐马尔可夫 Pólya 树AI 解读

The Pólya tree (PT) process is a general-purpose Bayesian nonparametric model that has found wide application in a range of inference problems. It has a simple analytic form and the posterior computation boils down to beta-binomial conjugate updates along a partition tree over the sample space. Recent development in PT models shows that performance of these models can be substantially improved by (i) allowing the partition tree to adapt to the structure of the underlying…

微生物组数据的贝叶斯图形成分回归AI 解读

An important task in microbiome studies is to test the existence of and give characterization to differences in the microbiome composition across groups of samples. Important challenges of this problem include the large within-group heterogeneities among samples and the existence of potential confounding variables that, when ignored, increase the chance of false discoveries and reduce the power for identifying true differences. We propose a probabilistic framework to…

基于Pólya树的相关密度贝叶斯层级模型AI 解读

Summary Bayesian hierarchical models are used to share information between related samples and to obtain more accurate estimates of sample level parameters, common structure and variation between samples. When the parameter of interest is the distribution or density of a continuous variable, a hierarchical model for continuous distributions is required. Various such models have been described in the literature using extensions of the Dirichlet process and related processes,…

用于依赖关系检验的 Fisher 精确扫描AI 解读

We introduce a method—called Fisher exact scanning (FES)—for testing and identifying variable dependency that generalizes Fisher’s exact test on 2 × 2 contingency tables to R × C contingency tables and continuous sample spaces. FES proceeds through scanning over the sample space using windows in the form of 2 × 2 tables of various sizes, and on each window completing a Fisher’s exact test. Based on a factorization of Fisher’s multivariate hypergeometric (MHG) likelihood into…

通过小波域马尔可夫树集合高效进行函数型方差分析AI 解读

We introduce a wavelet-domain method for functional analysis of variance (fANOVA). It is based on a Bayesian hierarchical model that employs a graphical hyperprior in the form of a Markov grove (MG)—that is, a collection of Markov trees—for linking the presence/absence of factor effects at all location-scale combinations, thereby incorporating the natural clustering of factor effects in the wavelet-domain across locations and scales. Inference under the model enjoys both…

识别两样本差异的概率多分辨率扫描AI 解读

Summary We propose a multi-resolution scanning approach to identifying two-sample differences. Windows of multiple scales are constructed through nested dyadic partitioning on the sample space and a hypothesis regarding the two-sample difference is defined on each window. Instead of testing the hypotheses on different windows independently, we adopt a joint graphical model, namely a Markov tree, on the null or alternative states of these hypotheses to incorporate spatial…

通过局部信息传播实现可扩展的贝叶斯模型平均AI 解读

This article shows that a probabilistic version of the classical forward-stepwise variable inclusion procedure can serve as a general data-augmentation scheme for model space distributions in (generalized) linear models. This latent variable representation takes the form of a Markov process, thereby allowing information propagation algorithms to be applied for sampling from model space posteriors. In particular, We propose a sequential Monte Carlo method for achieving…

通过递归混合建模进行条件关联的自适应检验AI 解读

In many case-control studies, a central goal is to test for association or dependence between the predictors and the response. Relevant covariates must be conditioned on to avoid false positives and loss in power. Conditioning on covariates is easy in parametric frameworks such as the logistic regression—by incorporating the covariates into the model as additional variables. In contrast, nonparametric methods such as the Cochran-Mantel-Haenszel test accomplish conditioning…

耦合可选 Pólya 树与两样本问题AI 解读

Testing and characterizing the difference between two data samples is of fundamental interest in statistics. Existing methods such as Kolmogorov–Smirnov and Cramer–von Mises tests do not scale well as the dimensionality increases and provide no easy way to characterize the difference should it exist. In this work, we propose a theoretical framework for inference that addresses these challenges in the form of a prior for Bayesian nonparametric analysis. The new prior is…

可选 Pólya 树与贝叶斯推断AI 解读

We introduce an extension of the Pólya tree approach for constructing distributions on the space of probability measures. By using optional stopping and optional choice of splitting variables, the construction gives rise to random measures that are absolutely continuous with piecewise smooth densities on partitions that can adapt to fit the data. The resulting “optional Pólya tree” distribution has large support in total variation topology and yields posterior distributions…