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噪声下函数局部极值的半参数贝叶斯推断AI 解读

There is a wide range of applications where the local extrema of a function are the key quantity of interest. However, there is surprisingly little work on methods to infer local extrema with uncertainty quantification in the presence of noise. By viewing the function as an infinite-dimensional nuisance parameter, a semiparametric formulation of this problem poses daunting challenges, both methodologically and theoretically, as (i) the number of local extrema may be unknown,…

用于分组数据聚类的分层归一化完全随机测度AI 解读

In this article, we propose a Bayesian nonparametric model for clustering grouped data. We adopt a hierarchical approach: at the highest level, each group of data is modeled according to a mixture, where the mixing distributions are conditionally independent normalized completely random measures (NormCRMs) centered on the same base measure, which is itself a NormCRM. The discreteness of the shared base measure implies that the processes at the data level share the same…

估计 fMRI 动态功能网络连接的贝叶斯方法AI 解读

Dynamic functional connectivity, i.e., the study of how interactions among brain regions change dynamically over the course of an fMRI experiment, has recently received wide interest in the neuroimaging literature. Current approaches for studying dynamic connectivity often rely on ad-hoc approaches for inference, with the fMRI time courses segmented by a sequence of sliding windows. We propose a principled Bayesian approach to dynamic functional connectivity, which is based…

多个高斯图模型的贝叶斯推断AI 解读

In this paper, we propose a Bayesian approach to inference on multiple Gaussian graphical models. Specifically, we address the problem of inferring multiple undirected networks in situations where some of the networks may be unrelated, while others share common features. We link the estimation of the graph structures via a Markov random field (MRF) prior which encourages common edges. We learn which sample groups have a shared graph structure by placing a spike-and-slab…

影像遗传学的整合贝叶斯建模方法AI 解读

In this paper we present a Bayesian hierarchical modeling approach for imaging genetics, where the interest lies in linking brain connectivity across multiple individuals to their genetic information. We have available data from a functional magnetic resonance (fMRI) study on schizophrenia. Our goals are to identify brain regions of interest (ROIs) with discriminating activation patterns between schizophrenic patients and healthy controls, and to relate the ROIs' activations…

利用二元 von Mises 分布与贝叶斯非参数方法估计蛋白质构象角密度AI 解读

Interest in predicting protein backbone conformational angles has prompted the development of modeling and inference procedures for bivariate angular distributions. We present a Bayesian approach to density estimation for bivariate angular data that uses a Dirichlet process mixture model and a bivariate von Mises distribution. We derive the necessary full conditional distributions to fit the model, as well as the details for sampling from the posterior predictive…

基于狄利克雷过程混合模型的聚类变量选择AI 解读

The increased collection of high-dimensional data in various fields has raised a strong interest in clustering algorithms and variable selection procedures. In this paper, we propose a model-based method that addresses the two problems simultaneously. We introduce a latent binary vector to identify discriminating variables and use Dirichlet process mixture models to define the cluster structure. We update the variable selection index using a Metropolis algorithm and obtain…

高维数据聚类中的贝叶斯变量选择AI 解读

Over the last decade, technological advances have generated an explosion of data with substantially smaller sample size relative to the number of covariates (p ≫ n). A common goal in the analysis of such data involves uncovering the group structure of the observations and identifying the discriminating variables. In this article we propose a methodology for addressing these problems simultaneously. Given a set of variables, we formulate the clustering problem in terms of a…

结肠癌发生中层级函数数据的小波非参数建模AI 解读

In this article we develop new methods for analyzing the data from an experiment using rodent models to investigate the effect of type of dietary fat on O6-methylguanine-DNA-methyltransferase (MGMT), an important biomarker in early colon carcinogenesis. The data consist of observed profiles over a spatial variable contained within a two-stage hierarchy, a structure that we dub hierarchical functional data. We present a new method providing a unified framework for modeling…

小波系数的协方差结构：理论与贝叶斯建模AI 解读

Summary We present theoretical results on the random wavelet coefficients covariance structure. We use simple properties of the coefficients to derive a recursive way to compute the within- and across-scale covariances. We point out a useful link between the algorithm proposed and the two-dimensional discrete wavelet transform. We then focus on Bayesian wavelet shrinkage for estimating a function from noisy data. A prior distribution is imposed on the coefficients of the…