Prior Processes and Their Applications: Nonparametric Bayesian Estimation
Posterior is sampled through an efficient Markov chain Monte Carlo procedure based on the Chinese restaurant process. This method is demonstrated on a variety of synthetic data and real data examples on protein structure analysis. Tumor cells are genetically heterogeneous.
Prior Processes and Their Applications
The collection of the entire tumor cell population consists of different subclones that can be characterized by mutations in sequence and structure at various genomic locations. Using next-generation sequencing data, we characterize tumor heterogeneity using Bayesian nonparametric inference. Specifically, we estimate the number of subclones in a tumor sample, and for each subclone, we estimate the subclonal copy number and single nucleotide mutations at a selected set of loci.
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The proposed method can handle a single or multiple tumor samples. Computation via Markov chain Monte Carlo yields posterior Monte Carlo samples of all three matrices, allowing for the assessment of any desired inference summary. Simulation and real-world examples are provided as illustration. We discuss a class of Bayesian nonparametric priors that can be used to model local dependence in a sequence of observations.
Many popular Bayesian nonparametric priors can be characterized in terms of exchangeable species sampling sequences.
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However, in some applications, common exchangeability assumptions may not be appropriate. We discuss a generalization of species sampling sequences, where the weights in the predictive probability functions are allowed to depend on a sequence of independent not necessarily identically distributed latent random variables.
Journal of the American Statistical Association , , —, We show how those processes can be used as a prior distribution in a hierarchical Bayes modeling framework, and, in particular, how the Beta-GOS can provide a reasonable alternative to the use of non-homogenous Hidden Markov models, further allowing unsupervised clustering of the observations in an unknown number of states. The usefulness of the approach in biostatistical applications is discussed and explicitly shown for the detection of chromosomal aberrations in breast cancer.
The aim of the paper is to discuss the association between SNP genotype data and a disease. For genetic association studies, the statistical analyses with multiple markers have been shown to be more powerful, efficient, and biologically meaningful than single marker association tests. As the number of genetic markers considered is typically large, here we cluster them and then study the association between groups of markers and disease. We propose a two-step procedure: first a Bayesian nonparametric cluster estimate under normalized generalized gamma process mixture models is introduced, so that we are able to incorporate the information from a large-scale SNP data with a much smaller number of explanatory variables.
Then, thanks to the introduction of a genetic score, we study the association between the relevant disease response and groups of markers using a logit model. Inference is obtained via an MCMC truncation method recently introduced in the literature.
We also provide a review of the state of art of Bayesian nonparametric cluster models and algorithms for the class of mixtures adopted here. Making inference on population structure from genotype data requires to identify the actual subpopulations and assign individuals to these populations. The source populations are assumed to be in Hardy-Weinberg equilibrium, but the allelic frequencies of these populations and even the number of populations present in a sample are unknown.
In this chapter we present a review of some Bayesian parametric and nonparametric models for making inference on population structure, with emphasis on model-based clustering methods. Our aim is to show how recent developments in Bayesian nonparametrics have been usefully exploited in order to introduce natural nonparametric counterparts of some of the most celebrated parametric approaches for inferring population structure. Bayesian methods have found many successful applications in high-throughput genomics.
We focus on approaches for network-based inference from gene expression data. Methods that employ sparse priors have been particularly successful, as they are properly designed to analyze large datasets in which the amount of measured variables can be greater than the number of observations. Here, we describe Bayesian approaches for both undirected and directed networks; we discuss novel approaches that are computationally efficient, do not rely on linearity assumptions, and perform comparatively better than state-of-the-art methods.
We demonstrate the utility of our methods via applications to glioblastoma gene expression data.
Yang Ni, Giovanni M. Marchetti, Veerabhadran Baladandayuthapani, Francesco C. The development of parsimonious models for reliable inference and prediction of responses in high-dimensional regression settings is often challenging due to relatively small sample sizes and the presence of complex interaction patterns between a large number of covariates. We propose an efficient, nonparametric framework for simultaneous variable selection, clustering and prediction in high-throughput regression settings with continuous outcomes. The proposed model utilizes the sparsity induced by Poisson-Dirichlet processes PDPs to group the covariates into lower-dimensional latent clusters consisting of covariates with similar patterns among the samples.
The data are permitted to direct the choice of a suitable cluster allocation scheme, choosing between PDPs and their special case, a Dirichlet process. Subsequently, the latent clusters are used to build a nonlinear prediction model for the responses using an adaptive mixture of linear and nonlinear elements, thus achieving a balance between model parsimony and flexibility. The second part contains the Bayesian solutions to certain estimation problems pertaining to the distribution function and its functional based on complete data.
Because of the conjugacy property of some of these processes, the resulting solutions are mostly in closed form. The third part treats similar problems but based on right censored data. Other applications are also included. A comprehensive list of references is provided in order to help readers explore further on their own. All rights reserved. Tel: Fax: Email: office. A non-subjective Bayesian method retains the advantages of the Bayesian paradigm without requiring a subjective prior elicitation.
In this research the investigator develops the theory, methods, and computational algorithms for implementing default Bayesian analyses of complex statistical models depending on infinite-dimensional parameters. The research is disseminated through the teaching of advanced courses and via the usual scientific channels of publications and seminars.
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The research provides new data-analytic tools for solving problems arising in diverse fields. Useful priors with known performance are cataloged and user friendly software is developed for ready applications to diverse fields. Thus the research has a major impact on the conduct of science in a number of highly-relevant application areas. Some full text articles may not yet be available without a charge during the embargo administrative interval. Some links on this page may take you to non-federal websites.
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Conference on BAYESIAN NONPARAMETRICS
Choudhuri, N. Gu, J. Roy, A. Wu, Y. Gu, JZ; Ghosal, S.