112 research outputs found
Bayesian solutions to the label switching problem
The label switching problem, the unidentifiability of the permutation of clusters or more generally latent variables, makes interpretation of results computed with MCMC sampling difficult. We introduce a fully Bayesian treatment of the permutations which performs better than alternatives. The method can be used to compute summaries of the posterior samples even for nonparametric Bayesian methods, for which no good solutions exist so far. Although being approximative in this case, the results are very promising. The summaries are intuitively appealing: A summarized cluster is defined as a set of points for which the likelihood of being in the same cluster is maximized
Some discussions of D. Fearnhead and D. Prangle's Read Paper "Constructing summary statistics for approximate Bayesian computation: semi-automatic approximate Bayesian computation"
This report is a collection of comments on the Read Paper of Fearnhead and Prangle (2011), to appear in the Journal of the Royal Statistical Society Series B, along with a reply from the authors
An Adaptive Interacting Wang-Landau Algorithm for Automatic Density Exploration
While statisticians are well-accustomed to performing exploratory analysis in
the modeling stage of an analysis, the notion of conducting preliminary
general-purpose exploratory analysis in the Monte Carlo stage (or more
generally, the model-fitting stage) of an analysis is an area which we feel
deserves much further attention. Towards this aim, this paper proposes a
general-purpose algorithm for automatic density exploration. The proposed
exploration algorithm combines and expands upon components from various
adaptive Markov chain Monte Carlo methods, with the Wang-Landau algorithm at
its heart. Additionally, the algorithm is run on interacting parallel chains --
a feature which both decreases computational cost as well as stabilizes the
algorithm, improving its ability to explore the density. Performance is studied
in several applications. Through a Bayesian variable selection example, the
authors demonstrate the convergence gains obtained with interacting chains. The
ability of the algorithm's adaptive proposal to induce mode-jumping is
illustrated through a trimodal density and a Bayesian mixture modeling
application. Lastly, through a 2D Ising model, the authors demonstrate the
ability of the algorithm to overcome the high correlations encountered in
spatial models.Comment: 33 pages, 20 figures (the supplementary materials are included as
appendices
Analysis of ChIP-seq data via Bayesian finite mixture models with a non-parametric component
In large discrete data sets which requires classification into signal and noise components, the distribution of the signal is often very bumpy and does not follow a standard distribution. Therefore the signal distribution is further modelled as a mixture of component distributions. However, when the signal component is modelled as a mixture of distributions, we are faced with the challenges of justifying the number of components and the label switching problem (caused by multimodality of the likelihood function). To circumvent these challenges, we propose a non-parametric structure for the signal component. This new method is more efficient in terms of precise estimates and better classifications. We demonstrated the efficacy of the methodology using a ChIP-sequencing data set
A Novel Test for Gene-Ancestry Interactions in Genome-Wide Association Data
Genome-wide association study (GWAS) data on a disease are increasingly available from multiple related populations. In this scenario, meta-analyses can improve power to detect homogeneous genetic associations, but if there exist ancestry-specific effects, via interactions on genetic background or with a causal effect that co-varies with genetic background, then these will typically be obscured. To address this issue, we have developed a robust statistical method for detecting susceptibility gene-ancestry interactions in multi-cohort GWAS based on closely-related populations. We use the leading principal components of the empirical genotype matrix to cluster individuals into “ancestry groups” and then look for evidence of heterogeneous genetic associations with disease or other trait across these clusters. Robustness is improved when there are multiple cohorts, as the signal from true gene-ancestry interactions can then be distinguished from gene-collection artefacts by comparing the observed interaction effect sizes in collection groups relative to ancestry groups. When applied to colorectal cancer, we identified a missense polymorphism in iron-absorption gene CYBRD1 that associated with disease in individuals of English, but not Scottish, ancestry. The association replicated in two additional, independently-collected data sets. Our method can be used to detect associations between genetic variants and disease that have been obscured by population genetic heterogeneity. It can be readily extended to the identification of genetic interactions on other covariates such as measured environmental exposures. We envisage our methodology being of particular interest to researchers with existing GWAS data, as ancestry groups can be easily defined and thus tested for interactions
Assessing Order Effects in Online Community-based Health Forums
Measuring the quality of health content in online health forums is a challenging task. The majority of the existing measures are based on evaluations of forum users and may not be reliable. We employed machine learning techniques, text mining methods, and Big Data platforms to construct four measures of textual quality to automatically determine the similarity of a given answer to professional answers. We then used them to assess the quality of 66,888 answers posted on Yahoo! Answers Health section. All four measures of textual quality revealed a higher quality for asker-selected best answers indicating that askers, to some extent, have a proper judgment to select the best answers. We also studied the presence of order effects in online health forums. Our results suggest that the textual quality of the first answer positively influences the mean textual quality of the subsequent answers and negatively influences the quantity of subsequent answers
Analyzing Th17 cell differentiation dynamics using a novel integrative modeling framework for time-course RNA sequencing data
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