Bayesian Partition Model Research Articles

A Bayesian model to identify multiple expression patterns with simultaneous FDR control for a multi-factor RNA-seq experiment.

It is often of research interest to identify genes that satisfy a particular expression pattern across different conditions such as tissues, genotypes, etc. One common practice is to perform differential expression analysis for each condition separately and then take the intersection of differentially expressed (DE) genes or non-DE genes under each condition to obtain genes that satisfy a particular pattern. Such a method can lead to many false positives, especially when the desired gene expression pattern involves equivalent expression under one condition. In this paper, we apply a Bayesian partition model to identify genes of all desired patterns while simultaneously controlling their false discovery rates (FDRs). Our simulation studies show that the common practice fails to control group specific FDRs for patterns involving equivalent expression while the proposed Bayesian method simultaneously controls group specific FDRs at all settings studied. In addition, the proposed method is more powerful when the FDR of the common practice is under control for identifying patterns only involving DE genes. Our simulation studies also show that it is an inherently more challenging problem to identify patterns involving equivalent expression than patterns only involving differential expression. Therefore, larger sample sizes are required to obtain the same target power to identify the former types of patterns than the latter types of patterns.

A Conditional Density Estimation Partition Model Using Logistic Gaussian Processes.

Conditional density estimation (density regression) estimates the distribution of a response variable y conditional on covariates x. Utilizing a partition model framework, a conditional density estimation method is proposed using logistic Gaussian processes. The partition is created using a Voronoi tessellation and is learned from the data using a reversible jump Markov chain Monte Carlo algorithm. The Markov chain Monte Carlo algorithm is made possible through a Laplace approximation on the latent variables of the logistic Gaussian process model. This approximation marginalizes the parameters in each partition element, allowing an efficient search of the posterior distribution of the tessellation. The method has desirable consistency properties. In simulation and applications, the model successfully estimates the partition structure and conditional distribution of y.

CLIC, a tool for expanding biological pathways based on co-expression across thousands of datasets.

In recent years, there has been a huge rise in the number of publicly available transcriptional profiling datasets. These massive compendia comprise billions of measurements and provide a special opportunity to predict the function of unstudied genes based on co-expression to well-studied pathways. Such analyses can be very challenging, however, since biological pathways are modular and may exhibit co-expression only in specific contexts. To overcome these challenges we introduce CLIC, CLustering by Inferred Co-expression. CLIC accepts as input a pathway consisting of two or more genes. It then uses a Bayesian partition model to simultaneously partition the input gene set into coherent co-expressed modules (CEMs), while assigning the posterior probability for each dataset in support of each CEM. CLIC then expands each CEM by scanning the transcriptome for additional co-expressed genes, quantified by an integrated log-likelihood ratio (LLR) score weighted for each dataset. As a byproduct, CLIC automatically learns the conditions (datasets) within which a CEM is operative. We implemented CLIC using a compendium of 1774 mouse microarray datasets (28628 microarrays) or 1887 human microarray datasets (45158 microarrays). CLIC analysis reveals that of 910 canonical biological pathways, 30% consist of strongly co-expressed gene modules for which new members are predicted. For example, CLIC predicts a functional connection between protein C7orf55 (FMC1) and the mitochondrial ATP synthase complex that we have experimentally validated. CLIC is freely available at www.gene-clic.org. We anticipate that CLIC will be valuable both for revealing new components of biological pathways as well as the conditions in which they are active.

A full Bayesian partition model for identifying hypo- and hyper-methylated loci from single nucleotide resolution sequencing data.

BackgroudDNA methylation is an epigenetic modification that plays important roles on gene regulation. Study of whole-genome bisulfite sequencing and reduced representation bisulfite sequencing brings the availability of DNA methylation at single CpG resolution. The main interest of study on DNA methylation data is to test the methylation difference under two conditions of biological samples. However, the high cost and complexity of this sequencing experiment limits the number of biological replicates, which brings challenges to the development of statistical methods.ResultsBayesian modeling is well known to be able to borrow strength across the genome, and hence is a powerful tool for high-dimensional- low-sample- size data. In order to provide accurate identification of methylation loci, especially for low coverage data, we propose a full Bayesian partition model to detect differentially methylated loci under two conditions of scientific study. Since hypo-methylation and hyper-methylation have distinct biological implication, it is desirable to differentiate these two types of differential methylation. The advantage of our Bayesian model is that it can produce one-step output of each locus being either equal-, hypo- or hyper-methylated locus without further post-hoc analysis. An R package named as MethyBayes implementing the proposed full Bayesian partition model will be submitted to the bioconductor website upon publication of the manuscript.ConclusionsThe proposed full Bayesian partition model outperforms existing methods in terms of power while maintaining a low false discovery rate based on simulation studies and real data analysis including bioinformatics analysis.Electronic supplementary materialThe online version of this article (doi:10.1186/s12859-015-0850-3) contains supplementary material, which is available to authorized users.

Bayesian Inference for Functional Dynamics Exploring in fMRI Data.

This paper aims to review state-of-the-art Bayesian-inference-based methods applied to functional magnetic resonance imaging (fMRI) data. Particularly, we focus on one specific long-standing challenge in the computational modeling of fMRI datasets: how to effectively explore typical functional interactions from fMRI time series and the corresponding boundaries of temporal segments. Bayesian inference is a method of statistical inference which has been shown to be a powerful tool to encode dependence relationships among the variables with uncertainty. Here we provide an introduction to a group of Bayesian-inference-based methods for fMRI data analysis, which were designed to detect magnitude or functional connectivity change points and to infer their functional interaction patterns based on corresponding temporal boundaries. We also provide a comparison of three popular Bayesian models, that is, Bayesian Magnitude Change Point Model (BMCPM), Bayesian Connectivity Change Point Model (BCCPM), and Dynamic Bayesian Variable Partition Model (DBVPM), and give a summary of their applications. We envision that more delicate Bayesian inference models will be emerging and play increasingly important roles in modeling brain functions in the years to come.

Bayesian Partition Models for Identifying Expression Quantitative Trait Loci

Expression quantitative trait loci (eQTLs) are genomic locations associated with changes of expression levels of certain genes. By assaying gene expressions and genetic variations simultaneously on a genome-wide scale, scientists wish to discover genomic loci responsible for expression variations of a set of genes. The task can be viewed as a multivariate regression problem with variable selection on both responses (gene expression) and covariates (genetic variations), including also multi-way interactions among covariates. Instead of learning a predictive model of quantitative trait given combinations of genetic markers, we adopt an inverse modeling perspective to model the distribution of genetic markers conditional on gene expression traits. A particular strength of our method is its ability to detect interactive effects of genetic variations with high power even when their marginal effects are weak, addressing a key weakness of many existing eQTL mapping methods. Furthermore, we introduce a hierarchical model to capture the dependence structure among correlated genes. Through simulation studies and a real data example in yeast, we demonstrate how our Bayesian hierarchical partition model achieves a significantly improved power in detecting eQTLs compared to existing methods. Supplementary materials for this article are available online.

Probabilistic Record Linkage in Astronomy: Directional Cross-Identification and Beyond

Modern astronomy increasingly relies upon systematic surveys, whose dedicated telescopes continuously observe the sky across varied wavelength ranges of the electromagnetic spectrum; some surveys also observe nonelectromagnetic messengers, such as high-energy particles or gravitational waves. Stars and galaxies look different through the eyes of different instruments, and their independent measurements have to be carefully combined to provide a complete, sound picture of the multicolor and eventful universe. The association of an object's independent detections is, however, a difficult problem scientifically, computationally, and statistically, raising varied challenges across diverse astronomical applications. The fundamental problem is finding records in survey databases with directions that match to within the direction uncertainties. Such astronomical versions of the record linkage problem are known by various terms in astronomy: cross-matching; cross-identification; and directional, positional, or spatiotemporal coincidence assessment. Astronomers have developed several statistical approaches for such problems, largely independent of related developments in other disciplines. Here, we review emerging approaches that compute (Bayesian) probabilities for the hypotheses of interest: possible associations or demographic properties of a cosmic population that depend on identifying associations. Many cross-identification tasks can be formulated within a hierarchical Bayesian partition model framework, with components that explicitly account for astrophysical effects (e.g., source brightness versus wavelength, source motion, or source extent), selection effects, and measurement error. We survey recent developments and highlight important open areas for future research.

Abstract 150: Trans-ethnic GWAS of Mri-defined Brain Infarcts: Charge Consortium

Introduction: MRI-defined brain infarcts (BI), most of which are small sub-cortical brain infarcts (SSBI), are highly prevalent in older persons. Most BI are covert, which is not associated with clinically overt stroke. Nonetheless, they are powerful predictors of future risk for stroke, cognitive decline, and dementia. Little is known about the genetic determinants of BI. Methods: We performed a trans-ethnic meta-analysis of GWAS of MRI-defined BI and SSBI in 20,949 participants belonging to 5 ethnic groups: Europeans, African-Americans, Hispanic-Americans, Malays, and Chinese. A total of 23 population-based studies from the CHARGE consortium participated in this effort, comprising of 3,726 cases and 17,223 controls for BI, 2,112 cases and 15,432 controls for SSBI. GWAS based on imputed genotypes using the 1000 Genomes phase 1, version 3 panel was performed in each study [using logistic regression]. Meta-analysis of association statistics was performed using a Bayesian partition model (MANTRA); secondary analyses used fixed effect (FE) inverse variance weighting. Loci with log 10 [Bayesian factor (BF)]>5 were considered genome-wide significant and loci with log 10 [BF]>4.5 and mean imputation accuracy score >0.80 were chosen for replication. Results: 33 variants (3 loci) reached genome-wide significance, in association with BI, on chromosome: 13q12 (Index SNP: log 10 [BF]=7, P FE =5.8х10 -9 , OR FE =1.2, minor allele frequency [MAF]=0.34), 5q23 (Index SNP: log 10 [BF]=6.5, P FE =1.8х10 -8 , OR FE =1.2, MAF=0.21) and 15q26 (Index SNP: log 10 [BF]=5.3, P FE =3.4х10 -7 , OR FE =1.8, MAF=0.03). These loci comprise genes involved in response to anti-hypertensive drugs, glucose transport, connective tissue assembly and synaptic transmission. Three additional loci showed suggestive associations (log 10 [BF] 4.5 to 5). Five of these six loci were associated with both BI and SSBI (Index SNP log 10 [BF]>2), but none reached genome-wide significance for SSBI. Conclusion: This large scale trans-ethnic GWAS meta-analysis identified three novel risk loci for MRI-defined BI. Replication analysis and functional validation are ongoing. These findings may provide novel insight into biological mechanisms underlying covert vascular brain injury

Varying dimensional Bayesian acoustic waveform inversion for 1D semi-infinite heterogeneous media

This paper introduces a methodology to infer the spatial variation of the acoustic characteristics of a 1D vertical elastic heterogeneous earth model via a Bayesian calibration approach, given a prescribed sequence of loading and the corresponding time history response registered at the ground level. This involves solving an inverse problem that maps the ground seismic response onto a random profile of the ground stratigraphy (i.e. a 1D continuous spatial random field). From a Bayesian point of view, the solution to an inverse problem is fully characterized by a posterior density function of the forward model random parameters, which explicitly overcomes the solution's non-uniqueness. This subsurface earth model is parameterized using a Bayesian partition model, where the number of soil layers, the location of the layers' interfaces, and their corresponding mechanical characteristics are defined as random variables. The partition model approach to an inverse problem is closely related to a Bayesian model selection problem, where the likely dimensionality of the inverse problem (number of unknowns) is inferred conditioned on the experimental observations. The main benefit of the proposed approach is that the explicit regularization of the inverted profile by global damping procedures is not required. A Reversible Jump Markov Chain Monte Carlo (RJMCMC) algorithm is used to sample the target posterior of varying dimension, dependent on the number of layers. A synthetic case study is provided to indicate the applicability of the proposed methodology.

On integrating multi-experiment microarray data.

With the extensive use of microarray technology as a potential prognostic and diagnostic tool, the comparison and reproducibility of results obtained from the use of different platforms is of interest. The integration of those datasets can yield more informative results corresponding to numerous datasets and microarray platforms. We developed a novel integration technique for microarray gene-expression data derived by different studies for the purpose of a two-way Bayesian partition modelling which estimates co-expression profiles under subsets of genes and between biological samples or experimental conditions. The suggested methodology transforms disparate gene-expression data on a common probability scale to obtain inter-study-validated gene signatures. We evaluated the performance of our model using artificial data. Finally, we applied our model to six publicly available cancer gene-expression datasets and compared our results with well-known integrative microarray data methods. Our study shows that the suggested framework can relieve the limited sample size problem while reporting high accuracies by integrating multi-experiment data.

Detecting Hepatitis B Viral Amino Acid Sequence Mutations in Occult Hepatitis B Infections via Bayesian Partition Model

Background: With advancements in technology, a number of Hepatitis B virus (HBV) infections, where viral DNA is present in the liver or plasma, without the concomitant detection of HBsAg in plasma have been reported, and have been termed occult Hepatitis B infections (OBI). Unfortunately, the etiology and pathogenesis of OBI remain elusive to date, and the genetic characteristics of HBV sequence that lead to the development of OBI are still poorly understood. Methods: 358 genotype-C (330 chronically infected patients and 28 occult infected patients) and 107 genotype-D (83 chronically infected patients and 24 occult infected patients) HBV Reverse Transcriptase (RT) amino acid sequences were collected. In addition to greedy search, a novel statistical approach, Bayesian Variable Partition Model is applied to pinpoint those positions, where amino acid mutations collaboratively discriminate OBI samples from chronically infected samples, in genotype-C and genotype-D, respectively. Results: Several discriminate and correlated positions were found in genotype-C (high-order position combinations listed in tables) and genotype-D (positions 126+138, 129+131 and 138+139) respectively. By comparing amino acid distributions in these positions between genotype-C and genotype-D, six position combinations were reported to have obvious different amino acid distributions in these two HBV genotypes. Conclusions: This paper furthers the understanding of the correlation between HBV sequence mutations and the differences of OBI in two HBV genotypes, by studying mutations in HBV RT amino acid sequences. Different from other traditional methods, the Bayesian-based method is able to analyze high-order combinations of positions.

Fine-scale mapping of disease susceptibility locus with Bayesian partition model

The causal relationship between genes and diseases has been investigated with the development of DNA sequence. Polymorphisms incorporated in the HapMap Project have enabled fine mapping with linkage disequilibrium (LD) and prior clustering of the haplotypes on the basis of a similarity measure has often been performed in an attempt to capture coalescent events because they can reduce the amount of computation. However an inappropriate choice of similarity measure can lead to wrong conclusions and we propose a new haplotype-based clustering algorithm for fine-scale mapping by using a Bayesian partition model. To handle phase-unknown genotypes, we propose a new algorithm based on a Metropolized Gibbs sampler and it is implemented in C++. Our simulation studies found that the proposed method improves the accuracy of the estimator for the disease susceptibility locus. We illustrated the practical implication of the new analysis method by an application to fine-scale mapping of CYP2D6 in drug metabolism.

Product partition models with correlated parameters

In sequentially observed data, Bayesian partition models aim at par- titioning the entire observation period into disjoint clusters. Each cluster is an aggregation of sequential observations and a simple model is adopted within each cluster. The main inferential problem is the estimation of the number and loca- tions of the clusters. We extend the well-known product partition model (PPM) by assuming that observations within the same cluster have their distributions in- dexed by correlated and difierent parameters. Such parameters are similar within a cluster by means of a Gibbs prior distribution. We carried out several simula- tions and real data set analyses showing that our model provides better estimates for all parameters, including the number and position of the temporal clusters, even for situations favoring the PPM. A free and open source code is available.

Similarity analysis in Bayesian random partition models

This work proposes a method to assess the influence of individual observations in the clustering generated by any process that involves random partitions. We call it Similarity Analysis. It basically consists of decomposing the estimated similarity matrix into an intrinsic and an extrinsic part, coupled with a new approach for representing and interpreting partitions. Individual influence is associated with the particular ordering induced by individual covariates, which in turn provides an interpretation of the underlying clustering mechanism. We present applications in the context of Species Sampling Mixture Models (SSMMs), including Bayesian density estimation and dependent linear regression models.

A Bayesian partition modelling approach to resolve spatial variability in climate records from borehole temperature inversion

SUMMARY Collections of suitably chosen borehole profiles can be used to infer large-scale trends in ground-surface temperature (GST) histories for the past few hundred years. These reconstructions are based on a large database of carefully selected borehole temperature measurements from around the globe. Since non-climatic thermal influences are difficult to identify, representative temperature histories are derived by averaging individual reconstructions to minimize the influence of these perturbing factors. This may lead to three potentially important drawbacks: the net signal of non-climatic factors may not be zero, meaning that the average does not reflect the best estimate of past climate; the averaging over large areas restricts the useful amount of more local climate change information available; and the inversion methods used to reconstruct the past temperatures at each site must be mathematically identical and are therefore not necessarily best suited to all data sets. In this work, we avoid these issues by using a Bayesian partition model (BPM), which is computed using a trans-dimensional form of a Markov chain Monte Carlo algorithm. This then allows the number and spatial distribution of different GST histories to be inferred from a given set of borehole data by partitioning the geographical area into discrete partitions. Profiles that are heavily influenced by non-climatic factors will be partitioned separately. Conversely, profiles with climatic information, which is consistent with neighbouring profiles, will then be inferred to lie in the same partition. The geographical extent of these partitions then leads to information on the regional extent of the climatic signal. In this study, three case studies are described using synthetic and real data. The first demonstrates that the Bayesian partition model method is able to correctly partition a suite of synthetic profiles according to the inferred GST history. In the second, more realistic case, a series of temperature profiles are calculated using surface air temperatures of a global climate model simulation. In the final case, 23 real boreholes from the United Kingdom, previously used for climatic reconstructions, are examined and the results compared with a local instrumental temperature series and the previous estimate derived from the same borehole data. The results indicate that the majority (17) of the 23 boreholes are unsuitable for climatic reconstruction purposes, at least without including other thermal processes in the forward model.

Statistical modelling using product partition models

Product partition models (PPMs) allow us to partition a set of objects into k sets. PPMs are a special case of Bayesian Partition models. They use partially exchangeable priors where given a partition ρ of the objects into k sets, the objects in the same set are exchangeable and the objects belonging to distinct sets are independent. PPMs specify prior probabilities for a random partition and update these into posterior distributions of the same form. They provide a convenient way of allowing the data to weight the partitions likely to hold. Posterior estimates of the parameter of interest are obtained by conditioning on the partition and averaging over all generated partitions. Markov chain Monte Carlo (MCMC) techniques are used to generate partitions of the data. PPMs can be applied to many diverse estimation problems and in this paper we outline two areas where they are useful.

Genetic Association Mapping via Evolution-Based Clustering of Haplotypes

Multilocus analysis of single nucleotide polymorphism haplotypes is a promising approach to dissecting the genetic basis of complex diseases. We propose a coalescent-based model for association mapping that potentially increases the power to detect disease-susceptibility variants in genetic association studies. The approach uses Bayesian partition modelling to cluster haplotypes with similar disease risks by exploiting evolutionary information. We focus on candidate gene regions with densely spaced markers and model chromosomal segments in high linkage disequilibrium therein assuming a perfect phylogeny. To make this assumption more realistic, we split the chromosomal region of interest into sub-regions or windows of high linkage disequilibrium. The haplotype space is then partitioned into disjoint clusters, within which the phenotype–haplotype association is assumed to be the same. For example, in case-control studies, we expect chromosomal segments bearing the causal variant on a common ancestral background to be more frequent among cases than controls, giving rise to two separate haplotype clusters. The novelty of our approach arises from the fact that the distance used for clustering haplotypes has an evolutionary interpretation, as haplotypes are clustered according to the time to their most recent common ancestor. Our approach is fully Bayesian and we develop a Markov Chain Monte Carlo algorithm to sample efficiently over the space of possible partitions. We compare the proposed approach to both single-marker analyses and recently proposed multi-marker methods and show that the Bayesian partition modelling performs similarly in localizing the causal allele while yielding lower false-positive rates. Also, the method is computationally quicker than other multi-marker approaches. We present an application to real genotype data from the CYP2D6 gene region, which has a confirmed role in drug metabolism, where we succeed in mapping the location of the susceptibility variant within a small error.

A Flexible Bayesian Framework for Modeling Haplotype Association with Disease, Allowing for Dominance Effects of the Underlying Causative Variants

Multilocus analysis of single-nucleotide-polymorphism (SNP) haplotypes may provide evidence of association with disease, even when the individual loci themselves do not. Haplotype-based methods are expected to outperform single-SNP analyses because (i) common genetic variation can be structured into haplotypes within blocks of strong linkage disequilibrium and (ii) the functional properties of a protein are determined by the linear sequence of amino acids corresponding to DNA variation on a haplotype. Here, I propose a flexible Bayesian framework for modeling haplotype association with disease in population-based studies of candidate genes or small candidate regions. I employ a Bayesian partition model to describe the correlation between marker-SNP haplotypes and causal variants at the underlying functional polymorphism(s). Under this model, haplotypes are clustered according to their similarity, in terms of marker-SNP allele matches, which is used as a proxy for recent shared ancestry. Haplotypes within a cluster are then assigned the same probability of carrying a causal variant at the functional polymorphism(s). In this way, I can account for the dominance effect of causal variants, here corresponding to any deviation from a multiplicative contribution to disease risk. The results of a detailed simulation study demonstrate that there is minimal cost associated with modeling these dominance effects, with substantial gains in power over haplotype-based methods that do not incorporate clustering and that assume a multiplicative model of disease risks.

Extensive multiallelic analysis of the relationship between HLA-DRB1 and rheumatoid arthritis using a Bayesian partition model

To analyse the association between individual HLA-DRB1 locus genotypes and rheumatoid arthritis (RA) susceptibility, taking in account the multiallelic nature of the shared epitope (SE). In total, 538 patients and 536 controls were genotyped for 12 alleles of the HLA-DRB1 locus. A Bayesian partition model and multivariate logistic models were used to assess the role of the SE and of its individual components. The SE was associated with RA susceptibility (odds ratio (OR) 2 versus 0 SE copy=9.99 (95 CI 4.69-15.30) and OR 1 versus 0 SE copy=3.16 (95% CI 2.42-4.12)). The Bayesian partition model supplied a permutation of the HLA-DRBA locus alleles ordered by increasing disease risk. Alleles associated with highest risks are those that code for the SE. The individual OR estimations for the HLA-DRB1 locus genotypes went from OR=1.00 (95% CI 1.00-1.25) for the less associated genotype to OR=21.40 (95% CI 8.02-65.79) for the most associated one. In conclusion, the allele order risk and the OR estimations for individual genotypes of the HLA-DRB1 locus were consistent with the SE theory. Using an exploratory statistical method without a priori hypothesis, our study allowed a detailed analysis of the multiallelic nature of the SE.

Bayesian Spatial Modelling of Gamma Ray Count Data

Gamma ray logging is a method routinely employed by geophysicists and environmental engineers in site geology evaluations. Modelling of gamma ray data from individual boreholes assists in the local identification of major lithological changes; modelling these data from a network of boreholes assists with lithological mapping and spatial stratigraphic correlation. In this paper we employ Bayesian spatial partition models to analyse gamma ray data spatially. In particular, a spatial partition is defined via a Voronoi tessellation and the mean intensity is assumed constant in each cell of the partition. The number of vertices generating the tessellation as well as the locations of vertices are assumed unknown, and uncertainty about these quantities is described via a hierarchical prior distribution. We describe the advantages of the spatial partition modelling approach in the context of smoothing gamma ray count data and describe an implementation that may be extended to the fitting of a more general model than a constant mean within each cell of the partition. As an illustration of the methodology we consider a data set collected from a network of eight boreholes, which is part of a geophysical study to assist in mapping the lithology of a site. Gamma ray logs are linked with geological information from cores and the spatial analysis of log data assists with predicting the lithology at unsampled locations.