An empirical Bayes approach to stochastic blockmodels and graphons: shrinkage estimation and model selection.
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ABSTRACT:
SUBMITTER: Peng Z
PROVIDER: S-EPMC9299287 | biostudies-literature |
REPOSITORIES: biostudies-literature
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Project description:MotivationGenomic studies often involve estimation of variances of thousands of genes (or other genomic units) from just a few measurements on each. For example, variance estimation is an important step in gene expression analyses aimed at identifying differentially expressed genes. A common approach to this problem is to use an Empirical Bayes (EB) method that assumes the variances among genes follow an inverse-gamma distribution. This distributional assumption is relatively inflexible; for example, it may not capture 'outlying' genes whose variances are considerably bigger than usual. Here we describe a more flexible EB method, capable of capturing a much wider range of distributions. Indeed, the main assumption is that the distribution of the variances is unimodal (or, as an alternative, that the distribution of the precisions is unimodal). We argue that the unimodal assumption provides an attractive compromise between flexibility, computational tractability and statistical efficiency.ResultsWe show that this more flexible approach provides competitive performance with existing methods when the variances truly come from an inverse-gamma distribution, and can outperform them when the distribution of the variances is more complex. In analyses of several human gene expression datasets from the Genotype Tissues Expression consortium, we find that our more flexible model often fits the data appreciably better than the single inverse gamma distribution. At the same time we find that in these data this improved model fit leads to only small improvements in variance estimates and detection of differentially expressed genes.Availability and implementationOur methods are implemented in an R package vashr available from http://github.com/mengyin/vashr CONTACT: mstephens@uchicago.eduSupplementary information: Supplementary data are available at Bioinformatics online.
| S-EPMC5181563 | biostudies-literature
Project description:The James-Stein estimator is an estimator of the multivariate normal mean and dominates the maximum likelihood estimator (MLE) under squared error loss. The original work inspired great interest in developing shrinkage estimators for a variety of problems. Nonetheless, research on shrinkage estimation for manifold-valued data is scarce. In this article, we propose shrinkage estimators for the parameters of the Log-Normal distribution defined on the manifold of N × N symmetric positive-definite matrices. For this manifold, we choose the Log-Euclidean metric as its Riemannian metric since it is easy to compute and has been widely used in a variety of applications. By using the Log-Euclidean distance in the loss function, we derive a shrinkage estimator in an analytic form and show that it is asymptotically optimal within a large class of estimators that includes the MLE, which is the sample Fréchet mean of the data. We demonstrate the performance of the proposed shrinkage estimator via several simulated data experiments. Additionally, we apply the shrinkage estimator to perform statistical inference in both diffusion and functional magnetic resonance imaging problems.
| S-EPMC11000275 | biostudies-literature
Project description:We combine two important ideas in the analysis of large-scale genomics experiments (e.g. experiments that aim to identify genes that are differentially expressed between two conditions). The first is use of Empirical Bayes (EB) methods to handle the large number of potentially-sparse effects, and estimate false discovery rates and related quantities. The second is use of factor analysis methods to deal with sources of unwanted variation such as batch effects and unmeasured confounders. We describe a simple modular fitting procedure that combines key ideas from both these lines of research. This yields new, powerful EB methods for analyzing genomics experiments that account for both sparse effects and unwanted variation. In realistic simulations, these new methods provide significant gains in power and calibration over competing methods. In real data analysis, we find that different methods, while often conceptually similar, can vary widely in their assessments of statistical significance. This highlights the need for care in both choice of methods and interpretation of results.
| S-EPMC8204175 | biostudies-literature
Project description:MotivationStatistical methods for comparing relative rates of synonymous and non-synonymous substitutions maintain a central role in detecting positive selection. To identify selection, researchers often estimate the ratio of these relative rates (dN/dS) at individual alignment sites. Fitting a codon substitution model that captures heterogeneity in dN/dS across sites provides a reliable way to perform such estimation, but it remains computationally prohibitive for massive datasets. By using crude estimates of the numbers of synonymous and non-synonymous substitutions at each site, counting approaches scale well to large datasets, but they fail to account for ancestral state reconstruction uncertainty and to provide site-specific dN/dS estimates.ResultsWe propose a hybrid solution that borrows the computational strength of counting methods, but augments these methods with empirical Bayes modeling to produce a relatively fast and reliable method capable of estimating site-specific dN/dS values in large datasets. Importantly, our hybrid approach, set in a Bayesian framework, integrates over the posterior distribution of phylogenies and ancestral reconstructions to quantify uncertainty about site-specific dN/dS estimates. Simulations demonstrate that this method competes well with more-principled statistical procedures and, in some cases, even outperforms them. We illustrate the utility of our method using human immunodeficiency virus, feline panleukopenia and canine parvovirus evolution examples.
| S-EPMC3579240 | biostudies-literature
Project description:Populations of non-European ancestry are substantially underrepresented in genome-wide association studies (GWAS). As genetic effects can differ between ancestries due to possibly different causal variants or linkage disequilibrium patterns, a meta-analysis that includes GWAS of all populations yields biased estimation in each of the populations and the bias disproportionately impacts non-European ancestry populations. This is because meta-analysis combines study-specific estimates with inverse variance as the weights, which causes biases towards studies with the largest sample size, typical of the European ancestry population. In this paper, we propose two empirical Bayes (EB) estimators to borrow the strength of information across populations although accounting for between-population heterogeneity. Extensive simulation studies show that the proposed EB estimators are largely unbiased and improve efficiency compared to the population-specific estimator. In contrast, even though the meta-analysis estimator has a much smaller variance, it yields significant bias when the genetic effect is heterogeneous across populations. We apply the proposed EB estimators to a large-scale trans-ancestry GWAS of stroke and demonstrate that the EB estimators reduce the variance of the population-specific estimator substantially, with the effect estimates close to the population-specific estimates.
| S-EPMC9892209 | biostudies-literature
Project description:BackgroundAn important question in the analysis of biochemical data is that of identifying subsets of molecular variables that may jointly influence a biological response. Statistical variable selection methods have been widely used for this purpose. In many settings, it may be important to incorporate ancillary biological information concerning the variables of interest. Pathway and network maps are one example of a source of such information. However, although ancillary information is increasingly available, it is not always clear how it should be used nor how it should be weighted in relation to primary data.ResultsWe put forward an approach in which biological knowledge is incorporated using informative prior distributions over variable subsets, with prior information selected and weighted in an automated, objective manner using an empirical Bayes formulation. We employ continuous, linear models with interaction terms and exploit biochemically-motivated sparsity constraints to permit exact inference. We show an example of priors for pathway- and network-based information and illustrate our proposed method on both synthetic response data and by an application to cancer drug response data. Comparisons are also made to alternative Bayesian and frequentist penalised-likelihood methods for incorporating network-based information.ConclusionsThe empirical Bayes method proposed here can aid prior elicitation for Bayesian variable selection studies and help to guard against mis-specification of priors. Empirical Bayes, together with the proposed pathway-based priors, results in an approach with a competitive variable selection performance. In addition, the overall procedure is fast, deterministic, and has very few user-set parameters, yet is capable of capturing interplay between molecular players. The approach presented is general and readily applicable in any setting with multiple sources of biological prior knowledge.
| S-EPMC3503557 | biostudies-literature
Project description:A number of empirical Bayes models (each with different statistical distribution assumptions) have now been developed to analyze differential DNA methylation using high-density oligonucleotide tiling arrays. However, it remains unclear which model performs best. For example, for analysis of differentially methylated regions for conservative and functional sequence characteristics (e.g., enrichment of transcription factor-binding sites (TFBSs)), the sensitivity of such analyses, using various empirical Bayes models, remains unclear. In this paper, five empirical Bayes models were constructed, based on either a gamma distribution or a log-normal distribution, for the identification of differential methylated loci and their cell division-(1, 3, and 5) and drug-treatment-(cisplatin) dependent methylation patterns. While differential methylation patterns generated by log-normal models were enriched with numerous TFBSs, we observed almost no TFBS-enriched sequences using gamma assumption models. Statistical and biological results suggest log-normal, rather than gamma, empirical Bayes model distribution to be a highly accurate and precise method for differential methylation microarray analysis. In addition, we presented one of the log-normal models for differential methylation analysis and tested its reproducibility by simulation study. We believe this research to be the first extensive comparison of statistical modeling for the analysis of differential DNA methylation, an important biological phenomenon that precisely regulates gene transcription.
| S-EPMC3432337 | biostudies-other
Project description:Expression quantitative trait locus (eQTL) analyses identify genetic markers associated with the expression of a gene. Most up-to-date eQTL studies consider the connection between genetic variation and expression in a single tissue. Multi-tissue analyses have the potential to improve findings in a single tissue, and elucidate the genotypic basis of differences between tissues. In this article, we develop a hierarchical Bayesian model (MT-eQTL) for multi-tissue eQTL analysis. MT-eQTL explicitly captures patterns of variation in the presence or absence of eQTL, as well as the heterogeneity of effect sizes across tissues. We devise an efficient Expectation-Maximization (EM) algorithm for model fitting. Inferences concerning eQTL detection and the configuration of eQTL across tissues are derived from the adaptive thresholding of local false discovery rates, and maximum a posteriori estimation, respectively. We also provide theoretical justification of the adaptive procedure. We investigate the MT-eQTL model through an extensive analysis of a 9-tissue data set from the GTEx initiative.
| S-EPMC6366007 | biostudies-literature
Project description:Reconstruction of a high-dimensional network may benefit substantially from the inclusion of prior knowledge on the network topology. In the case of gene interaction networks such knowledge may come for instance from pathway repositories like KEGG, or be inferred from data of a pilot study. The Bayesian framework provides a natural means of including such prior knowledge. Based on a Bayesian Simultaneous Equation Model, we develop an appealing Empirical Bayes (EB) procedure that automatically assesses the agreement of the used prior knowledge with the data at hand. We use variational Bayes method for posterior densities approximation and compare its accuracy with that of Gibbs sampling strategy. Our method is computationally fast, and can outperform known competitors. In a simulation study, we show that accurate prior data can greatly improve the reconstruction of the network, but need not harm the reconstruction if wrong. We demonstrate the benefits of the method in an analysis of gene expression data from GEO. In particular, the edges of the recovered network have superior reproducibility (compared to that of competitors) over resampled versions of the data.
| S-EPMC5510725 | biostudies-literature
Project description:Motivation: Computational inference methods that make use of graphical models to extract regulatory networks from gene expression data can have difficulty reconstructing dense regions of a network, a consequence of both computational complexity and unreliable parameter estimation when sample size is small. As a result, identification of hub genes is of special difficulty for these methods.Methods: We present a new algorithm, Empirical Light Mutual Min (ELMM), for large network reconstruction that has properties well suited for dense graph recovery. ELMM reconstructs the undirected graph of a regulatory network using empirical Bayes conditional independence testing with a heuristic relaxation of independence constraints in dense areas of the graph. This relaxation allows only one gene of a pair with a putative relation to be aware of the network connection, an approach that is aimed at easing multiple testing problems associated with recovering densely connected structures.Results: Using in silico data, we show that ELMM has better performance than commonly used network inference algorithms including PC Algorithm, GeneNet, and ARACNE. We also apply ELMM to reconstruct a network among 5,400 genes expressed in human lung airway epithelium of healthy nonsmokers, healthy smokers, and smokers with pulmonary diseases assayed using microarrays. The analysis identifies dense subnetworks that are consistent with known regulatory relationships in the lung airway and also suggests novel hub regulatory relationships among a number of genes that play roles in oxidative stress, wound response, and secretion.
2024-06-05 | GSE32030 | GEO