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Luke Tierney

Bio: Luke Tierney is an academic researcher from University of Iowa. The author has contributed to research in topics: Lisp & Markov chain Monte Carlo. The author has an hindex of 23, co-authored 48 publications receiving 20016 citations. Previous affiliations of Luke Tierney include Carnegie Mellon University & University of Minnesota.

Papers
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Journal ArticleDOI
TL;DR: Details of the aims and methods of Bioconductor, the collaborative creation of extensible software for computational biology and bioinformatics, and current challenges are described.
Abstract: The Bioconductor project is an initiative for the collaborative creation of extensible software for computational biology and bioinformatics. The goals of the project include: fostering collaborative development and widespread use of innovative software, reducing barriers to entry into interdisciplinary scientific research, and promoting the achievement of remote reproducibility of research results. We describe details of our aims and methods, identify current challenges, compare Bioconductor to other open bioinformatics projects, and provide working examples.

12,142 citations

Journal ArticleDOI
TL;DR: Several Markov chain methods are available for sampling from a posterior distribution as discussed by the authors, including Gibbs sampler and Metropolis algorithm, and several strategies for constructing hybrid algorithms, which can be used to guide the construction of more efficient algorithms.
Abstract: Several Markov chain methods are available for sampling from a posterior distribution. Two important examples are the Gibbs sampler and the Metropolis algorithm. In addition, several strategies are available for constructing hybrid algorithms. This paper outlines some of the basic methods and strategies and discusses some related theoretical and practical issues. On the theoretical side, results from the theory of general state space Markov chains can be used to obtain convergence rates, laws of large numbers and central limit theorems for estimates obtained from Markov chain methods. These theoretical results can be used to guide the construction of more efficient algorithms. For the practical use of Markov chain methods, standard simulation methodology provides several variance reduction techniques and also give guidance on the choice of sample size and allocation.

3,780 citations

Journal ArticleDOI
TL;DR: These approximations to the posterior means and variances of positive functions of a real or vector-valued parameter, and to the marginal posterior densities of arbitrary parameters can also be used to compute approximate predictive densities.
Abstract: This article describes approximations to the posterior means and variances of positive functions of a real or vector-valued parameter, and to the marginal posterior densities of arbitrary (ie, not necessarily positive) parameters These approximations can also be used to compute approximate predictive densities To apply the proposed method, one only needs to be able to maximize slightly modified likelihood functions and to evaluate the observed information at the maxima Nevertheless, the resulting approximations are generally as accurate and in some cases more accurate than approximations based on third-order expansions of the likelihood and requiring the evaluation of third derivatives The approximate marginal posterior densities behave very much like saddle-point approximations for sampling distributions The principal regularity condition required is that the likelihood times prior be unimodal

2,081 citations

Journal ArticleDOI
TL;DR: The Metropolis-Hastings algorithm is a method of constructing a reversible Markov transition kernel with a specified invariant distribution as discussed by the authors, which is used to construct reversible transition kernels.
Abstract: The Metropolis-Hastings algorithm is a method of constructing a reversible Markov transition kernel with a specified invariant distribution. This note describes necessary and sufficient conditions on the candidate generation kernel and the acceptance probability function for the resulting transition kernel and invariant distribution to satisfy the detailed balance conditions. A simple general formulation is used that covers a range of special cases treated separately in the literature. In addition, results on a useful partial ordering of finite state space reversible transition kernels are extended to general state spaces and used to compare the performance of two approaches to using mixtures in Metropolis-Hastings kernels.

411 citations

Journal ArticleDOI
TL;DR: In this paper, the authors extend the fully exponential method to apply to expectations and variances of nonpositive functions, and obtain a second-order approximation to an expectation E(g(θ).
Abstract: Tierney and Kadane (1986) presented a simple second-order approximation for posterior expectations of positive functions They used Laplace's method for asymptotic evaluation of integrals, in which the integrand is written as f(θ)exp(-nh(θ)) and the function h is approximated by a quadratic The form in which they applied Laplace's method, however, was fully exponential: The integrand was written instead as exp[− nh(θ) + log f(θ)]; this allowed first-order approximations to be used in the numerator and denominator of a ratio of integrals to produce a second-order expansion for the ratio Other second-order expansions (Hartigan 1965; Johnson 1970; Lindley 1961, 1980; Mosteller and Wallace 1964) require computation of more derivatives of the log-likelihood function In this article we extend the fully exponential method to apply to expectations and variances of nonpositive functions To obtain a second-order approximation to an expectation E(g(θ)), we use the fully exponential method to approximate

347 citations


Cited by
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Journal ArticleDOI
TL;DR: This work presents DESeq2, a method for differential analysis of count data, using shrinkage estimation for dispersions and fold changes to improve stability and interpretability of estimates, which enables a more quantitative analysis focused on the strength rather than the mere presence of differential expression.
Abstract: In comparative high-throughput sequencing assays, a fundamental task is the analysis of count data, such as read counts per gene in RNA-seq, for evidence of systematic changes across experimental conditions. Small replicate numbers, discreteness, large dynamic range and the presence of outliers require a suitable statistical approach. We present DESeq2, a method for differential analysis of count data, using shrinkage estimation for dispersions and fold changes to improve stability and interpretability of estimates. This enables a more quantitative analysis focused on the strength rather than the mere presence of differential expression. The DESeq2 package is available at http://www.bioconductor.org/packages/release/bioc/html/DESeq2.html .

47,038 citations

Journal ArticleDOI
TL;DR: EdgeR as mentioned in this paper is a Bioconductor software package for examining differential expression of replicated count data, which uses an overdispersed Poisson model to account for both biological and technical variability and empirical Bayes methods are used to moderate the degree of overdispersion across transcripts, improving the reliability of inference.
Abstract: Summary: It is expected that emerging digital gene expression (DGE) technologies will overtake microarray technologies in the near future for many functional genomics applications. One of the fundamental data analysis tasks, especially for gene expression studies, involves determining whether there is evidence that counts for a transcript or exon are significantly different across experimental conditions. edgeR is a Bioconductor software package for examining differential expression of replicated count data. An overdispersed Poisson model is used to account for both biological and technical variability. Empirical Bayes methods are used to moderate the degree of overdispersion across transcripts, improving the reliability of inference. The methodology can be used even with the most minimal levels of replication, provided at least one phenotype or experimental condition is replicated. The software may have other applications beyond sequencing data, such as proteome peptide count data. Availability: The package is freely available under the LGPL licence from the Bioconductor web site (http://bioconductor.org).

29,413 citations

Journal ArticleDOI
TL;DR: The philosophy and design of the limma package is reviewed, summarizing both new and historical features, with an emphasis on recent enhancements and features that have not been previously described.
Abstract: limma is an R/Bioconductor software package that provides an integrated solution for analysing data from gene expression experiments. It contains rich features for handling complex experimental designs and for information borrowing to overcome the problem of small sample sizes. Over the past decade, limma has been a popular choice for gene discovery through differential expression analyses of microarray and high-throughput PCR data. The package contains particularly strong facilities for reading, normalizing and exploring such data. Recently, the capabilities of limma have been significantly expanded in two important directions. First, the package can now perform both differential expression and differential splicing analyses of RNA sequencing (RNA-seq) data. All the downstream analysis tools previously restricted to microarray data are now available for RNA-seq as well. These capabilities allow users to analyse both RNA-seq and microarray data with very similar pipelines. Second, the package is now able to go past the traditional gene-wise expression analyses in a variety of ways, analysing expression profiles in terms of co-regulated sets of genes or in terms of higher-order expression signatures. This provides enhanced possibilities for biological interpretation of gene expression differences. This article reviews the philosophy and design of the limma package, summarizing both new and historical features, with an emphasis on recent enhancements and features that have not been previously described.

22,147 citations

Journal ArticleDOI
TL;DR: The program MRBAYES performs Bayesian inference of phylogeny using a variant of Markov chain Monte Carlo, and an executable is available at http://brahms.rochester.edu/software.html.
Abstract: Summary: The program MRBAYES performs Bayesian inference of phylogeny using a variant of Markov chain Monte Carlo. Availability: MRBAYES, including the source code, documentation, sample data files, and an executable, is available at http://brahms.biology.rochester.edu/software.html.

20,627 citations

Posted ContentDOI
17 Nov 2014-bioRxiv
TL;DR: This work presents DESeq2, a method for differential analysis of count data, using shrinkage estimation for dispersions and fold changes to improve stability and interpretability of estimates, which enables a more quantitative analysis focused on the strength rather than the mere presence of differential expression.
Abstract: In comparative high-throughput sequencing assays, a fundamental task is the analysis of count data, such as read counts per gene in RNA-Seq data, for evidence of systematic changes across experimental conditions. Small replicate numbers, discreteness, large dynamic range and the presence of outliers require a suitable statistical approach. We present DESeq2, a method for differential analysis of count data. DESeq2 uses shrinkage estimation for dispersions and fold changes to improve stability and interpretability of the estimates. This enables a more quantitative analysis focused on the strength rather than the mere presence of differential expression and facilitates downstream tasks such as gene ranking and visualization. DESeq2 is available as an R/Bioconductor package.

17,014 citations