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
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Moderated estimation of fold change and dispersion for RNA-seq data with DESeq2

We describe latent Dirichlet allocation (LDA), a generative probabilistic model for collections of discrete data such as text corpora. LDA is a three-level hierarchical Bayesian model, in which each item of a collection is modeled as a finite mixture over an underlying set of topics. Each topic is, in turn, modeled as an infinite mixture over an underlying set of topic probabilities. In the context of text modeling, the topic probabilities provide an explicit representation of a document. We present efficient approximate inference techniques based on variational methods and an EM algorithm for empirical Bayes parameter estimation. We report results in document modeling, text classification, and collaborative filtering, comparing to a mixture of unigrams model and the probabilistic LSI model.

/pdf/latent-dirichlet-allocation-4gmscb06en.pdf

Latent dirichlet allocation

The extent of heterogeneity in a meta-analysis partly determines the difficulty in drawing overall conclusions. This extent may be measured by estimating a between-study variance, but interpretation is then specific to a particular treatment effect metric. A test for the existence of heterogeneity exists, but depends on the number of studies in the meta-analysis. We develop measures of the impact of heterogeneity on a meta-analysis, from mathematical criteria, that are independent of the number of studies and the treatment effect metric. We derive and propose three suitable statistics: H is the square root of the chi2 heterogeneity statistic divided by its degrees of freedom; R is the ratio of the standard error of the underlying mean from a random effects meta-analysis to the standard error of a fixed effect meta-analytic estimate, and I2 is a transformation of (H) that describes the proportion of total variation in study estimates that is due to heterogeneity. We discuss interpretation, interval estimates and other properties of these measures and examine them in five example data sets showing different amounts of heterogeneity. We conclude that H and I2, which can usually be calculated for published meta-analyses, are particularly useful summaries of the impact of heterogeneity. One or both should be presented in published meta-analyses in preference to the test for heterogeneity.

Quantifying heterogeneity in a meta‐analysis

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.

/pdf/moderated-estimation-of-fold-change-and-dispersion-for-rna-59glcgpwlk.pdf

Arlequin ver 3.0 is a software package integrating several basic and advanced methods for population genetics data analysis, like the computation of standard genetic diversity indices, the estimation of allele and haplotype frequencies, tests of departure from linkage equilibrium, departure from selective neutrality and demographic equilibrium, estimation or parameters from past population expansions, and thorough analyses of population subdivision under the AMOVA framework. Arlequin 3 introduces a completely new graphical interface written in C++, a more robust semantic analysis of input files, and two new methods: a Bayesian estimation of gametic phase from multi-locus genotypes, and an estimation of the parameters of an instantaneous spatial expansion from DNA sequence polymorphism. Arlequin can handle several data types like DNA sequences, microsatellite data, or standard multi-locus genotypes. A Windows version of the software is freely available on http://cmpg.unibe.ch/software/arlequin3.

/pdf/arlequin-version-3-0-an-integrated-software-package-for-4cs6nd3y2p.pdf

Arlequin (version 3.0): An integrated software package for population genetics data analysis

The generation of values of sets of functions such as the Bessel functions Jnix) and Ynix) is a problem which one encounters frequently in numerical calculations. The present paper is concerned with describing a method which has been found particularly useful on high speed computers. The basic idea is due to J. C. P. Miller and is described in detail [as applied to the Bessel functions /„(*)] in the introduction to the second volume [1] of Bessel functions published by BAAS. The tables in the BA volume were computed by hand as were the tables by Fox [2]. However, the method is particularly suited to large scale computers. In preparing a general purpose routine to compute J„ix) and Y„ix) one is faced with various obstacles. The power series representation of Jnix) is useful for values of x which are not too large. In addition to the slowness of convergence the form of Ynix) becomes complicated. The asymptotic expansions of J„ix) and Ynix) are useful when x is large with respect to re. In the regiqn where both re and x are large neither of these representations is useful and a third form must be used. It is clear that any program which employs these representations and which should be generally useful must automatically choose the proper form for computation. The method of Miller avoids these difficulties and provides a simple algorithm not only for Jnix) but for many other functions with a similar behavior. Specifically, the method is as follows (the theory supporting the method is given in [1], p. xvii): 1. Choose k larger than the greater of re or x, assume Jk+\\ = 0, Jk = a ^ 0, where a is some arbitrarily chosen constant. 2. If z = 1/x, generate the sequence Jk-i, Jk~2, • • ■ , Ji, Jo from the recurrence relation J p—i = 2pzJ p — Jp+i

/pdf/generation-of-bessel-functions-on-high-speed-computers-4ry8ciuka5.pdf

Generation of Bessel functions on high speed computers

Pocketbook of Mathematical Functions--Abridged Edition of Handbook of Mathematical Functions, Milton Abramowitz and Irene A. Stegun.

https://www.jstor.org/stable/info/2098786

Irene A. Stegun

Papers

Generation of Bessel functions on high speed computers

Pocketbook of Mathematical Functions--Abridged Edition of Handbook of Mathematical Functions, Milton Abramowitz and Irene A. Stegun.

Pitfalls in Computation

Handbook of Mathematical Functions.

Generation of Coulomb Wave Functions by Means of Recurrence Relations