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
 .

/pdf/moderated-estimation-of-fold-change-and-dispersion-for-rna-3ywnbkcan0.pdf

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

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

The second edition of this acclaimed graduate text provides a unified treatment of two methods used in contemporary econometric research, cross section and data panel methods. By focusing on assumptions that can be given behavioral content, the book maintains an appropriate level of rigor while emphasizing intuitive thinking. The analysis covers both linear and nonlinear models, including models with dynamics and/or individual heterogeneity. In addition to general estimation frameworks (particular methods of moments and maximum likelihood), specific linear and nonlinear methods are covered in detail, including probit and logit models and their multivariate, Tobit models, models for count data, censored and missing data schemes, causal (or treatment) effects, and duration analysis. Econometric Analysis of Cross Section and Panel Data was the first graduate econometrics text to focus on microeconomic data structures, allowing assumptions to be separated into population and sampling assumptions. This second edition has been substantially updated and revised. Improvements include a broader class of models for missing data problems; more detailed treatment of cluster problems, an important topic for empirical researchers; expanded discussion of "generalized instrumental variables" (GIV) estimation; new coverage (based on the author's own recent research) of inverse probability weighting; a more complete framework for estimating treatment effects with panel data, and a firmly established link between econometric approaches to nonlinear panel data and the "generalized estimating equation" literature popular in statistics and other fields. New attention is given to explaining when particular econometric methods can be applied; the goal is not only to tell readers what does work, but why certain "obvious" procedures do not. The numerous included exercises, both theoretical and computer-based, allow the reader to extend methods covered in the text and discover new insights.

/pdf/econometric-analysis-of-cross-section-and-panel-data-3jzr8emmtf.pdf

Econometric Analysis of Cross Section and Panel Data

SciPy is an open source scientific computing library for the Python programming language. SciPy 1.0 was released in late 2017, about 16 years after the original version 0.1 release. SciPy has become a de facto standard for leveraging scientific algorithms in the Python programming language, with more than 600 unique code contributors, thousands of dependent packages, over 100,000 dependent repositories, and millions of downloads per year. This includes usage of SciPy in almost half of all machine learning projects on GitHub, and usage by high profile projects including LIGO gravitational wave analysis and creation of the first-ever image of a black hole (M87). The library includes functionality spanning clustering, Fourier transforms, integration, interpolation, file I/O, linear algebra, image processing, orthogonal distance regression, minimization algorithms, signal processing, sparse matrix handling, computational geometry, and statistics. In this work, we provide an overview of the capabilities and development practices of the SciPy library and highlight some recent technical developments.

/pdf/scipy-1-0-fundamental-algorithms-for-scientific-computing-in-111lr790ol.pdf

SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python

Many problems of recent interest in statistics and machine learning can be posed in the framework of convex optimization. Due to the explosion in size and complexity of modern datasets, it is increasingly important to be able to solve problems with a very large number of features or training examples. As a result, both the decentralized collection or storage of these datasets as well as accompanying distributed solution methods are either necessary or at least highly desirable. In this review, we argue that the alternating direction method of multipliers is well suited to distributed convex optimization, and in particular to large-scale problems arising in statistics, machine learning, and related areas. The method was developed in the 1970s, with roots in the 1950s, and is equivalent or closely related to many other algorithms, such as dual decomposition, the method of multipliers, Douglas–Rachford splitting, Spingarn's method of partial inverses, Dykstra's alternating projections, Bregman iterative algorithms for l1 problems, proximal methods, and others. After briefly surveying the theory and history of the algorithm, we discuss applications to a wide variety of statistical and machine learning problems of recent interest, including the lasso, sparse logistic regression, basis pursuit, covariance selection, support vector machines, and many others. We also discuss general distributed optimization, extensions to the nonconvex setting, and efficient implementation, including some details on distributed MPI and Hadoop MapReduce implementations.

/pdf/distributed-optimization-and-statistical-learning-via-the-8s9gtddw0d.pdf

Distributed Optimization and Statistical Learning Via the Alternating Direction Method of Multipliers

A method is described for the minimization of a function of n variables, which depends on the comparison of function values at the (n 41) vertices of a general simplex, followed by the replacement of the vertex with the highest value by another point. The simplex adapts itself to the local landscape, and contracts on to the final minimum. The method is shown to be effective and computationally compact. A procedure is given for the estimation of the Hessian matrix in the neighbourhood of the minimum, needed in statistical estimation problems.

A simplex method for function minimization

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. Blackwell Publishing and Royal Statistical Society are collaborating with JSTOR to digitize, preserve and extend access to Journal of the Royal Statistical Society. Series A (General). SUMMARY The technique of iterative weighted linear regression can be used to obtain maximum likelihood estimates of the parameters with observations distributed according to some exponential family and systematic effects that can be made linear by a suitable transformation. A generalization of the analysis of variance is given for these models using log-likelihoods. These generalized linear models are illustrated by examples relating to four distributions; the Normal, Binomial (probit analysis, etc.), Poisson (contingency tables) and gamma (variance components). The implications of the approach in designing statistics courses are discussed.

Generalized Linear Models

We consider hierarchical generalized linear models which allow extra error components in the linear predictors of generalized linear models. The distribution of these components is not restricted to be normal; this allows a broader class of models, which includes generalized linear mixed models. We use a generalization of Henderson's joint likelihood, called a hierarchical or h-likelihood, for inferences from hierarchical generalized linear models. This avoids the integration that is necessary when marginal likelihood is used. Under appropriate conditions maximizing the h-likelihood gives fixed effect estimators that are asymptotically equivalent to those obtained from the use of marginal likelihood; at the same time we obtain the random effect estimates that are asymptotically best unbiased predictors. An adjusted profile h-likelihood is shown to give the required generalization of restricted maximum likelihood for the estimation of dispersion components. A scaled deviance test for the goodness of fit, a model selection criterion for choosing between various dispersion models and a graphical method for checking the distributional assumption of random effects are proposed. The ideas of quasi-likelihood and extended quasi-likelihood are generalized to the new class. We give examples of the Poisson-gamma, binomial-beta and gamma-inverse gamma hierarchical generalized linear models. A resolution is proposed for the apparent difference between population-averaged and subject-specific models. A unified framework is provided for viewing and extending many existing methods.

https://rss.onlinelibrary.wiley.com/doi/pdf/10.1111/j.2517-6161.1996.tb02105.x

Hierarchical Generalized Linear Models

The GLIM System Release 3.

LIST OF NOTATIONS PREFACE INTRODUCTION CLASSICAL LIKELIHOOD THEORY Definition Quantities derived from the likelihood Profile likelihood Distribution of the likelihood-ratio statistic Distribution of the MLE and the Wald statistic Model selection Marginal and conditional likelihoods Higher-order approximations Adjusted profile likelihood Bayesian and likelihood methods Jacobian in likelihood methods GENERALIZED LINEAR MODELS Linear models Generalized linear models Model checking Examples QUASI-LIKELIHOOD Examples Iterative weighted least squares Asymptotic inference Dispersion models Extended Quasi-likelihood Joint GLM of mean and dispersion Joint GLMs for quality improvement EXTENDED LIKELIHOOD INFERENCES Two kinds of likelihood Inference about the fixed parameters Inference about the random parameters Optimality in random-parameter estimation Canonical scale, h-likelihood and joint inference Statistical prediction Regression as an extended model Missing or incomplete-data problems Is marginal likelihood enough for inference about fixed parameters? Summary: likelihoods in extended framework NORMAL LINEAR MIXED MODELS Developments of normal mixed linear models Likelihood estimation of fixed parameters Classical estimation of random effects H-likelihood approach Example Invariance and likelihood inference HIERARCHICAL GLMS HGLMs H-likelihood Inferential procedures using h-likelihood Penalized quasi-likelihood Deviances in HGLMs Examples Choice of random-effect scale HGLMS WITH STRUCTURED DISPERSION HGLMs with structured dispersion Quasi-HGLMs Examples CORRELATED RANDOM EFFECTS FOR HGLMS HGLMs with correlated random effects Random effects described by fixed L matrices Random effects described by a covariance matrix Random effects described by a precision matrix Fitting and model-checking Examples Twin and family data Ascertainment problem SMOOTHING Spline models Mixed model framework Automatic smoothing Non-Gaussian smoothing RANDOM-EFFECT MODELS FOR SURVIVAL DATA Proportional-hazard model Frailty models and the associated h-likelihood *Mixed linear models with censoring Extensions Proofs DOUBLE HGLMs DHGLMs Models for finance data H-likelihood procedure for fitting DHGLMs Random effects in the ? component Examples FURTHER TOPICS Model for multivariate responses Joint model for continuous and binary data Joint model for repeated measures and survival time Missing data in longitudinal studies Denoising signals by imputation REFERENCE DATA INDEX AUTHOR INDEX SUBJECT INDEX

Generalized Linear Models with Random Effects: Unified Analysis via H-likelihood

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