Topic
Negative binomial distribution
About: Negative binomial distribution is a research topic. Over the lifetime, 4762 publications have been published within this topic receiving 144255 citations.
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TL;DR: A method based on the negative binomial distribution, with variance and mean linked by local regression, is proposed and an implementation, DESeq, as an R/Bioconductor package is presented.
Abstract: High-throughput sequencing assays such as RNA-Seq, ChIP-Seq or barcode counting provide quantitative readouts in the form of count data. To infer differential signal in such data correctly and with good statistical power, estimation of data variability throughout the dynamic range and a suitable error model are required. We propose a method based on the negative binomial distribution, with variance and mean linked by local regression and present an implementation, DESeq, as an R/Bioconductor package.
13,356 citations
01 Jan 1950
TL;DR: A First Course in Probability (8th ed.) by S. Ross is a lively text that covers the basic ideas of probability theory including those needed in statistics.
Abstract: Office hours: MWF, immediately after class or early afternoon (time TBA). We will cover the mathematical foundations of probability theory. The basic terminology and concepts of probability theory include: random experiments, sample or outcome spaces (discrete and continuous case), events and their algebra, probability measures, conditional probability A First Course in Probability (8th ed.) by S. Ross. This is a lively text that covers the basic ideas of probability theory including those needed in statistics. Theoretical concepts are introduced via interesting concrete examples. In 394 I will begin my lectures with the basics of probability theory in Chapter 2. However, your first assignment is to review Chapter 1, which treats elementary counting methods. They are used in applications in Chapter 2. I expect to cover Chapters 2-5 plus portions of 6 and 7. You are encouraged to read ahead. In lectures I will not be able to cover every topic and example in Ross, and conversely, I may cover some topics/examples in lectures that are not treated in Ross. You will be responsible for all material in my lectures, assigned reading, and homework, including supplementary handouts if any.
10,221 citations
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TL;DR: Zero-inflated Poisson (ZIP) regression as discussed by the authors is a model for counting data with excess zeros, which assumes that with probability p the only possible observation is 0, and with probability 1 − p, a Poisson(λ) random variable is observed.
Abstract: Zero-inflated Poisson (ZIP) regression is a model for count data with excess zeros. It assumes that with probability p the only possible observation is 0, and with probability 1 – p, a Poisson(λ) random variable is observed. For example, when manufacturing equipment is properly aligned, defects may be nearly impossible. But when it is misaligned, defects may occur according to a Poisson(λ) distribution. Both the probability p of the perfect, zero defect state and the mean number of defects λ in the imperfect state may depend on covariates. Sometimes p and λ are unrelated; other times p is a simple function of λ such as p = l/(1 + λ T ) for an unknown constant T . In either case, ZIP regression models are easy to fit. The maximum likelihood estimates (MLE's) are approximately normal in large samples, and confidence intervals can be constructed by inverting likelihood ratio tests or using the approximate normality of the MLE's. Simulations suggest that the confidence intervals based on likelihood ratio test...
3,440 citations
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01 Jan 2007TL;DR: In this article, the authors introduce the concept of risk in count response models and assess the performance of count models, including Poisson regression, negative binomial regression, and truncated count models.
Abstract: Preface 1. Introduction 2. The concept of risk 3. Overview of count response models 4. Methods of estimation and assessment 5. Assessment of count models 6. Poisson regression 7. Overdispersion 8. Negative binomial regression 9. Negative binomial regression: modeling 10. Alternative variance parameterizations 11. Problems with zero counts 12. Censored and truncated count models 13. Handling endogeneity and latent class models 14. Count panel models 15. Bayesian negative binomial models Appendix A. Constructing and interpreting interactions Appendix B. Data sets and Stata files References Index.
2,967 citations
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TL;DR: In this article, a new implementation of hurdle and zero-inflated regression models in the functions hurdle() and zeroinfl() from the package pscl is introduced, which reuses design and functionality of the basic R functions just as the underlying conceptual tools extend the classical models.
Abstract: The classical Poisson, geometric and negative binomial regression models for count data belong to the family of generalized linear models and are available at the core of the statistics toolbox in the R system for statistical computing. After reviewing the conceptual and computational features of these methods, a new implementation of hurdle and zero-inflated regression models in the functions hurdle() and zeroinfl() from the package pscl is introduced. It re-uses design and functionality of the basic R functions just as the underlying conceptual tools extend the classical models. Both hurdle and zero-inflated model, are able to incorporate over-dispersion and excess zeros-two problems that typically occur in count data sets in economics and the social sciences-better than their classical counterparts. Using cross-section data on the demand for medical care, it is illustrated how the classical as well as the zero-augmented models can be fitted, inspected and tested in practice.
1,971 citations