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Large-Scale Inference: Empirical Bayes Methods for Estimation, Testing, and Prediction (Institute of Mathematical Statistics Monographs, Series Number 1)
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About Large-Scale Inference: Empirical Bayes Methods For
Product Description We live in a new age for statistical inference, where modern scientific technology such as microarrays and fMRI machines routinely produce thousands and sometimes millions of parallel data sets, each with its own estimation or testing problem. Doing thousands of problems at once is more than repeated application of classical methods. Taking an empirical Bayes approach, Bradley Efron, inventor of the bootstrap, shows how information accrues across problems in a way that combines Bayesian and frequentist ideas. Estimation, testing, and prediction blend in this framework, producing opportunities for new methodologies of increased power. New difficulties also arise, easily leading to flawed inferences. This book takes a careful look at both the promise and pitfalls of large-scale statistical inference, with particular attention to false discovery rates, the most successful of the new statistical techniques. Emphasis is on the inferential ideas underlying technical developments, illustrated using a large number of real examples. Review An Interview with Brad Efron of Stanford "In the last decade, Efron has played a leading role in laying down the foundations of largescale inference, not only in bringing back and developing old ideas, but also linking them with more recent developments, including the theory of false discovery rates and Bayes methods. We are indebted to him for this timely, readable and highly informative monograph, a book he is uniquely qualified to write. it is a synthesis of many of Efron’s own contributions over the last decade with that of closely related material, together with some connecting theory, valuable comments, and challenges for the future. His avowed aim is “not to have the last word” but to help us deal “with the burgeoning statistical problems of the 21st century”. He has succeeded admirably." Terry Speed, International Statistical Review "This is the first major text on the methods useful for large-scale inference which are being applied to microarrays and fMRI imaging data. It is the first step in the development of an exciting new branch of statistics addressed at some important modern medical problems. ... The difficulty here is that the scientists want to conduct hundreds or thousands of formal hypothesis tests using the microarray data. The theory of multiple testing came about to correct inference on an individual test due to the fact that it was one of many being tested. ... I recommend the book be read to understand the tests in more detail as well as the applications. I have not looked at Brad Efron's course on large scale inference, which is certainly very new. Nothing like it was available in the 1970s when I was at Stanford. I can say from first-hand experience that Efron is a terrific instructor and that he writes in a very clear and intuitive way." Michael R. Chernick, Significance "Undoubtedly, the monograph will contribute to the further development of the simultaneous inference technique and its application to genetics, quality control, sociology, medicine, etc. Moreover, the material of the book opens up a new area in the d-posterior approach to the problem of statistical inference guarantee applications." I.N. Volodin, Mathematical Reviews "Max H. Stein Professor of Statistics and Biostatistics at Stanford, Bradley Efron, is one of today's greatest statisticians. The book is actually good reading. The mathematical level of the material presented is not really high, and an undergraduate student with a second course in statistics could follow the text quite easily, even if some linear algebra is necessary to get on with some of the more technical parts. Demonstrations are found in the end of sections so as not to stop the reading flow, whereas examples and exercises are very well used as devices to keep the reader focused and interested. In summary I think this book is a pretty good gateway to the statistics of the future for the future Fishers and Ne
