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Statistical Foundations of Data Science
Statistical Foundations of Data Science gives a thorough introduction to commonly used statistical models, contemporary statistical machine learning techniques and algorithms, along with their mathematical insights and statistical theories. It aims to serve as a graduate-level textbook and a research monograph on high-dimensional statistics, sparsity and covariance learning, machine learning, and statistical inference. It includes ample exercises that involve both theoretical studies as well as empirical applications. The book begins with an introduction to the stylized features of big data and their impacts on statistical analysis. It then introduces multiple linear regression and expands t...
Random Walk, Sequential Analysis And Related Topics: A Festschrift In Honor Of Yuan-shih Chow
This volume is a collection of papers in celebration of the 80th birthday of Yuan-Shih Chow, whose influential work in probability and mathematical statistics has contributed greatly to mathematics education and the development of statistics research and application in Taiwan and mainland China.The twenty-two papers cover a wide range of problems reflecting both the broad scope of areas where Professor Chow has made major contributions and recent advances in probability theory and statistics.
A Mixture Model Approach to Empirical Bayes Testing and Estimation
Many modern statistical problems require making similar decisions or estimates for many different entities. For example, we may ask whether each of 10,000 genes is associated with some disease, or try to measure the degree to which each is associated with the disease. As in this example, the entities can often be divided into a vast majority of "null" objects and a small minority of interesting ones. Empirical Bayes is a useful technique for such situations, but finding the right empirical Bayes method for each problem can be difficult. Mixture models, however, provide an easy and effective way to apply empirical Bayes. This thesis motivates mixture models by analyzing a simple high-dimensional problem, and shows their practical use by applying them to detecting single nucleotide polymorphisms.
On the Efficient Determination of Most Near Neighbors
The time-worn aphorism "close only counts in horseshoes and hand grenades" is clearly inadequate. Close also counts in golf, shuffleboard, archery, darts, curling, and other games of accuracy in which hitting the precise center of the target isn't to be expected every time, or in which we can expect to be driven from the target by skilled opponents. This book is not devoted to sports discussions, but to efficient algorithms for determining pairs of closely related web pages—and a few other situations in which we have found that inexact matching is good enough — where proximity suffices. We will not, however, attempt to be comprehensive in the investigation of probabilistic algorithms, ap...
How to Gamble If You Must
Revised and updated edition of the classic of advanced statistics. Uses concepts of gambling to develop important ideas in probability theory. "Strongly recommended." — Journal of the American Statistical Association. 2014 edition.
Discrete Tomography
Goals of the Book Overthelast thirty yearsthere has been arevolutionindiagnostic radiology as a result oftheemergenceofcomputerized tomography (CT), which is the process of obtaining the density distribution within the human body from multiple x-ray projections. Since an enormous variety of possible density values may occur in the body, a large number of projections are necessary to ensure the accurate reconstruction oftheir distribution. There are other situations in which we desire to reconstruct an object from its projections, but in which we know that the object to be recon structed has only a small number of possible values. For example, a large fraction of objects scanned in industrial...
Markov Chains and Stochastic Stability
New up-to-date edition of this influential classic on Markov chains in general state spaces. Proofs are rigorous and concise, the range of applications is broad and knowledgeable, and key ideas are accessible to practitioners with limited mathematical background. New commentary by Sean Meyn, including updated references, reflects developments since 1996.
Statistical Data Analysis Based on the L1-Norm and Related Methods
This volume contains a selection of invited papers, presented to the fourth International Conference on Statistical Data Analysis Based on the L1-Norm and Related Methods, held in Neuchâtel, Switzerland, from August 4–9, 2002. The contributions represent clear evidence to the importance of the development of theory, methods and applications related to the statistical data analysis based on the L1-norm.
