David Siegmund - Böcker

Gene mapping is used in experimental genetics to improve the hardiness or productivity of animals or plants of agricultural value, to explore basic mechanisms of inheritance, or to study animal models of human inheritance. In human populations it is used as a first step to identify genes associated with human health and disease. This book presents a unified discussion of the statistical concepts applied in gene mapping, first in the experimental context of crosses of inbred lines and then in outbred populations, primarily humans. The development involves elementary principles of probability and statistics, which are implemented by computational tools based on the R programming language to simulate genetic experiments and evaluate statistical analyses. The viewpoint reflects the modern approach of using anonymous DNA markers distributed throughout the genome to identify regions likely to contain genes of interest. The reader is assumed to have some familiarity with probability/statistics and with elementary genetics. Important topics are reviewed in the first three chapters. The R programming language is developed in the text. Each chapter contains exercises, both theoretical and computational, some routine and others that are more challenging. The book is suitable for upper level undergraduate students or graduate students of genetics or statistics.

The modern theory of Sequential Analysis came into existence simultaneously in the United States and Great Britain in response to demands for more efficient sampling inspection procedures during World War II. The develop­ ments were admirably summarized by their principal architect, A. Wald, in his book Sequential Analysis (1947). In spite of the extraordinary accomplishments of this period, there remained some dissatisfaction with the sequential probability ratio test and Wald's analysis of it. (i) The open-ended continuation region with the concomitant possibility of taking an arbitrarily large number of observations seems intol­ erable in practice. (ii) Wald's elegant approximations based on "neglecting the excess" of the log likelihood ratio over the stopping boundaries are not especially accurate and do not allow one to study the effect oftaking observa­ tions in groups rather than one at a time. (iii) The beautiful optimality property of the sequential probability ratio test applies only to the artificial problem of testing a simple hypothesis against a simple alternative. In response to these issues and to new motivation from the direction of controlled clinical trials numerous modifications of the sequential probability ratio test were proposed and their properties studied-often by simulation or lengthy numerical computation. (A notable exception is Anderson, 1960; see III.7.) In the past decade it has become possible to give a more complete theoretical analysis of many of the proposals and hence to understand them better.

Gene mapping is used in experimental genetics to improve the hardiness or productivity of animals or plants of agricultural value, to explore basic mechanisms of inheritance, or to study animal models of human inheritance. In human populations it is used as a first step to identify genes associated with human health and disease. This book presents a unified discussion of the statistical concepts applied in gene mapping, first in the experimental context of crosses of inbred lines and then in outbred populations, primarily humans. The development involves elementary principles of probability and statistics, which are implemented by computational tools based on the R programming language to simulate genetic experiments and evaluate statistical analyses. The viewpoint reflects the modern approach of using anonymous DNA markers distributed throughout the genome to identify regions likely to contain genes of interest. The reader is assumed to have some familiarity with probability/statistics and with elementary genetics. Important topics are reviewed in the first three chapters. The R programming language is developed in the text. Each chapter contains exercises, both theoretical and computational, some routine and others that are more challenging. The book is suitable for upper level undergraduate students or graduate students of genetics or statistics.

The modern theory of Sequential Analysis came into existence simultaneously in the United States and Great Britain in response to demands for more efficient sampling inspection procedures during World War II. The develop­ ments were admirably summarized by their principal architect, A. Wald, in his book Sequential Analysis (1947). In spite of the extraordinary accomplishments of this period, there remained some dissatisfaction with the sequential probability ratio test and Wald's analysis of it. (i) The open-ended continuation region with the concomitant possibility of taking an arbitrarily large number of observations seems intol­ erable in practice. (ii) Wald's elegant approximations based on "neglecting the excess" of the log likelihood ratio over the stopping boundaries are not especially accurate and do not allow one to study the effect oftaking observa­ tions in groups rather than one at a time. (iii) The beautiful optimality property of the sequential probability ratio test applies only to the artificial problem of testing a simple hypothesis against a simple alternative. In response to these issues and to new motivation from the direction of controlled clinical trials numerous modifications of the sequential probability ratio test were proposed and their properties studied-often by simulation or lengthy numerical computation. (A notable exception is Anderson, 1960; see III.7.) In the past decade it has become possible to give a more complete theoretical analysis of many of the proposals and hence to understand them better.

In June 2010, a conference, Probability Approximations and Beyond, was held at the National University of Singapore (NUS), in honor of pioneering mathematician Louis Chen. Chen made the first of several seminal contributions to the theory and application of Stein’s method. One of his most important contributions has been to turn Stein’s concentration inequality idea into an effective tool for providing error bounds for the normal approximation in many settings, and in particular for sums of random variables exhibiting only local dependence.  This conference attracted a large audience that came to pay homage to Chen and to hear presentations by colleagues who have worked with him in special ways over the past 40+ years.  The papers in this volume attest to how Louis Chen’s cutting-edge ideas influenced and continue to influence such areas as molecular biology and computer science. He has developed applications of his work on Poisson approximation to problems of signal detection in computational biology. The original papers contained in this book provide historical context for Chen’s work alongside commentary on some of his major contributions by noteworthy statisticians and mathematicians working today.