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."

This book details the statistical concepts used in gene mapping, first in the experimental context of crosses of inbred lines and then in outbred populations, primarily humans. It presents 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. Each chapter contains exercises, both theoretical and computational, some routine and others that are more challenging. The R programming language is developed in the text.

Herbert Robbins is widely recognized as one of the most creative and original mathematical statisticians of our time. The purpose of this book is to reprint, on the occasion of his seventieth birthday, some of his most outstanding research. In making selections for reprinting we have tried to keep in mind three potential audiences: (1) the historian who would like to know Robbins' seminal role in stimulating a substantial proportion of current research in mathematical statistics; (2) the novice who would like a readable, conceptually oriented introduction to these subjects; and (3) the expert who would like to have useful reference material in a single collection. In many cases the needs of the first two groups can be met simulta neously. A distinguishing feature of Robbins' research is its daring originality, which literally creates new specialties for subsequent generations of statisticians to explore. Often these seminal papers are also models of exposition serving to introduce the reader, in the simplest possible context, to ideas that are important for contemporary research in the field. An example is the paper of Robbins and Monro which initiated the subject of stochastic approximation. We have also attempted to provide some useful guidance to the literature in various subjects by supplying additional references, particularly to books and survey articles, with some remarks about important developments in these areas.

This book details the statistical concepts used in gene mapping, first in the experimental context of crosses of inbred lines and then in outbred populations, primarily humans. It presents 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. Each chapter contains exercises, both theoretical and computational, some routine and others that are more challenging. The R programming language is developed in the text.

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.

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."