Probability Approximations and Beyond

ISBN-13: 9781461419655 / Angielski / Miękka / 2011 / 159 str.

Hock Peng Chan; Andrew Barbour; David Siegmund

Opis

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.

Spis treści

Couplings for Irregular Combinatorial Assemblies.- Berry-Esseen Inequality for Unbounded Exchangeable Pairs.- Clubbed Binomial Approximation for the Lightbulb Process.- Coverage of Random Discs Driven by a Posson Point Process.- On the Optimality of Stein Factors.- Basic Estimates of Stability Rate for One-dimensional Diffusions.- Trend Analysis of Extreme Values.- Renormalizations in White Noise Analysis.- M-dependence Approximation for Dependent Random Variables.- Variable Selection for Classification and Regression in Large p, Small n Problems.

Blurb

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. Louis is perhaps best known for his elegant Poisson approximation method, developed from Stein’s original approach to normal approximation. Another of his 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.  The conference attracted a large audience that came to pay homage to Louis, 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 ideas have influenced and continue to influence such diverse areas as molecular biology and computer science. He himself 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 Louis’s work, alongside commentary on some of his major contributions by noteworthy statisticians and mathematicians working today.

The papers in this volume attest to how Louis Chen’s ideas have influenced and continue to influence such diverse areas as molecular biology and computer science. He himself 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 Louis’s work, alongside commentary on some of his major contributions by noteworthy statisticians and mathematicians working today.