Probability and Mathematical Genetics

Papers in Honour of Sir John Kingman

N. H. Bingham, C. M. Goldie

• Publisher: Cambridge University Press
• Year: 2010
• Print ISBN:
  9780521145770
• eBook ISBN:
  9781139119313
• Topic: Mathematics
• Subtopic: Probability & Statistics
• Index: Mathematics

Focussing on the work of Sir John Kingman, one of the world's leading researchers in probability and mathematical genetics, this book touches on the important areas of these subjects in the last 50 years. Leading authorities give a unique insight into a wide range of currently topical problems. Papers in probability concentrate on combinatorial and structural aspects, in particular exchangeability and regeneration. The Kingman coalescent links probability with mathematical genetics and is fundamental to the study of the latter. This has implications across the whole of genomic modelling including the Human Genome Project. Other papers in mathematical population genetics range from statistical aspects including heterogeneous clustering, to the assessment of molecular variability in cancer genomes. Further papers in statistics are concerned with empirical deconvolution, perfect simulation, and wavelets. This book will be warmly received by established experts as well as their students and others interested in the content.

Table of contents

• Cover
• Title
• Copyright
• Contents
• List of contributors
• Preface
• Bibliography of J. F. C. Kingman
• 1 A fragment of autobiography, 1957–1967
• 2 More uses of exchangeability: representations of complex random structures
• 3 Perfect simulation using dominated coupling from the past with application to area-interaction point processes and wavelet thresholding
• 4 Assessing molecular variability in cancer genomes
• 5 Branching out
• 6 Kingman, category and combinatorics
• 7 Long-range dependence in a Cox process directed by an alternating renewal process
• 8 Kernel methods and minimum contrast estimators for empirical deconvolution
• 9 The coalescent and its descendants
• 10 Kingman and mathematical population genetics
• 11 Characterizations of exchangeable partitions and random discrete distributions by deletion properties
• 12 Applying coupon-collecting theory to computer-aided assessments
• 13 Colouring and breaking sticks: random distributions and heterogeneous clustering
• 14 The associated random walk and martingales in random walks with stationary increments
• 15 Diffusion processes and coalescent trees
• 16 Three problems for the clairvoyant demon
• 17 Homogenization for advection-diffusion in a perforated domain
• 18 Heavy traffic on a controlled motorway
• 19 Coupling time distribution asymptotics for some couplings of the Lévy stochastic area
• 20 Queueing with neighbours
• 21 Optimal information feed
• 22 A dynamical-system picture of a simple branching-process phase transition
• Index