Graphical Models for Genetic Analyses

This paper introduces graphical models as a natural environment in which to formulate and solve problems in genetics and related areas. Particular emphasis is given to the relationships between various local computation algorithms which have been developed within the hitherto mostly separate areas of graphical models and genetics. The potential of graphical models is explored and illustrated through a number of example applications where the genetic element is substantial or dominating.

[1]  G. Mendel Experiments in plant hybridisation , 1966 .

[2]  N. Morton Sequential tests for the detection of linkage. , 1955, American journal of human genetics.

[3]  D. Falconer,et al.  Introduction to Quantitative Genetics. , 1961 .

[4]  R. Elston,et al.  A general model for the genetic analysis of pedigree data. , 1971, Human heredity.

[5]  L. Baum,et al.  An inequality and associated maximization technique in statistical estimation of probabilistic functions of a Markov process , 1972 .

[6]  K. Lange,et al.  Extensions to pedigree analysis I. Likehood calculations for simple and complex pedigrees. , 1975, Human heredity.

[7]  Robert C. Elston,et al.  Extensions to Pedigree Analysis , 1975 .

[8]  Probability functions on complex pedigrees , 1978 .

[9]  W. Silvers The Coat Colors of Mice , 1979, Springer New York.

[10]  E. Thompson,et al.  Pedigree analysis of Hodgkin's disease in a Newfoundland genealogy , 1981, Annals of human genetics.

[11]  M. Yannakakis Computing the Minimum Fill-in is NP^Complete , 1981 .

[12]  D. Falconer Introduction to quantitative genetics. 1. ed. , 1984 .

[13]  A. Monaco,et al.  Detection of deletions spanning the Duchenne muscular dystrophy locus using a tightly linked DNA segment , 1985, Nature.

[14]  E. Thompson Pedigree Analysis in Human Genetics , 1985 .

[15]  M. Spence,et al.  Analysis of human genetic linkage , 1986 .

[16]  Judea Pearl,et al.  Fusion, Propagation, and Structuring in Belief Networks , 1986, Artif. Intell..

[17]  S. Adalsteinsson,et al.  Fox colors in relation to colors in mice and sheep. , 1987, The Journal of heredity.

[18]  E. Lander,et al.  Construction of multilocus genetic linkage maps in humans. , 1987, Proceedings of the National Academy of Sciences of the United States of America.

[19]  David J. Spiegelhalter,et al.  Local computations with probabilities on graphical structures and their application to expert systems , 1990 .

[20]  Prakash P. Shenoy,et al.  Axioms for probability and belief-function proagation , 1990, UAI.

[21]  Judea Pearl,et al.  Probabilistic reasoning in intelligent systems , 1988 .

[22]  Kristian G. Olesen,et al.  HUGIN - A Shell for Building Bayesian Belief Universes for Expert Systems , 1989, IJCAI.

[23]  L. Tsui,et al.  Erratum: Identification of the Cystic Fibrosis Gene: Cloning and Characterization of Complementary DNA , 1989, Science.

[24]  Kristian G. Olesen,et al.  HUGIN - a Shell for Building Belief Universes for Expert Systems , 1989, IJCAI 1989.

[25]  Alan George,et al.  The Evolution of the Minimum Degree Ordering Algorithm , 1989, SIAM Rev..

[26]  L. Tsui,et al.  Identification of the cystic fibrosis gene: cloning and characterization of complementary DNA. , 1989, Science.

[27]  Steffen L. Lauritzen,et al.  Bayesian updating in causal probabilistic networks by local computations , 1990 .

[28]  T. Peters,et al.  Identification of the cystic fibrosis gene. , 1990, BMJ.

[29]  D. Spiegelhalter Probabilistic reasoning in expert systems , 1991 .

[30]  G. P. Vogler,et al.  Efficient methods for computing linkage likelihoods of recessive diseases in inbred pedigrees , 1991, Genetic epidemiology.

[31]  Uffe Kjærulff Optimal decomposition of probabilistic networks by simulated annealing , 1992 .

[32]  A. P. Dawid,et al.  Applications of a general propagation algorithm for probabilistic expert systems , 1992 .

[33]  A A Schäffer,et al.  Faster sequential genetic linkage computations. , 1993, American journal of human genetics.

[34]  B. Hansen,et al.  Analysing complex pedigrees using Gibbs sampling , 1994 .

[35]  F. Skjøth,et al.  Genetic models for the inheritance of the silver colour mutation of foxes. , 1994, Genetical research.

[36]  P. Gill,et al.  Identification of the remains of the Romanov family by DNA analysis , 1994, Nature Genetics.

[37]  E. Lander,et al.  Genetic dissection of complex traits science , 1994 .

[38]  E. Thompson Monte Carlo Likelihood in Genetic Mapping , 1994 .

[39]  Uffe Kjærulff,et al.  Blocking Gibbs sampling in very large probabilistic expert systems , 1995, Int. J. Hum. Comput. Stud..

[40]  K Lange,et al.  Descent graphs in pedigree analysis: applications to haplotyping, location scores, and marker-sharing statistics. , 1996, American journal of human genetics.

[41]  L Kruglyak,et al.  Parametric and nonparametric linkage analysis: a unified multipoint approach. , 1996, American journal of human genetics.

[42]  Steffen L. Lauritzen,et al.  Graphical models in R , 1996 .

[43]  Patrick R. Amestoy,et al.  An Approximate Minimum Degree Ordering Algorithm , 1996, SIAM J. Matrix Anal. Appl..

[44]  A. P. Dawid,et al.  Coherent Analysis of Forensic Identification Evidence , 1996 .

[45]  J. Witte,et al.  Genetic dissection of complex traits , 1996, Nature Genetics.

[46]  R. Frankham Introduction to quantitative genetics (4th edn): by Douglas S. Falconer and Trudy F.C. Mackay Longman, 1996. £24.99 pbk (xv and 464 pages) ISBN 0582 24302 5 , 1996 .

[47]  P. Sham Statistics in human genetics , 1997 .

[48]  Claus Skaanning Blocking Gibbs Sampling for Inference in Large and Complex Bayesian Networks with Applications in Genetics , 1997 .

[49]  Dan Geiger,et al.  A Practical Algorithm for Finding Optimal Triangulations , 1997, AAAI/IAAI.

[50]  A. Dawid,et al.  Forensic identification with imperfect evidence , 1998 .

[51]  S. Pulst Genetic linkage analysis. , 1999 .

[52]  M. Lund,et al.  Blocking Gibbs sampling in the mixed inheritance model using graph theory , 1999, Genetics Selection Evolution.

[53]  C S Jensen,et al.  Blocking Gibbs sampling for linkage analysis in large pedigrees with many loops. , 1999, American journal of human genetics.

[54]  E. Thompson,et al.  Estimation of conditional multilocus gene identity among relatives , 1999 .

[55]  Michael I. Jordan,et al.  Probabilistic Networks and Expert Systems , 1999 .

[56]  Anne Berry,et al.  Generating All the Minimal Separators of a Graph , 1999, Int. J. Found. Comput. Sci..

[57]  Alun Thomas,et al.  Multilocus linkage analysis by blocked Gibbs sampling , 2000, Stat. Comput..

[58]  N. Sheehan On the Application of Markov Chain Monte Carlo Methods to Genetic Analyses on Complex Pedigrees , 2000 .

[59]  T Egeland,et al.  Beyond traditional paternity and identification cases. Selecting the most probable pedigree. , 2000, Forensic science international.

[60]  Anne Berry,et al.  Generating All the Minimal Separators of a Graph , 2000, Int. J. Found. Comput. Sci..

[61]  Elizabeth A. Thompson,et al.  Monte Carlo Methods on Genetic Structures , 2000 .

[62]  Jeffrey R. O’Connell,et al.  Rapid Multipoint Linkage Analysis via Inheritance Vectors in the Elston-Stewart Algorithm , 2001, Human Heredity.

[63]  Steffen L. Lauritzen,et al.  Causal Inference from Graphical Models , 2001 .

[64]  S. Fernandez,et al.  Sampling genotypes in large pedigrees with loops , 2001, Genetics Selection Evolution.

[65]  Ioan Todinca,et al.  Treewidth and Minimum Fill-in: Grouping the Minimal Separators , 2001, SIAM J. Comput..

[66]  A. Dawid,et al.  Non-fatherhood or mutation? A probabilistic approach to parental exclusion in paternity testing. , 2001, Forensic science international.

[67]  N. Sheehan,et al.  Bayesian MCMC Mapping of Quantitative Trait Loci in a Half‐sib Design: a Graphical Model Perspective , 2002 .

[68]  Dw Van Boxel,et al.  Probabilistic Expert Systems for Forensic Inference from Genetic Markers , 2002 .

[69]  Dan Geiger,et al.  Exact genetic linkage computations for general pedigrees , 2002, ISMB.

[70]  David J. Spiegelhalter,et al.  Bayesian graphical modelling: a case‐study in monitoring health outcomes , 2002 .

[71]  Elizabeth A. Thompson,et al.  Statistical inference from genetic data on pedigrees , 2003 .

[72]  A. Dawid,et al.  Probabilistic expert systems for DNA mixture profiling. , 2003, Theoretical population biology.

[73]  Steffen L. Lauritzen,et al.  Local computation with valuations from a commutative semigroup , 1997, Annals of Mathematics and Artificial Intelligence.