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Random Algorithms for the Loop Cutset Problem
 Journal of Artificial Intelligence Research
, 1999
"... We show how to find a minimum loop cutset in a Bayesian network with high probability. Finding such a loop cutset is the first step in Pearl's method of conditioning for inference. Our random algorithm for finding a loop cutset, called RepeatedWGuessI, outputs a minimum loop cutset, after O(c ..."
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Cited by 81 (2 self)
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We show how to find a minimum loop cutset in a Bayesian network with high probability. Finding such a loop cutset is the first step in Pearl's method of conditioning for inference. Our random algorithm for finding a loop cutset, called RepeatedWGuessI, outputs a minimum loop cutset, after O(c \Delta 6 k kn) steps, with probability at least 1 \Gamma (1 \Gamma 1 6 k ) c6 k , where c ? 1 is a constant specified by the user, k is the size of a minimum weight loop cutset, and n is the number of vertices. We also show empirically that a variant of this algorithm, called WRA, often finds a loop cutset that is closer to the minimum loop cutset than the ones found by the best deterministic algorithms known. 1
Faster sequential genetic linkage computations
 AMERICAN JOURNAL OF HUMAN GENETICS
, 1993
"... Linkage analysis using maximum likelihood estimation is a powerful tool for locating genes. As available data sets have grown, the computation required for analysis has grown exponentially, and become a significant impediment. Others have previously shown that parallel computation is applicable to l ..."
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Cited by 36 (1 self)
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Linkage analysis using maximum likelihood estimation is a powerful tool for locating genes. As available data sets have grown, the computation required for analysis has grown exponentially, and become a significant impediment. Others have previously shown that parallel computation is applicable to linkage analysis and can yield order of magnitude improvements in speed. In this paper, we demonstrate that algorithmic modifications can also yield order of magnitude improvements, and sometimes much more. Using the software package LINKAGE, we describe a variety of algorithmic improvements we have implemented, demonstrating how these techniques are applied, and their power. Experiments show that these improvements speed up the programs by an order of magnitude on problems of moderate and large size. All improvements were made only in the combinatorial part of the code, without resorting to parallel computers. These improvements synthesize biological principles with computer science techniques to effectively restructure the timeconsuming computations in genetic linkage analysis.
Unified Bayesian and conditional frequentist testing for discrete distributions
 Sankya Series B, Indian Journal of Statistics
, 2001
"... SUMMARY. Testing of hypotheses for discrete distributions is considered in this paper. The goal is to develop conditional frequentist tests that allow the reporting of datadependent error probabilities such that the error probabilities have a strict frequentist interpretation and also reflect the ac ..."
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Cited by 4 (2 self)
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SUMMARY. Testing of hypotheses for discrete distributions is considered in this paper. The goal is to develop conditional frequentist tests that allow the reporting of datadependent error probabilities such that the error probabilities have a strict frequentist interpretation and also reflect the actual amount of evidence in the observed data. The resulting randomized tests are also seen to be Bayesian tests, in the strong sense that the reported error probabilities are also the posterior probabilities of the hypotheses. new procedure is illustrated for a variety of testing situations, both simple and composite, involving discrete distributions. Testing linkage heterogeneity with the new procedure is given as an illustrative example. 1.
Genotyping of Pooled Microsatellite Markers By Combinatorial Optimization Techniques
 Dis. Appl. Math
, 1998
"... An important everyday task for geneticists and molecular biologists is that of isolating and analyzing some particular DNA regions (markers), each drawn from a limited and known set of possible values (alleles). This procedure is called genotyping and is based on DNA amplification and size separatio ..."
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Cited by 2 (1 self)
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An important everyday task for geneticists and molecular biologists is that of isolating and analyzing some particular DNA regions (markers), each drawn from a limited and known set of possible values (alleles). This procedure is called genotyping and is based on DNA amplification and size separation. In order to increase the throughput of genotyping, recently a new experiment has been proposed which tries to analyze many different markers of similar size at once. We study the mathematical problem corresponding to this model and give a branch and bound algorithm for its solution. We show that by using the techniques described in this paper, genotyping of pooled markers can be computed effectively, thus potentially achieving a considerable reduction in time and expense. 1 Introduction In this paper we investigate the possibility of using combinatorial optimization techniques to increase the rate at which genotyping is currently performed on individuals. A brief simplified description of...
Asthma And Allergic Diseases In Australian Twins And Their Families
, 1997
"... The occurrence of asthma or wheezing, and other allergic diseases, in 3808 pairs of twins aged 18 to 88 years was recorded by mailed questionnaire in 1980 (a pairwise response rate of 64%; individual, 69%). This sample (Cohort 1) was resurveyed in 1988 (78% pairwise followup), and a further 2159 pai ..."
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Cited by 1 (0 self)
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The occurrence of asthma or wheezing, and other allergic diseases, in 3808 pairs of twins aged 18 to 88 years was recorded by mailed questionnaire in 1980 (a pairwise response rate of 64%; individual, 69%). This sample (Cohort 1) was resurveyed in 1988 (78% pairwise followup), and a further 2159 pairs aged 18 to 25 years (Cohort 2) responded usefully to a similar item on asthma on another instrument in 1989 sent to 4078 pairs (pairwise 53%). The crude cumulative incidence of wheezing was 13.2% in 1980, 18.9% in 1988, and 21.8% in 1989. Genetic analyses performed using this screening data suggested a strong genetic component to wheezing, hayfever and allergy, and sizeable genetic correlations between different atopic conditions. Genetic influences specific to particular traits such as wheezing were also detectable. A secular increase in incidence of wheeze experienced by consecutive birth cohorts seemed to be due to nonfamilial environmental factors. A more detailed respiratory symptoms...
Confidence intervals for gene location  The effect of model misspecification and smoothing
, 1998
"... Contents List of Tables vii List of Figures ix Overview x 1 Model misspecification in linkage analysis 1 1.1 Data for linkage analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 The likelihood function for gene location . . . . . . . . . . . . . . . . . ..."
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Contents List of Tables vii List of Figures ix Overview x 1 Model misspecification in linkage analysis 1 1.1 Data for linkage analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 The likelihood function for gene location . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 Models to reduce dimensionality and model misspecification . . . . . . . . . . . . . . . . . . . . . . 5 1.4 Choosing a sharing statistic and, implicitly, a model . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.5 Data from more than one kind of pedigree: smoothing . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2 Data on affected relative pairs 8 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.2 Probability of sharing an allele IBD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.3 Properties of the sharing process f
A More Powerful Method to Evaluate PValues in GENEHUNTER
"... The determination of statistical significance in genetic linkage studies is complicated by many factors, such as missing individuals or uninformative markers, and the validity of theoretical results is often questionable. Although many simulationbased methods have been proposed to determine empiric ..."
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The determination of statistical significance in genetic linkage studies is complicated by many factors, such as missing individuals or uninformative markers, and the validity of theoretical results is often questionable. Although many simulationbased methods have been proposed to determine empirically the statistical significance, they are either not generally applicable to complex pedigree structures, or not able to preserve the observed genetic information content at each locus in the pedigrees. We have developed and implemented a general and computationally efficient randomization procedure in GENEHUNTER that applies to arbitrary pedigree structure and preserves the observed information content at each locus. We applied this method to the Problem 1 data set of the Genetic Analysis Workshop 11. The performance of this new method was similar to the method implemented in GENEHUNTERPLUS, and both outperformed the conservative approach in GENEHUNTER.
Erlang Renewal Models for Genetic Recombination
, 2000
"... Closed form expressions for multilocus probabilities are given for the crossover process when it is a renewal process with the distance between crossovers modeled by a Erlang distribution. Closed form expressions are also given for the multilocus probabilities for the chiasma process on the four str ..."
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Closed form expressions for multilocus probabilities are given for the crossover process when it is a renewal process with the distance between crossovers modeled by a Erlang distribution. Closed form expressions are also given for the multilocus probabilities for the chiasma process on the four strand bundle under the same model of recombination for single gamete and for tetrad data. These expressions yield explicit formulas for the map functions, coincidence functions and distributions of the identitybydescent process for a class of models that incorporate interference. The alternating renewal models used may beofinterest in other elds, e.g. telecommunication networks and queues, where they can be used to model the busy/nonbusy state of a system with bu ers. Abbreviated title: Erlang models for recombination AMS 1991 subject calssi cations: Primary 92D10 � secondary 60K05. Key words and phrases: Erlang renewal processes, genetic recombination, multilocus