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

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 time-consuming computations in genetic linkage analysis.

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...

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...

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