M. Boehnke, K. Lange, and D.R. Cox. Statistical Methods for Multipoint Radiation Hybrid Mapping. Am. J. Hum. Genet., 49:1174--88, 1991.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....which, as exhaustive search, guarantees to find the optimal order is branch andbound. In a branch and bound algorithm, a large number of candidate orders are eliminated without having been considered in detail, which in most cases improves the running time compared to exhaustive search. In [BLC91] Boehnke et al. describes the branch and bound algorithm used for RH mapping in RHMAP. Although the branch and bound algorithm is faster than exhaustive search, it may still have a running time exponential in the number of markers. In RHMAP,two other heuristics have therefore been implemented, ....

....map. RHMAPPER is faster than the RHMAP program and has been used for large scale mapping projects [HSG 95] In [Slo96] Slonim describes two greedy maximum likelihood algorithms. The first one is called Basic Greedy and is identical to the stepwise locus ordering algorithm described in [BLC91] with the likelihood as ranking criterion. It is pointed out that this algorithm is slow, and the use is limited to small instances and as a subroutine to other algorithms. The second algorithm is called Parallel Greedy. In the initial step of this algorithm, ordered subsets (called subgroups) ....

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Michael Boehnke, Kenneth Lange, and David R. Cox. Statistical methods for multipoint radiation hybrid mapping. American Journal of Human Genetics, 49:1174--1188, 1991.

....OCB or the MLE formulation of the experimental results to the traveling salesman problem (TSP) The latter combinatorial optimization problem is then solved, and its solution is interpreted as a linear order of the RH markers, together with an estimate of their distances. OCBs The OCBs approach (Boehnke et al. 1991; Barrett 1992; 1 Corresponding author. Present address: Department of Computer Science and Engineering, University of Washington, Seattle, Washington 98195 USA. 2 Present address: Department of Computer Science, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213 USA. E MAIL ....

....such that the likelihood of the resulting map is maximized. The likelihood of a map (consisting of an ordered list of markers and the distances between them) is the probability to observe the RH data, given the map (in a suitable probability model of the experiment) Markov model was used by Boehnke et al. 1991) and Lunetta and Boehnke (1994) to compute the likelihood of a map for haploid, error free data. Lange et al. 1995) extended this approach to diploid data that accounts for laboratory errors as well, using a hidden Markov model. A very similar hidden Markov model is presented by Slonim (1996) and ....

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Boehnke, M., K. Lange, and D. Cox. 1991. Statistical methods for multipoint radiation hybrid mapping. Am. J. Hum. Genet.

....from the human genome. The fundamental idea behind this type of mapping is that the closer two markers lie to one another, the greater the chance that they will be co retained by a cell. Several researchers have used this observation to develop algorithms and software for radiation hybrid mapping [24, 18, 4]. A second type of STS mapping protocol is STS content mapping. In this method, 5 as in shotgun sequencing, the target region is assumed to be covered redundantly by a clone library. Each clone is then probed to determine which STS markers it contains; the set of markers is referred to as the ....

Michael Boehnke, Kenneth Lanage, and David Cox. Statistical methods for multipoint radiation hybrid mapping. American Journal of Human Genetics, 49:1174-1188, 1991.

....DNA mapping problems, but they are based on distance estimates from techniques other than FISH, and are tailored to the particular statistical properties of the distance measurements. Two among many examples are the distance geometry algorithm of [7] based on recombination frequency data, and [2], which investigated branch and bound, simulated annealing, and maximum likelihood algorithms based on data from radiation hybrid mapping. 1.2 Outline We present two algorithms for finding least squares solutions to the probe placement problem. One is a branch and bound algorithm that can find ....

Michael Boehnke, Kenneth Lange, and David Cox. Statistical methods for multipoint radiation hybrid mapping. Am. J. Hum. Genet., 49:1174--1188, 1991.

.... large scale radiation hybrid maps, and has been used successfully to create whole genome maps containing thousands of markers at the Whitehead Institute MIT Center for Genome Research [3] Features Maximum Likelihood Calculations on Diploid RH Panels RHMAPPER uses a hidden Markov model (HMM) [4] to perform maximum likelihood calculations on multipoint maps. It can be used on data from radiation hybrid panels derived from diploid cells, such as those used in whole genomic mapping. It can also be used for haploid panels. Accomodation of Laboratory Error A central problem with radiation ....

M. Boehnke, K. Lange, and D. Cox (1991). "Statistical methods for multipoint radiation hybrid mapping. Am. J. Hum. Genet. 49: 1174-1188.

....from techniques other than FISH. The other algorithms are tailored to the particular statistical properties of the distance measurements. 1.2 Work Presented in This Paper 3 One example is the distance geometry algorithm of [Newell 92] based on recombination frequency data. Another example is [Boehnke 91] which investigated branch and bound, simulated annealing, and maximum likelihood algorithms based on data from radiation hybrid mapping. 1.2 Work Presented in This Paper In this work, we chose a sum of squares cost function to evaluate different probe orderings and positions. From this model, ....

Boehnke, Michael, Lange, Kenneth, and Cox, David. Statistical Methods for Multipoint Radiation Hybrid Mapping. Am. J. Hum. Genet., 49:11741188, 1991.

....was followed by separate retention of the two resulting fragments. Similarly, two simultaneously lost markers can reflect the loss of a single fragment lacking a break or the loss of two separate fragments. 2 Notation and summary of existing approaches To construct maps from multiple markers, Boehnke, Lange Cox (1991) proposed ordering the markers so as to minimize the obligate breaks criterion. In the absence of assay error and for a given marker order, at least one break must be introduced to explain each discordancy between adjacent markers. Denote the observed data by x ij , i = 1; 2; n, j = 1; 2; ....

.... = 1) Gamma 1 Gamma jj 0 Delta r jj 0 r 2 b jj 0 = Pr(x ij = 0; x i;j 0 = 0) Gamma 1 Gamma jj 0 Delta (1 Gamma r) jj 0 (1 Gamma r) 2 c jj 0 = Pr(x ij = 1; x i;j 0 = 0) jj 0 r(1 Gamma r) e jj 0 = Pr(x ij = 0; x i;j 0 = 1) jj 0 r(1 Gamma r) 3) Boehnke et al. 1991) and Jones (1996) discuss more complicated fragment retention models. Letting = s jj 0 = P i x ij x ij 0 and t jj 0 = P i (1 Gamma x ij ) 1 Gamma x ij 0 ) represent the two remaining concordant counts for markers j and j 0 ; the likelihood for the data for pair j; j 0 a s jj 0 ....

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Boehnke, M., Lange, K. & Cox, D. (1991), `Statistical methods for multipoint radiation hybrid mapping', Am. J. Hum. Genet. 49, 1174--1188.

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M. Boehnke, K. Lange, and D.R. Cox. Statistical Methods for Multipoint Radiation Hybrid Mapping. Am. J. Hum. Genet., 49:1174--88, 1991.

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Boehnke M, Lange K, Cox D (1991) Statistical methods for multipoint radiation hybrid mapping. Am J Hum Genet 49:1174-1188

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M. Boehnke, K. Lange, and D.R. Cox. Statistical methods for multipoint radiation hybrid mapping. Am. J. Hum. Genet., 49:1174--1188, 1991.

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