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SHARON GUY BROWNING |
Analysis of Infinitely Dense Genetic Data |
My work during this period had two
parts, both relating to the analysis of data that is infinitely dense along
the genome. The first was some work on calculating the power of Lander
& Botsteinís (1989, Genetics) interval mapping of quantitative trait
loci (QTLs). If the data to which interval mapping is being applied is
from B1 backcross on inbred strains, and markers are infinitely dense,
then, as the number of individuals increases, the LOD score, viewed as
a process along the genome, converges to a Gaussian process. Approximations
to boundary hitting probabilities for Gaussian processes can be used to
calculate power. Feingold, Brown and Siegmund (1993, Am. J. Hum.
Genet.) outlined this approach but did not present results. I formulated
an approximation that is valid when power is low. |
The second area of work was to include interference in my Monte Carlo likelihood calculation method. If one has infinitely dense identity by descent (IBD) data for two related individuals and wishes to infer the relationship between the individuals or make inferences about other genetic parameters (such as interference) then one can use a likelihood approach. In most cases the likelihood cannot be calculated analytically, but can be estimated via Monte Carlo. The ìchi-squareî model of interference (see, for example, Zhao, Speed and McPeek, 1995, Genetics) can be included in the procedure in such a way
that the Marko structure is not lost, enabling straightforward simulation and calculation. |
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