UCLA

Sophisticated Bayesian methods are often used to identify a collection of alleles

that are jointly associated with a particular disease. A disease might not be

expressed when only one of these alleles is present, but each associated allele

might interact with each other in a rather complicated way, causing a disease to

be expressed. In investigating a patient's susceptibility to a disease, it is often

useful to group the collection of associated alleles according to their risk factors.

Our goal is to find the most likely grouping structure of alleles

associated with Rheumatoid Arthritis given a case-control data. The number

of ways to group these m alleles is given by the mth Bell number Bm. For 10 alleles, this

translates to 115,975 groupings. For m = 15, we have over a billion ways to group

the alleles. Clearly computing the probability for each grouping soon become

intractable. A combination of Metropolis-Hastings and local search algorithm is

proposed to accomplish this task. This strategy is first implemented on simulated

data, with a sufficiently large sample size and a known grouping structure, and

the correct grouping is obtained. Stable results are obtained as the algorithm is

run multiple times on Rheumatoid Arthritis data.