To detect the positions of disease loci,
LOD scores need to be calculated within a (several)
pedigree(s) for a given set of markers at multiple chromosomal positions.
Exact LOD score calculations are often impossible when the size of the
pedigree and the number of markers are both large. In this case, a Markov
Chain Monte Carlo (MCMC) approach is able to provide an approximation.
However, the mixing performance, to provide accurate results,
within a reasonable amount of time,
is always a key issue in these MCMC methods.
In this paper, we propose a new approach,
which divides a large pedigree into several parts by conditioning
on the haplotypes of some key individuals.
We perform exact calculations for the descendant
parts where more data are often available, and combine this information
to sample the hidden variables for the ancestral parts. We also improve
the ancestral sampling part using a mixture of several conditional Hidden
Markov Chains across loci or meiosis. Our approach is expected to be useful
for a complicated, large pedigree with a lot of missing data,
in which case most current methods cannot give satisfactory results.
The results from simulation studies are encouraging,
comparing to other MCMC methods.