[ < ] | [ > ] | [ << ] | [ Up ] | [ >> ] | [Top] | [Contents] | [Index] |
lm_lods
, lm_markers
and lm_bayes
lm_lods
estimates location LOD scores by working along the
chromosome, estimating likelihood ratios between adjacent locations of
the trait locus, starting from unlinked, and proceeding through the
linkage group to unlinked again. We have three methods of combining
these local likelihood ratios into an overall LOD score method. One
reduces to an eigenvalue method used by Thompson (2000: sec 9.2, P.118).
Other alternatives are simply to combine the ratios from the left, or
from the right. Weighted combinations do a better job (William
Stewart), but we do not pursue this here as better methods are available
in lm_bayes
and lm_markers
.
lm_markers
is an implementation of the Lange-Sobel estimator,
using our LM-sampler. It is so-named because only the meiosis
indicators at marker loci are sampled, and only conditional on the
marker data. The Lange-Sobel estimate works reasonably well in
reasonable time, provided a good MCMC sampler is used, and provided the
trait data do not have strong impact on the conditional distribution of
meiosis indicators. Recall that the method samples meiosis indicators
conditionally only on the marker data. Because of this the method can
produce quite accurate LOD scores in the absence of linkage, but can be
inaccurate in estimating the strength of linkage signals. As well as
producing the LOD score, our current method provides a batch-means
pointwise estimate of the Monte Carlo standard error of the LOD-score
estimate.
lm_bayes
is currently our preferred method. It samples trait
locations from a posterior distribution, and then divides it by the
prior to produce the likelihood and hence the LOD score. Estimation is
in two phases. A preliminary run with discrete uniform prior gives
order-of-magnitude relative likelihoods. Then, using the inverse of
these likelihoods as prior weights (to produce an approximately uniform
posterior) a second run is made to estimate the likelihood. It is
important that the initial run is long enough for all points to be
sampled, and for the unlinked trait position to have a reasonable number
of realizations. For locations at which LOD scores are very negative, or
for the unlinked position when there is some location with strong
positive LOD score this can be problematic.
Our current implementation of lm_bayes
provides two LOD score
estimates. The first is a crude estimate which counts realizations of
locations sampled to estimate the posterior: as can be seen from the
output this can be quite erratic. The Rao-Blackwellized estimator is
much preferred, and produces good estimates in reasonable time.
[ < ] | [ > ] | [ << ] | [ Up ] | [ >> ] | [Top] | [Contents] | [Index] |