Newport iServer MicroServer iTHX-M Operator's Manual page 374

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Affymetrix GeneChip ®
W = The 6x6 block-diagonal variance-covariance matrix of
within-genotype variances and covariances. The entries of the
matrix are w with w
i,j
may be null, if there are not at least two DM initial estimates of
one or more of the three genotypes.
N = A 6x6 diagonal matrix with entries (nAA, nAA, nAB, nAB,
nBB, nBB), the number of DM initial estimates for each of the
three genotypes.
• SNP-Specific Posterior Estimates:
μ
= The 6-dimensional posterior estimate of cluster center
coordinates to be used in the prototype for calling genotype
estimates.
Σ
= The 6x6 block-diagonal estimate of within-genotype variances
of transformed allele signal estimates. The entries of the matrix are
σ σ
with = 0 for |i-j| > 1.
i,j i,j
Having set up this notation, the posterior estimates are derived by a
two-step process. First, a posterior estimate of the nine, non-zero
parameters in S is obtained by doing point-wise shrinkage towards the
prior estimate, using an effective number of observations p which is
selected up front:
= ((n
σ
-1) w + p s
i,j i,j i,j
This Bayesian update has the intuitively sensible property that when
there is little or no data available for a genotype within an SNP
(n small), the variance-covariance matrix to be used for the genotype
i,j
is predominantly driven by the typical variance-covariance that is seen
across most SNPs. Conversely, if there is abundant information for a
particular genotype of an SNP (n
prior and the estimate will primarily be based on data specific to the
SNP. The point of transition between the reliance on prior and
observed is tuned by the number of pseudo-observations, p, and
performance is insensitive to the setting of p. The GTYPE software has
a fixed setting of 40 for p.
The final step is to derive a posterior estimate of the cluster centers,
The assumption is made that cluster variances are independent of the
centers. The update rule is:
Genotyping Analysis Software User's Guide
= 0 for |i-j| > 1. Some or all of these entries
i,j
) / ((n
-1) + p)
i,j i,j
large), there is little reliance on the
i,j
= (M
μ
-1
+ (NS)
) (Μ
-1 -1 -1
m + (NS)
μ
.
-1
v).