The integration about VC results continues today

Numerical stuff for LR first.

Single family,
E(NCP) = n•q²/e²/4
if we take the comparison of QTL allele ^~q² as a variable, then ^~q²/q² follows a χ² distribution with 1 degree of freedom.
Then the power = ∫Pχ²₍₁₎•[1-F_cdf(threshold, df1, df2, c•χ²₍₁₎)] dχ²₍₁₎.
where, c = E(NCP)
Above obtained very good results for single families.

It is easy to consider multiple families like this:
E(NCP) = Σ(c•^~q²_i/q²) = c•(Σ^~q²_i/q²) = c•χ²_(nf)
where nf is the number of families.

The theoretical results turned out much larger than empirical results.

To explore the source of difference, I calculated some results as below:
nf: 2
n: 30
df1: =nf
df2: =nf•(n-2)
q²: .2
h²: .4
Then:
ENCP=3.53
Ev


To be continued ....

Today's tasks

1. Numerical integeration about LR method.
2. Approximation about VC method

Both above are about random model.

btw, Peter's guess about VC NCP is great. I will put it here later.

Starting of the blog

This blog will keep a track of my progresses on the bioinformatics studying. Comments from collaborators and peers are welcomed.