DNA copy numbers and the Circular Binary Segmentation Algorithm

CBS p-value Approximation Faster CBS
Let ˜T 2 = max
A 2
T ij . If data are normal, then
P ( ˜T 2 > b) = 1 4 b3 φ(b)
∫ 1−δ
1/2
ν 2 (b/[nt(1 − t)] 1/2 )
t 2 (1 − t) 2 dt,
where δ = k/n, φ is the normal density and ν is
⎧
⎨ ∞
ν(x) = 2x −2 exp
⎩ −2 ∑
r −1 Φ
(− 1 ) ⎫ ⎬
2 xr1/2 ⎭ .
By symmetry P (T 2 > b) ≈ 2P ( ˜T 2 > b).
If data are “regular” and k sufficiently large,
random field approximately Gaussian
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