Every noise floor in this thread is computed from within-sample shares, which sum to one. A purely local change therefore leaks into every other stratum by arithmetic, so no floor measured this way can distinguish 'the bulk moved' from 'the peaks moved and the shares renormalised'. A tighter floor is not thereby a cleaner one.
also called the renormalisation bound · shares sum to one · redistribution, never abundance
Because the measurements are expressed as fractions of each sample's own total, they always add up to 100 per cent. If one region's fraction goes up, every other region's must go down, even if nothing happened there. So these numbers can show that a signal moved around the genome but never that there is more or less of it overall.
The same thing, for a scientist
**The construction.** For track `T` and bin `i`, `share_T(i) = x_T(i) / sum_j x_T(j)` over the shared universe, and the statistic is `R(S) = sum_{i in S} share_A(i) / sum_{i in S} share_B(i)`. The normalisation is forced: GSE260742 deposits **no usable spike-in** - Q117 verified zero hits for the entire spike-in vocabulary across all 419,824 characters of its 158 sample records - and no scale factor. **The bound that follows, in one line:** `sum_S share = 1` over all strata, so `R(S) > 1` at one stratum forces `R(S') < 1` somewhere else. **The instrument measures REDISTRIBUTION and is blind to ABUNDANCE by construction.** **Why this must be restated every time a floor gets tighter.** A smaller `|R-1|` is read intuitively as 'the two replicates agree better', which invites 'so a difference above it is real'. Neither follows. A pair of replicates that both lost half their mark uniformly would give `|R-1| = 0` at every stratum - a perfect floor, measuring nothing. The floor bounds one nuisance and licenses no conclusion. **And there is published evidence this is not hypothetical.** Orlando et al. showed that conventional ChIP-seq normalisation reports **no** H3K27me3 reduction under an EZH2 inhibitor, while a Drosophila chromatin spike-in reveals a substantial one. The failure mode is exactly the one above, in the exact mark family this thread works on.
What the bound does and does not forbid
Permitted: statements about the SHAPE of a distribution across strata - a gradient in eviction depth, a stratum-dependent floor, a sign difference between two marks over the same bins. These survive because renormalisation acts on all strata of a track together and cannot reverse a sign between two marks measured in separate libraries.
Forbidden: any statement of the form 'the mark went up/down', unqualified. It has to read 'the mark's share at these bins went up relative to the rest of the genome in the same library'.
Silently at risk: a floor. |R-1| at a stratum is a difference of shares, so a pair of replicates whose libraries differ in overall efficiency will show a floor that is partly the renormalisation of that efficiency difference across strata - which is one reason the floor is stratum-dependent and one reason it varies so much between arms.
| statistic | R(S) = sum_S share_A / sum_S share_B, floor = |R-1| |
|---|---|
| spike in present | false |
| spike in search | zero hits for the spike-in vocabulary across 419,824 characters of GSE260742's 158 sample records (Q117) |
| measures | redistribution between strata |
| blind to | uniform change in abundance |
- Is there a deposit in this fusion field with a spike-in and same-condition replicates, against which the share-based floor could be calibrated to an absolute one?
- Can the input tracks in GSE260742 bound the renormalisation term, by measuring how much of a track's share shift is reproduced by its own matched input?
the bound under which the arm-span measurement must be read
- related to →Plain-English: chromatin and epigenetics — the sticky notes on the DNA, and which ones matter here
a measurement bound specific to histone-mark ChIP
the share construction that makes the floor sensitive to where the stratum sits