By definition, this quantity (τ̂g) is an alternate estimate of cancer ploidy (note an additional factor of 2 is added when HSCRs are used). Because (τ̂g) is a weighted average over discrete states in the modeled data, it is expected to be more robust to experimental fluctuations that shift or scale the copy-profile slightly. Note that, for this computation, the q̂ij were calculated with θ̂z = 0, so that the above expectation is over integer states only.