[RF] Nested `RooSimultaneous` double counts extended sub-pdfs

[stalbrec]

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Description

Consider a RooSimultaneous over some category (e.g. region) that is itself put into an outer RooSimultaneous over a second category (e.g. analysis), alongside a plain pdf that does not depend on region. RooFit flattens the two levels into one, indexed by the super-category analysis x region. The model is built from three pdfs, but the super-category has four states, and the pdf without a region split is the one selected in two of them. If all pdfs are extended, its expected number of events is therefore counted twice.

This is the shape of an analysis combination: analysis A fits a signal and a control region simultaneously, analysis B measures the same signal in a single region. Below A contributes 10 and 50 events and B contributes 40, so the intended total is 100. Tested with ROOT 6.40.02, sole dependency ROOT.

Consequences

{B;CR} does not exist — analysis B has no control region — but pdf_B is selected there and contributes its yield a second time:

super-category state	pdf	expectedEvents
{A;SR}	pdf_A_SR	10
{A;CR}	pdf_A_CR	50
{B;SR}	pdf_B	40
{B;CR}	pdf_B	40

Nothing records that a pdf has already contributed, so everything that sums over the index is affected alike:

	actual	if pdf_B counted once
comb.expectedEvents({x, comb.indexCat()})	140	100
generated analysis=B fraction	0.570 (= 80/140)	0.400
fitted nB	20	40

Only nB is biased: the extended term expects it in both B states while the data has 40 events in one and none in the other, minimizing at nB = 20. The factor is the number of states of the inner category. Non-extended nesting is unaffected, one state being active at a time and each normalized on its own.

Note also that analysis and region are no longer servers of comb after the flattening, so comb.expectedEvents({x, analysis, region}) returns the current state's yield rather than the sum.

Question

Is the right-hand column intended? I'd assume a component that does not depend on the inner category should contribute its yield once (total 100, generated B fraction 0.4) so the flattening should either deduplicate it or split its yield across the replicated states.

If the replication is deliberate instead, 140 is correct and the problem is only that nesting silently changes the model. Should the initialize() INFO then be a warning when a component does not depend on all index categories?

Workarounds for the former: one flat RooSimultaneous over the super-category with a dummy/zero pdf for the combinations that do not exist, or pdf_B made a RooSimultaneous over region too, with its yield split explicitly.

Reproducer

import ROOT

x = ROOT.RooRealVar("x", "x", -8, 8)
mean = ROOT.RooRealVar("mean", "mean", 0)
sigma = ROOT.RooRealVar("sigma", "sigma", 2)
shape = ROOT.RooGaussian("shape", "shape", x, mean, sigma)

# analysis A: signal region + control region.  analysis B: one region only.
nA_SR = ROOT.RooRealVar("nA_SR", "nA_SR", 10, 0, 1e6)
nA_CR = ROOT.RooRealVar("nA_CR", "nA_CR", 50, 0, 1e6)
nB = ROOT.RooRealVar("nB", "nB", 40, 0, 1e6)
pdf_A_SR = ROOT.RooExtendPdf("pdf_A_SR", "pdf_A_SR", shape, nA_SR)
pdf_A_CR = ROOT.RooExtendPdf("pdf_A_CR", "pdf_A_CR", shape, nA_CR)
pdf_B = ROOT.RooExtendPdf("pdf_B", "pdf_B", shape, nB)

region = ROOT.RooCategory("region", "region", {"SR": 0, "CR": 1})
analysis = ROOT.RooCategory("analysis", "analysis", {"A": 0, "B": 1})

anaA = ROOT.RooSimultaneous("anaA", "anaA", {"SR": pdf_A_SR, "CR": pdf_A_CR}, region)
comb = ROOT.RooSimultaneous("comb", "comb", {"A": anaA, "B": pdf_B}, analysis)
ROOT.RooMsgService.instance().setGlobalKillBelow(ROOT.RooFit.WARNING)  # quiet the fit

for state in comb.indexCat():
    label = str(state.first)
    print(f"{label:<8} -> {comb.getPdf(label).GetName()}")
print("expected:", comb.expectedEvents(ROOT.RooArgSet(x, comb.indexCat())), "(intended 100)")

# toy generation follows the inflated total
toy = comb.generate(ROOT.RooArgSet(x, analysis, region), 100_000)
for a, r in (("A", "SR"), ("A", "CR"), ("B", "SR"), ("B", "CR")):
    n = toy.sumEntries(f"analysis==analysis::{a} && region==region::{r}")
    print(f"generated {{{a};{r}}}: {n / toy.numEntries():.3f}")

# an extended fit to the dataset the combination actually has: A in SR and CR,
# B in its single region, nothing in {B;CR}
w = ROOT.RooRealVar("w", "w", 0, 1e6)
data = ROOT.RooDataSet("data", "data", ROOT.RooArgSet(x, analysis, region, w), WeightVar=w)
for a, r, n in (("A", "SR", 10), ("A", "CR", 50), ("B", "SR", 40)):
    analysis.setLabel(a), region.setLabel(r), x.setVal(0)
    data.add(ROOT.RooArgSet(x, analysis, region), n)

comb.fitTo(data, Extended=True, PrintLevel=-1)
for v, truth in ((nA_SR, 10), (nA_CR, 50), (nB, 40)):
    print(f"fitted {v.GetName()}: {v.getVal():.1f} (truth {truth})")

[#1] INFO:InputArguments -- RooSimultaneous::initialize(comb) INFO: one or more input
component of simultaneous p.d.f.s are simultaneous p.d.f.s themselves, rewriting composite
expressions as one-level simultaneous p.d.f. in terms of final constituents and extended
index category
{A;CR}   -> pdf_A_CR
{A;SR}   -> pdf_A_SR
{B;CR}   -> pdf_B
{B;SR}   -> pdf_B
expected: 140.0 (intended 100)
generated {A;SR}: 0.072
generated {A;CR}: 0.358
generated {B;SR}: 0.285
generated {B;CR}: 0.284
fitted nA_SR: 10.0 (truth 10)
fitted nA_CR: 50.0 (truth 50)
fitted nB: 20.0 (truth 40)

ROOT version

---

| Welcome to ROOT 6.40.02 https://root.cern |
| (c) 1995-2025, The ROOT Team; conception: R. Brun, F. Rademakers |
| Built for macosxarm64 on Aug 31 2026, 16:31:09 |
| From tags/6-40-02@6-40-02 |
| With std202302 |
| Try '.help'/'.?', '.demo', '.license', '.credits', '.quit'/'.q' |

Installation method

conda-forge https://conda.anaconda.org/conda-forge/osx-arm64/root-6.40.02-py314h5c24228_4.conda

Operating system

macOS 26.6.1

Additional context

No response