[RF] RooParamHistFunc: analytical integral inconsistent with value for paramRelative = false #24003

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Description

With paramRelative = false, the value of a RooParamHistFunc in bin i is the parameter p_i, but its analytical integral is Σ p_i · w_i · vol_i, where w_i is the content of the histogram the function was built from. The integral should be Σ p_i · vol_i, consistent with the value.

evaluate() multiplies by the nominal content only if _relParam is set:

double ret = (static_cast<RooAbsReal*>(_p.at(idx)))->getVal() ;
return _relParam ? ret * getNominal(idx) : ret;

while analyticalIntegralWN() always sums the histogram weights, scaled by the parameters, regardless of _relParam:

auto getBinScale = [&](int iBin){ return static_cast<const RooAbsReal&>(_p[iBin]).getVal(); };
return const_cast<RooDataHist&>(_dh).sum(_x, sliceSet, true, false, ranges, getBinScale);

For paramRelative = true (the default), both agree.

Reproducer

void paramhist_relparam()
{
   RooRealVar x{"x", "x", 0.0, 2.0};
   x.setBins(2);
   RooDataHist dh{"dh", "dh", x};
   x.setBin(0);
   dh.set(x, 2.0);
   x.setBin(1);
   dh.set(x, 3.0);

   for (bool relParam : {true, false}) {
      RooParamHistFunc f{"f", "f", dh, x, nullptr, relParam};
      double sumOfValues = 0.0;
      for (int i = 0; i < 2; ++i) {
         x.setBin(i);
         sumOfValues += f.getVal() * 1.0; // bin width 1
      }
      std::unique_ptr<RooAbsReal> integral{f.createIntegral(x)};
      std::cout << "relParam=" << relParam << ": sum of value*width = " << sumOfValues
                << ", createIntegral(x) = " << integral->getVal() << std::endl;
   }
}

Output:

relParam=1: sum of value*width = 5, createIntegral(x) = 5
relParam=0: sum of value*width = 5, createIntegral(x) = 13

With paramRelative = false, the parameters are initialized to the bin contents (2 and 3), so the integral comes out as 2·2 + 3·3 = 13 instead of 2 + 3 = 5.

ROOT version

master (6.41.01), at 507d28258e0.

Installation method

Built from source.

Operating system

Ubuntu 26.04, GCC 15.2.

Additional context

The range handling of this integral was fixed in #7182; the RooDataHist::sum with a bin-scale lambda is probably from that change.

This came up while mapping RooParamHistFunc to HS3 (the RooFit JSON format). #24002 writes a RooParamHistFunc with relative parameters like a HistFactory sample: a product of a RooHistFunc and the HistFactory ParamHistFunc (whose HS3 I/O is reworked in #24001). For absolute parameters, the natural mapping would be a ParamHistFunc alone. Its integral is consistent with its value, so it would differ from the current integral of RooParamHistFunc. #24002 therefore rejects absolute parameters with an error for now.

Question to the RooFit developers: will this be fixed, or is RooParamHistFunc going to be deprecated (in favour of ParamHistFunc), so that bugs in it won't be fixed any more? That decides whether #24002 should map absolute parameters to ParamHistFunc (changing the integral to the consistent one) or keep rejecting them.