Asimov Datasets

What is an Asimov dataset?

An Asimov dataset is the expected observation under a specific hypothesis, generated by predict_fn(state) at a chosen POI value (mu_asimov). It provides a deterministic substitute for real data, giving the median expected outcome under the assumed hypothesis.

When is it needed?

The Asimov dataset is used to compute q_asimov, the test statistic evaluated on Asimov data. Some asymptotic distributions need q_asimov for p-value computation:

Distribution	null p-value	alt p-value	expected bands
TMuAsymptotic	no Asimov needed	needs Asimov	needs Asimov
QMuAsymptotic	no Asimov needed	needs Asimov	needs Asimov
Q0Asymptotic	no Asimov needed	needs Asimov	needs Asimov
QTildeAsymptotic	needs Asimov	needs Asimov	needs Asimov
TMuTildeAsymptotic	needs Asimov	needs Asimov	needs Asimov

What happens without it?

When predict_fn is not provided and no asimov_observation is given, q_asimov is None. Computations that need it issue a warning and return None. Downstream effects:

• CLs returns None if palt is None

• calc.expected() returns None

Practical summary: If you only need null_pval with TMu/QMu/Q0 distributions, no Asimov is needed. For CLs limits or Brazil bands, you need it.

How to provide Asimov data

There are two ways:

1. predict_fn (standard): Passed to AsymptoticCalculator or directly to the test statistic. The Asimov dataset is generated at mu_asimov.

   calc = AsymptoticCalculator(
       nll_fn=nll,
       params=params,
       observation=observed,
       poi_key="mu",
       predict_fn=predict,
       mu_asimov=0.0,  # background-only Asimov
   )
   

2. asimov_observation (pre-computed): Pass a pre-computed Asimov dataset directly to the test statistic.

   result = QTilde().compute(
       nll,
       params,
       observed,
       "mu",
       poi_test=1.0,
       asimov_observation={"n": 5.0},
   )
   

Choosing mu_asimov

• mu_asimov=0.0 (default): Background-only hypothesis. Use for exclusion tests and upper limits.

• mu_asimov=1.0: Signal+background hypothesis. Use for discovery tests.

Asimov as observation proxy

Separately from variance estimation, passing an Asimov dataset as observation to fit() or calc.test() gives expected results under a hypothesis. This is useful for computing expected limits or expected significances without real data.