definition 11.70 Profile likelihood

open in the book · parts/02-mathematical-methods/09-probability-statistics.tex:2206 · p. 397

ground object -- no derivation owed

Rests on

depends_on definition 11.54 Likelihood ¶
- depends_on definition 11.53 Statistical model ¶
depends_on definition 11.56 Maximum-likelihood estimator ¶
- depends_on definition 11.54 Likelihood ¶ ↺

Supports

assumes experiment The Higgs Boson Discovery ¶
- cites (method) derived bib 08 The ATLAS Experiment at the CERN Large Hadron Collider ¶
- cites (method) derived bib 08 The ATLAS Experiment at the CERN Large Hadron Collider ¶ ↺
- cites (method) derived bib 08 The ATLAS Experiment at the CERN Large Hadron Collider ¶ ↺
- cites (evidence) derived bib 1 Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC ¶
- cites (data) derived bib 1 Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC ¶ ↺
- cites (data) derived bib 1 Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC ¶ ↺
- cites (data) derived bib 1 Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC ¶ ↺
- cites (data) derived bib 1 Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC ¶ ↺
- cites (data) derived bib 1 Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC ¶ ↺
- cites (evidence) derived bib 1 Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC ¶ ↺
- cites (data) derived bib 1 Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC ¶ ↺
- cites (data) derived bib 1 Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC ¶ ↺
- … 128 more
depends_on corollary 11.89 Degrees of freedom with nuisance parameters ¶
- depends_on example 11.107 Degrading a local five sigma ¶
- depends_on proposition 11.93 $Z=\sqrt{q}$ ¶
  - depends_on example 11.107 Degrading a local five sigma ¶ ↺
  - depends_on proposition 113.15 Why categorizing helps, and by how much ¶
  - depends_on proposition 113.12 Sensitivity is set by ratio, not by rate ¶
- depends_on remark 11.90 Failure I: a parameter on the boundary ¶
depends_on definition 11.87 Likelihood-ratio test statistic ¶
- depends_on definition A.203 The constraint surface ¶
  - depends_on lemma A.212 Second-order flatness ¶
    - depends_on lemma A.213 The three minima ¶
      - depends_on theorem A.214 Wilks, $k$ parameters and $r$ constraints ¶
- depends_on theorem 11.88 Wilks ¶
  - depends_on corollary 11.89 Degrees of freedom with nuisance parameters ¶ ↺
depends_on proposition 11.71 Elementary properties ¶

Neighborhood

Every logical edge within two steps of this node.

declared and complete
partly declared
a check failed
not graded
declared in the source
inferred from structure

Edges

type	direction	node	provenance	where
`depends_on`	→	Likelihood	declared	parts/02-mathematical-methods/09-probability-statistics.tex:2218
`depends_on`	→	Maximum-likelihood estimator	declared	parts/02-mathematical-methods/09-probability-statistics.tex:2218
`assumes`	←	The Higgs Boson Discovery	declared	parts/11-qft-standard-model/15-exp-higgs-discovery.tex:4
`depends_on`	←	Degrees of freedom with nuisance parameters	declared	parts/02-mathematical-methods/09-probability-statistics.tex:2815
`depends_on`	←	Likelihood-ratio test statistic	declared	parts/02-mathematical-methods/09-probability-statistics.tex:2695
`depends_on`	←	Elementary properties	declared	parts/02-mathematical-methods/09-probability-statistics.tex:2224