definition 11.96 Local, global, trials factor
open in the book ·
parts/02-mathematical-methods/09-probability-statistics.tex:2992
· p. 406
- ground object -- no derivation owed
Rests on
-
depends_on
definition 11.75
$p$-value
¶
-
depends_on
definition 11.74
Hypotheses and tests
¶
- depends_on definition 11.53 Statistical model ¶
-
depends_on
definition 11.74
Hypotheses and tests
¶
- depends_on equation 11.89 eq:prob-p-one-sided ¶
- depends_on equation 11.88 eq:prob-q0 ¶
Supports
- depends_on corollary 11.105 Trials factor at high significance ¶
-
depends_on
definition 11.100
Upcrossings
¶
-
depends_on
definition A.218
The hypotheses
¶
- depends_on lemma A.220 At each point, field and derivative are independent Gaussians ¶
-
depends_on
theorem A.219
Rice's formula
¶
- depends_on corollary A.227 The stationary case ¶
- depends_on lemma A.221 Counting identity ¶
- depends_on theorem A.219 Rice's formula ¶ ↺
-
depends_on
theorem 11.101
Davies' bound
¶
- depends_on corollary 11.105 Trials factor at high significance ¶ ↺
- depends_on example 11.107 Degrading a local five sigma ¶
-
depends_on
theorem 11.103
Level dependence of the mean upcrossing
count
¶
- depends_on corollary 11.105 Trials factor at high significance ¶ ↺
- depends_on example 11.107 Degrading a local five sigma ¶ ↺
-
depends_on
theorem 11.102
Rice's formula
¶
- depends_on theorem 11.103 Level dependence of the mean upcrossing count ¶ ↺
-
depends_on
definition A.218
The hypotheses
¶
- depends_on proposition 113.19 The trials factors of the 2012 result ¶
- depends_on proposition 11.97 The trials factor is at least one ¶
-
depends_on
proposition 11.98
Union bound and the naive estimate
¶
- depends_on example 11.107 Degrading a local five sigma ¶ ↺
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 |
→ | $p$-value | declared | parts/02-mathematical-methods/09-probability-statistics.tex:3008 |
depends_on |
→ | eq:prob-p-one-sided | declared | parts/02-mathematical-methods/09-probability-statistics.tex:3008 |
depends_on |
→ | eq:prob-q0 | declared | parts/02-mathematical-methods/09-probability-statistics.tex:3008 |
depends_on |
← | Trials factor at high significance | declared | parts/02-mathematical-methods/09-probability-statistics.tex:3236 |
depends_on |
← | Upcrossings | declared | parts/02-mathematical-methods/09-probability-statistics.tex:3086 |
depends_on |
← | The trials factors of the 2012 result | declared | parts/11-qft-standard-model/15-exp-higgs-discovery.tex:2013 |
depends_on |
← | The trials factor is at least one | declared | parts/02-mathematical-methods/09-probability-statistics.tex:3014 |
depends_on |
← | Union bound and the naive estimate | declared | parts/02-mathematical-methods/09-probability-statistics.tex:3041 |