theorem 11.101 Davies' bound

open in the book · parts/02-mathematical-methods/09-probability-statistics.tex:3094 · p. 407

Rests on

depends_on definition 11.100 Upcrossings ¶
- depends_on definition 11.96 Local, global, trials factor ¶
  - depends_on definition 11.75 $p$-value ¶
    - depends_on definition 11.74 Hypotheses and tests ¶
      - depends_on definition 11.53 Statistical model ¶
  - depends_on equation 11.89 eq:prob-p-one-sided ¶
  - depends_on equation 11.88 eq:prob-q0 ¶
depends_on lemma 11.50 Markov and Chebyshev inequalities ¶
- depends_on definition 11.6 Moments, variance, standard deviation ¶
  - depends_on proposition 11.5 Transfer, linearity, monotonicity ¶
    - depends_on definition 11.4 Expectation ¶
      - depends_on definition 7.45 Series ¶
      - depends_on definition 11.3 Discrete random variable ¶
    - depends_on proposition 11.2 Elementary rules ¶
      - depends_on definition 11.1 Discrete probability space ¶
      - proves proof ch:09-probability-statistics@proof-1 ¶
    - proves proof ch:09-probability-statistics@proof-2 ¶
- depends_on proposition 11.5 Transfer, linearity, monotonicity ¶ ↺
- proves proof ch:09-probability-statistics@proof-18 ¶
depends_on theorem 7.23 Intermediate value theorem ¶
- depends_on axiom 7.1 Completeness of $\R$ ¶
- depends_on definition 7.20 Continuity at a point ¶
  - depends_on definition 7.16 Limit ¶
    - depends_on definition 7.2 Absolute value ¶
    - depends_on definition 7.9 Real function ¶
      - depends_on definition 3.43 Map ¶
  - depends_on equation 7.7 eq:ana-limit-left ¶
  - depends_on equation 7.5 eq:ana-limit-right ¶
- proves proof ch:05-real-analysis@proof-8 ¶
proves proof ch:09-probability-statistics@proof-44 ¶

Supports

depends_on corollary 11.105 Trials factor at high significance ¶
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`	→	Upcrossings	declared	parts/02-mathematical-methods/09-probability-statistics.tex:3101
`depends_on`	→	Markov and Chebyshev inequalities	declared	parts/02-mathematical-methods/09-probability-statistics.tex:3101
`depends_on`	→	Intermediate value theorem	declared	parts/02-mathematical-methods/09-probability-statistics.tex:3101
`depends_on`	←	Trials factor at high significance	declared	parts/02-mathematical-methods/09-probability-statistics.tex:3236
`depends_on`	←	Degrading a local five sigma	declared	parts/02-mathematical-methods/09-probability-statistics.tex:3350
`proves`	←	ch:09-probability-statistics@proof-44	declared	parts/02-mathematical-methods/09-probability-statistics.tex:3104