Theorems · Theorem · statistics

ProbabilityTheory.bayesRisk_le_avgRisk

∀ {Θ : Type u_1} {𝓧 : Type u_2} {𝓨 : Type u_4} {mΘ : MeasurableSpace Θ} {m𝓧 : MeasurableSpace 𝓧}
  {m𝓨 : MeasurableSpace 𝓨} (ℓ : Θ → 𝓨 → ENNReal) (P : ProbabilityTheory.Kernel Θ 𝓧) (κ : ProbabilityTheory.Kernel 𝓧 𝓨)
  (π : MeasureTheory.Measure Θ) [hκ : ProbabilityTheory.IsMarkovKernel κ],
  ProbabilityTheory.bayesRisk ℓ P π ≤ ProbabilityTheory.avgRisk ℓ P κ π

Defined in: Mathlib.Probability.Decision.Risk.Basic
Cited by: 2 results in Mathlib
Foundations: Depth 216 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: ProbabilityTheory.IsMarkovKernel

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Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

MeasurableSpacestatement and proof · cited by 13,106
MeasureTheory.Measurestatement and proof · cited by 10,939
ENNRealstatement and proof · cited by 9,879
ProbabilityTheory.Kernelstatement and proof · cited by 1,281
ProbabilityTheory.IsMarkovKernelstatement and proof · cited by 124
iInf₂_leproof · cited by 45
ProbabilityTheory.bayesRiskstatement · cited by 31
ProbabilityTheory.avgRiskstatement · cited by 25

Cited by2

Results whose statement or proof uses this declaration.

ProbabilityTheory.bayesRisk_le_mul'proof · cited by 2
ProbabilityTheory.IsArgminEstimator.isBayesEstimatorproof · cited by 1