Theorems · Definition · statistics

ProbabilityTheory.bayesRisk

{Θ : Type u_1} →
  {𝓧 : Type u_2} →
    {𝓨 : Type u_3} →
      {mΘ : MeasurableSpace Θ} →
        {m𝓧 : MeasurableSpace 𝓧} →
          [MeasurableSpace 𝓨] → (Θ → 𝓨 → ENNReal) → ProbabilityTheory.Kernel Θ 𝓧 → MeasureTheory.Measure Θ → ENNReal

The Bayes risk with respect to a prior π, defined as the infimum of the average risks of all estimators.

Defined in

Mathlib.Probability.Decision.Risk.Defs

Cited by

31 results in Mathlib

Foundations

Depth 215 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpace