OAI/NumberTheory/Ostmann/Construction/FiniteProductPrior.lean

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5 declarations, 0 contain sorry, 0 declared as axioms

Finite independent priors used for the arithmetic samples

  1. def OAI.Ostmann.productPrior line 14
  2. theorem OAI.Ostmann.productPrior_nonneg line 17
  3. theorem OAI.Ostmann.productPrior_mass line 21
  4. theorem OAI.Ostmann.productPrior_cons line 28
  5. theorem OAI.Ostmann.sum_productPrior_cons line 34

    Source documentation

    Integrate the first sample last, keeping the product prior on all remaining samples.

    theorem sum_productPrior_cons {A : Type*} [Fintype A] {n : ℕ}
    (μ : Fin (n + 1) → A → ℝ) (f : (Fin (n + 1) → A) → ℝ) :
    (∑ v, productPrior μ v * f v) =
      ∑ x : Fin n → A, productPrior (fun i => μ i.succ) x *
        ∑ a : A, μ 0 a * f (Fin.cons a x) := by
…

    Mentions: OAI.Ostmann.productPrior