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dd14c26 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 | import Mathlib
import OAI.Probability.LogConcave.OraclePrograms.Program
namespace OAI
section
noncomputable section
namespace LogConcaveSampling.OracleCompiler.Program
open MeasureTheory ProbabilityTheory Function
open scoped Classical
variable {Ω E R : Type*} [MeasurableSpace Ω] [MeasurableSpace E] [MeasurableSpace R] {d q r : ℕ}
def independentSeq (A : Program Ω d q E) (B : Program (E × R) d r E) :
Program (Ω × R) d (q+r) E :=
(A.seedMap Prod.fst measurable_fst).seq
(B.seedMap (fun p => (p.2,p.1.2)) (by fun_prop))
lemma independentSeq_run (A : Program Ω d q E) (B : Program (E × R) d r E)
(V : Point d → ℝ) (p : Ω × R) :
(A.independentSeq B).run V p=B.run V (A.run V p.1,p.2) := by
rw [independentSeq,seq_run,seedMap_run,seedMap_run]
lemma independentSeq_law (A : Program Ω d q E) (B : Program (E × R) d r E)
{V : Point d → ℝ} (hV : Measurable (firstOrderReply V)) (μ : Measure Ω) (γ : Measure R)
[IsProbabilityMeasure μ] [IsProbabilityMeasure γ] :
(μ.prod γ).map ((A.independentSeq B).run V)=((μ.map (A.run V)).prod γ).map (B.run V) := by
have hm := Measure.map_prod_map μ γ (A.measurable_run V hV) measurable_id
rw [Measure.map_id] at hm
rw [hm,Measure.map_map (B.measurable_run V hV) ((A.measurable_run V hV).prodMap measurable_id)]
congr 1
funext p
exact independentSeq_run A B V p
end LogConcaveSampling.OracleCompiler.Program
end
end
end OAI
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