`iterFilter_cons`

proved

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module: IndisputableMonolith.Statistics.BayesianFilteringFromVFE
domain: Statistics
line: 56 · github
papers citing: none yet

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IndisputableMonolith.Statistics.BayesianFilteringFromVFE on GitHub at line 56.

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formal source

  53theorem iterFilter_nil (L : Likelihood ι Obs) (p : ProbDist ι) :
  54    iterFilter L [] p = p := rfl
  55
  56theorem iterFilter_cons (L : Likelihood ι Obs) (o : Obs) (os : List Obs) (p : ProbDist ι) :
  57    iterFilter L (o :: os) p = iterFilter L os (bayesStep p L o) := rfl
  58
  59structure BayesianFilteringCert where
  60  evidence_positive : ∀ (prior : ProbDist ι) (L : Likelihood ι Obs) (o : Obs),
  61    0 < evidence prior L o
  62  bayes_step_update : ∀ (prior : ProbDist ι) (L : Likelihood ι Obs) (o : Obs) (i : ι),
  63    (bayesStep prior L o).prob i =
  64      prior.prob i * L.like o i / evidence prior L o
  65
  66theorem bayesianFilteringCert_holds : BayesianFilteringCert (ι := ι) (Obs := Obs) :=
  67{ evidence_positive := evidence_pos
  68  bayes_step_update := fun prior L o i => bayesStep_is_update prior L o i }
  69
  70end
  71
  72end IndisputableMonolith.Statistics.BayesianFilteringFromVFE

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