In Search of a Global Belief In Search of a Global Belief Model for - PowerPoint PPT Presentation

May 03, 2023 •24 likes •194 views

In Search of a Global Belief In Search of a Global Belief Model for Discrete-time Model for Discrete-time Uncertain Models Uncertain Models Natan TJoens, Jasper De Bock, Gert de Cooman Natan TJoens, Jasper De Bock, Gert de Cooman Time

In Search of a Global Belief In Search of a Global Belief Model for Discrete-time Model for Discrete-time Uncertain Models Uncertain Models Natan T’Joens, Jasper De Bock, Gert de Cooman Natan T’Joens, Jasper De Bock, Gert de Cooman
Time … … 1 2 n = state at time n X 1 X 2 X n … … x x … y x … z … … y y ⇤ z … z …
Time … … 1 2 n X 1 X 2 X n … … x x … y x … z … … y y ⇤ = z state space X … finite! z …
Time … … 1 2 n X 1 X 2 X n … … x x … y x … z … … y y ⇤ z … z …
Time … … 1 2 n X 1 X 2 X n … … x x … y x … z … … y y ⇤ z … Q yz : L ( X ) → R z … C1. Q yz ( f ) ≤ sup f = Coherent C2. Q yz ( f + g ) ≤ Q yz ( f ) + Q yz ( g ) C3. Q yz ( λ f ) = λ Q yz ( f )
Time … … 1 2 n X 1 X 2 X n … … x x … y x … z … … y y ⇤ z … probability that the state will ever be x ? z …
Time … … 1 2 n X 1 X 2 X n path ω = yx · · · x · · · … … … x x … y x … z … … y y ⇤ z … z …
Time … … 1 2 n X 1 X 2 X n … ω = yx · · · x · · · … … x x … y x … sample space z … Ω := X N … y y ⇤ z … z …
… … x x … y x … z … … y y ⇤ Local models { Q s } s ∈ X ∗ z … z … ??? global model E
What properties should satisfy? E
… f ( X 1:2 ) is a finitary gamble ⇤ …
Cool thing #1 P1-P5 is consistent + There is a unique largest model!
Cool thing #2 Coincides with a version of Shafer and Vovk’s game- theoretic upper expectation! strong properties + alternative definition
Interested? Come see us at our poster!

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