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

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in search of a global belief in search of a global belief

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

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In Search of a Global Belief Model for Discrete-time Uncertain Models

Natan T’Joens, Jasper De Bock, Gert de Cooman

In Search of a Global Belief Model for Discrete-time Uncertain Models

Natan T’Joens, Jasper De Bock, Gert de Cooman

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1 X1 2 X2 n Xn ⇤ x y z x y z … … … … … x y z … … … Time

… …

= state at time n

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1 X1 2 X2 n Xn ⇤ x y z x y z … … … … … x y z … … … Time

… …

state space X = finite!

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1 X1 2 X2 n Xn ⇤ x y z x y z … … … … … x y z … … … Time

… …

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1 X1 2 X2 n Xn ⇤ x y z x y z … … … … … x y z … … … Time

… …

= Coherent

Qyz : L (X ) → R

C1. Qyz(f) ≤ sup f
C2. Qyz(f + g) ≤ Qyz(f) + Qyz(g)
C3. Qyz(λf) = λQyz(f)

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1 X1 2 X2 n Xn ⇤ x y z x y z … … … … … x y z … … … Time

… … probability that the state will ever be x?

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1 X1 2 X2 n Xn ⇤ x y z x y z … … … … … x y z … … … Time

… …

…

path ω = yx · · · x · · ·

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1 X1 2 X2 n Xn ⇤ x y z x y z … … … … … x y z … … … Time

… …

…

ω = yx · · · x · · ·

Ω := X N

sample space

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⇤ x y z x y z … … … … … x y z … … …

??? E

global model

Local models {Qs}s∈X ∗

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What properties should satisfy?

E

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⇤ … …

f(X1:2)

is a finitary gamble

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Cool thing #1

P1-P5 is consistent + There is a unique largest model!

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Cool thing #2

Coincides with a version of Shafer and Vovk’s game- theoretic upper expectation! strong properties + alternative definition

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Interested? Come see us at our poster!