Is marginal constraints equivalent to linear constraints?

Thread starter Edwinkumar
Start date Dec 11, 2009
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Constraints Equivalent Linear Marginal

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Marginal constraints on probability distributions can be expressed as linear constraints through the use of expected values. This involves formulating the problem such that the expected values of certain functions equal specified constants. The discussion seeks clarity on the equivalence of marginal constraints and linear constraints in probability distributions. Understanding this relationship is crucial for effectively modeling and analyzing probability spaces. The inquiry highlights the need for a mathematical framework to transition between these two types of constraints.

Dec 11, 2009

Edwinkumar

If I have a set of Probability distributions on a product space with marginal constraints, is there any way to (how to) express the same as a linear family of PD's ( i.e. all P s.t. E_P[ f_i] =a_i for some f_i, a_i )

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Dec 12, 2009

Edwinkumar

Could someone answer this?

Thread 'Formal derivation of statement from Peano Arithmetic system'

I was reading a Bachelor thesis on Peano Arithmetic (PA). PA has the following axioms (not including the induction schema): $$\begin{align} & (A1) ~~~~ \forall x \neg (x + 1 = 0) \nonumber \\ & (A2) ~~~~ \forall xy (x + 1 =y + 1 \to x = y) \nonumber \\ & (A3) ~~~~ \forall x (x + 0 = x) \nonumber \\ & (A4) ~~~~ \forall xy (x + (y +1) = (x + y ) + 1) \nonumber \\ & (A5) ~~~~ \forall x (x \cdot 0 = 0) \nonumber \\ & (A6) ~~~~ \forall xy (x \cdot (y + 1) = (x \cdot y) + x) \nonumber...

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