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Statistical Methods for Fuzzy Data by Reinhard Viertl

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14.2 Updating fuzzy a priori distributions

For stochastic quantities X with parametric probability distribution p(.|θ) or f (.|θ), given observed data 1, … , n the a priori distribution has to be updated in order to obtain up-to-date information concerning the parameter θ.

This updated information is the conditional distribution of , shown as P* (·|1, … , n), conditional on the sample 1, … , n·

For a discrete stochastic model X ~ p (·|θ); θ ∈ Θ with discrete parameter space

Unnumbered Display Equation

the a posteriori distribution P* (·|1 … , n) is given by its conditional point probabilities p* (θj|1 … ,n), j = 1(1)k. These ...

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