Generalized Bayes Decision Functions, Admissibility and the Exponential Family
Generalized Bayes Decision Functions, Admissibility and the Exponential Family
For the experiment $\mathscr{E}$, given by $\mathscr{E} = \lbrack x$ (in space $X$) distributed with probability element $f(x \mid \theta) d\mu(x), \{\theta\} = \Theta$ the parameter space, $W(d, \theta)$ a non-negative loss function for decision $d \epsilon D\rbrack$, the definition of a (non-randomized) strict Bayes decision function (BDF) can, following …