Conditional independence for Markov kernels
Conditional independence is extended to the framework of Markov kernels. A representation result of such a conditional independence in terms of random variables and a characterization when densities are available, are also obtained.
Moreover, a result by the same authors relating conditional and unconditional independence is generalized to this more abstract context. The mentioned result, part of a paper by Nogales and Pérez (2018, arXiv:1706.03955), uses independence of Markov kernels (see Nogales (2013a)) and the conditional distribution of a Markov kernel given another (see Nogales (2013b)) to obtain a minimal condition which added to conditional independence implies independence. Namely, the theorem reads as follows: Let K, L, M be three Markov kernels. If K and L are conditionally independent given M, then K and L are independent if and only if the conditional distributions of K and L given M are independent.
Palabras clave / Keywords: conditional independence Markov kernel
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