In a text I am using, there is a constant echo of separable distribution. I haven't been able to find more information of this on any resources.
Would someone kindly explain to me its intuitive idea and provide an analogy of what a separable and non - separable distribution is?
I am guessing separable is used to mean independent but I cannot be sure.
Context: on the topic of metropolis method in high dimensions
Consider the case of a target distribution that is an N - dimension Gaussian, and a proposal distribution that is a spherical Gaussian of standard deviation $\epsilon$ in each direction. Without loss of generality, we can assume that the target distribution is a separable distribution aligned with the axes ${x_{n}}$, and that ...