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If the goal is to randomly probe the parameter space of a model, the author is correct that independent Gaussian random numbers are a poor choice (although it's
by streptomycin 14y ago
If the goal is to randomly probe the parameter space of a model, the author is correct that independent Gaussian random numbers are a poor choice (although it's not really related to the central limit theorem). However, this isn't a novel revelation. There are other/better ways to do it, for instance http://en.wikipedia.org/wiki/Latin_hypercube_sampling http://en.wikipedia.org/wiki/Latin_hypercube_sampling
- mturmon 14y agoSmart suggestion. There is a grain of truth in what the article says, but it's a little confused. The article is also conflating two things: the (unknown) internal state of the system, which could live in a very high-dimensional space, and the system inputs, which move the internal state around in a not-understood way, but which you at least get to choose directly. The cases the article examines use an internal state of a number, inputs of +1 or -1, and the system dynamics: state(t) = state(t-1) + input(t) (E.g., "state" is "number of open files".) The CLT does apply in this case, but it's clear that this is a very narrow case. I'm not aware of convergence results that hold in any generality here. There are concepts from control theory of observability and controllability (where can the internal state go, and how can you read it out). And there are the concepts from nonlinear dynamics of attractors.