I’ll find somewhere to stick it and link it to the post.
The somewhat harder bullet to swallow is the assumption that the random variables are Markovian; that is, they are “memoryless” in the sense that only the present state determines the future.
This is not quite correct as a description of the SGS-Pearl system.
Yeah, sloppy writing on my part; the “time” that appears here is only an observer’s sequence of observations of the system’s state. I agree with what you say about discrete-time models.
On its face, stating the usual global causal Markov axiom—but assuming densely-ordered times, rather than non-densely-ordered times, is non-obvious.
What was assumed there is not that, because in this development I have not gotten to the point of finding a directed graph of variables anywhere. Presumably I’ll need a local corollary of Pearl’s theorem 1.4.1, i.e., every causal flow model (probably subject to some technical restrictions) locally induces a graph model with a compatible joint probability distribution. This has some hope of succeeding; if a distribution is consistent with a graph model, then small perturbations of it are also consistent with it.
Sorry, my real life job intervened and killed most of this week. There’s a slight kink in the current draft that I need to rewrite (it’s not a game-breaker), but that’ll have to wait until I get some free time. I also need to find some free webspace somewhere; it seems that the Megaupload debacle killed all the free filesending platforms.
My attempts at finding semi-stable webspace failed. In the meanwhile, for the sake of Nisan’s razor, here is a temporary link to the .pdf. It hasn’t been fixed yet; the ending is not very rigorous. I probably got a bit too excited near the end.
I’ll find somewhere to stick it and link it to the post.
Yeah, sloppy writing on my part; the “time” that appears here is only an observer’s sequence of observations of the system’s state. I agree with what you say about discrete-time models.
What was assumed there is not that, because in this development I have not gotten to the point of finding a directed graph of variables anywhere. Presumably I’ll need a local corollary of Pearl’s theorem 1.4.1, i.e., every causal flow model (probably subject to some technical restrictions) locally induces a graph model with a compatible joint probability distribution. This has some hope of succeeding; if a distribution is consistent with a graph model, then small perturbations of it are also consistent with it.
This is what I meant to assume: that X is a continuous-time markov process.
Ah! Yes, that makes sense. I’m looking forward to reading the paper.
Sorry, my real life job intervened and killed most of this week. There’s a slight kink in the current draft that I need to rewrite (it’s not a game-breaker), but that’ll have to wait until I get some free time. I also need to find some free webspace somewhere; it seems that the Megaupload debacle killed all the free filesending platforms.
My attempts at finding semi-stable webspace failed. In the meanwhile, for the sake of Nisan’s razor, here is a temporary link to the .pdf. It hasn’t been fixed yet; the ending is not very rigorous. I probably got a bit too excited near the end.