MCMC and principal eigenvectors

[gustavolacerda]

I am wondering if, instead of running MCMC and hoping that it has "mixed" ("achieved stationarity"), there are approaches based on computing (or approximating) the principal left eigenvector of the transition matrix

Comments

[en_ki]

To all appearances, solutions are one-off. My Brownian motion book cites Kac for the case of one-dimensional Brownian motion; I don't seem to have access to Kac's papers from here.

[gustavolacerda]

by "one-off" do you mean: improvised? non-generalizable? few and far between?

[en_ki]

All of the above, though "non-generalizable" is the usual meaning of one-off.

It appears that the problem more or less reduces to solving differential equations in the space of interest and, as with solving DEs, you may be able to get a general solution for a tiny but useful class of problems (like linear DEs or one-dimensional Brownian motion), but in general you have to either discover rare completely ungeneral tricks or do numerical approximations.

[gustavolacerda]

Sounds like a good lead, thanks. But I thought that Brownian motion means you get full diffusion.

I'm thinking I should ask a statistical physicist about this.