most recent 30 from http://mathoverflow.net 2013-05-19T08:23:01Z http://mathoverflow.net/feeds/question/97992 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/97992/simultaneous-confidence-bands-for-gaussian-processes Tanya T 2012-05-25T21:50:32Z 2012-05-25T21:50:32Z

<p>I'm looking at the problem of computing the simultaneous confidence bands for Gaussian processes. It can be stated at, given a Gaussian process X(t) with mean function \mu(t), covariance function k(t, t') and a coverage probability (1-\alpha), find c such that: Pr{ X(t) \in [\mu(t) - c\sqrt{\k(t, t)}, \mu(t) + c\sqrt{\k(t, t)} \forall t \in [a, b]} = \alpha.</p> <p>I know that "Simultaneous confidence bands for random functions" (Knowles, 1988) gives the result for one-dimensional functions. But for high-dimensional functions, it only has asymptotic results for the case $t \rightarrow \infty$. My question is, Is there other result that is general and applies for all t in the high-dimensional case? Thanks!</p>