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- W2083261149 abstract "Let {f(t) : t ∈ T} be a smooth Gaussian random field over a parameter space T, where T may be a subset of Euclidean space or, more generally, a Riemannian manifold. We provide a general formula for the distribution of the height of a local maximum [Formula: see text] is a local maximum of f(t)} when f is non-stationary. Moreover, we establish asymptotic approximations for the overshoot distribution of a local maximum [Formula: see text] is a local maximum of f(t) and f(t0) > v} as v → ∞. Assuming further that f is isotropic, we apply techniques from random matrix theory related to the Gaussian orthogonal ensemble to compute such conditional probabilities explicitly when T is Euclidean or a sphere of arbitrary dimension. Such calculations are motivated by the statistical problem of detecting peaks in the presence of smooth Gaussian noise." @default.
- W2083261149 created "2016-06-24" @default.
- W2083261149 creator A5002249428 @default.
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- W2083261149 date "2014-12-11" @default.
- W2083261149 modified "2023-09-28" @default.
- W2083261149 title "Distribution of the height of local maxima of Gaussian random fields" @default.
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- W2083261149 doi "https://doi.org/10.1007/s10687-014-0211-z" @default.
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