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- W4220687856 abstract "<p>We establish a theoretical framework, an algorithmic basis, and a&#160;computational workflow for the statistical analysis of multi-variate&#160;multi-dimensional random fields - sampled (possibly irregularly, with missing data) and finite (possibly bounded irregularly). Our research is practically motivated by geodetic and scientific problems of topography and gravity&#160;analysis in geophysics and planetary physics, but our solutions fulfill the more general need for sophisticated methods of&#160;inference that can be applied to massive remote-sensing data sets, and as such, our mathematical, statistical, and computational solutions transcend any particular&#160;application.&#160;The generic problem that we are addressing is: two (or more) spatial&#160;fields are observed, e.g., by passive or active sensing, and we desire&#160;a parsimonious statistical description of them, individually and in&#160;their relation to one another. We consider the fields to be&#160;realizations of a random process, parameterized as a Matern covariance&#160;structure, a very flexible description that includes, as special&#160;cases, many of the known models in popular use (e.g. exponential,&#160;autoregressive, von Karman, Gaussian, Whittle, ...) Our&#160;fundamental question is how to find estimates of the parameters of a&#160;Matern process, and the distribution of those estimates for&#160;uncertainty quantification. Our answer is, fundamentally: via&#160;maximum-likelihood estimation. &#160;We now provide a computationally and statistically efficient method for&#160;estimating the parameters of a stochastic covariance model observed on a&#160;regular spatial grid in any number of dimensions. Our proposed method, which we call the Debiased Spatial Whittle likelihood, makes important corrections&#160;to the well-known Whittle likelihood to account for large sources of bias&#160;caused by boundary effects and aliasing. We generalise the approach to&#160;flexibly allow for significant volumes of missing data including those with&#160;lower-dimensional substructure, and for irregular sampling boundaries. We&#160;build a theoretical framework under relatively weak assumptions which&#160;ensures consistency and asymptotic normality in numerous practical settings&#160;including missing data and non-Gaussian processes. We also&#160;extend our consistency results to multivariate processes. We provide&#160;detailed implementation guidelines which ensure the estimation procedure can&#160;still be conducted in O(n log n) operations, where n is the&#160;number of points of the encapsulating rectangular grid, thus keeping the&#160;computational scalability of Fourier and Whittle-based methods for large&#160;data sets. We validate our procedure over a range of simulated and real&#160;world settings, and compare with state-of-the-art alternatives,&#160;demonstrating the enduring practical appeal of Fourier-based methods,&#160;provided they are corrected and augmented by the procedures that we developed.</p>" @default.
- W4220687856 created "2022-04-03" @default.
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- W4220687856 date "2022-03-28" @default.
- W4220687856 modified "2023-10-03" @default.
- W4220687856 title "Efficient Parameter Estimation of Sampled Random Fields Using the Debiased Spatial Whittle Likelihood" @default.
- W4220687856 doi "https://doi.org/10.5194/egusphere-egu22-10879" @default.
- W4220687856 hasPublicationYear "2022" @default.
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