SEMINARS IN STATISTICS @ COLLEGIO CARLO ALBERTO

Venerdì 24/04/2026, presso il Collegio Carlo Alberto, in Piazza Arbarello 8, Torino, si terrà il seguente seminario:

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12.00-13.00

Speaker: Randolf ALTMEYER (IMPERIAL COLLEGE LONDON)

Title: PARAMETER ESTIMATION FOR MATÉRN RANDOM FIELDS FROM LOCAL MEASUREMENTS

Abstract: Gaussian random fields with Matérn covariance structure are fundamental models in spatial statistics and widely used in applications. Given discrete observations on a regular grid, we study the parametric estimation of key parameters governing variance, range, and smoothness. Our approach is based on the representation of the random field as the solution to an elliptic stochastic partial differential equation (SPDE), which provides a structural framework for inference. A key insight from this representation is that the model parameters exhibit distinct local scaling behavior, reflecting the local structure of the underlying differential operator.

Building on this idea, we construct spatially localized linear combinations of the data, referred to as local measurements, which approximate localized features of the field. By analyzing how these quantities scale across resolutions, we develop a novel class of estimators based on localized quadratic functionals. This can be viewed as a multi-dimensional extension of quadratic variation techniques from time series analysis. By carefully designing test functions with prescribed moment cancellation properties, we obtain explicit estimators for the variance, range, and smoothness parameters. We establish asymptotic normality under infill asymptotics and derive explicit expressions for the estimator variances using Gaussian moment identities.

The resulting methods are computationally efficient, with linear complexity in the number of observations. Numerical experiments demonstrate that the proposed estimators are competitive with existing approaches while offering substantial computational advantages.

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Sarà possibile seguire il seminario anche in streaming: chiunque volesse collegarsi è pregato di inviare un’email a matteo.giordano@unito.it

Il webinar è organizzato dalla "de Castro" Statistics Initiative (www.carloalberto.org/stats) in collaborazione con il Collegio Carlo Alberto.

Cordiali saluti,