Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1410.2113

Sparse approximations of fractional Matérn fields

Lassi Roininen·Sari Lasanen·Mikko Orispää·Simo Särkkä
View original source ↗Read source document ↗Export metadata ↓

Abstract

We consider a fast approximation method for a solution of a certain stochastic non-local pseudodifferential equation. This equation defines a Matérn class random field. The approximation method is based on the spectral compactness of the solution. We approximate the pseudodifferential operator with a Taylor expansion. By truncating the expansion, we can construct an approximation with Gaussian Markov random fields. We show that the solution of the truncated version can be constructed with an over-determined system of stochastic matrix equations with sparse matrices. We solve the system of equations with a sparse Cholesky decomposition. We consider the convergence of the discrete approximation of the solution to the continuous one. Finally numerical examples are given.

Explore related subjects

math.STstat.TH

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Lassi Roininen, Sari Lasanen, Mikko Orispää, Simo Särkkä. 2014-10-08. Sparse approximations of fractional Matérn fields. https://arxiv.org/abs/1410.2113

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

A note on the distribution of the partial correlation coefficient with nonparametrically estimated marginal regressions

There has been much interest in the nonparametric testing of conditional independence in the econometric and statistical literature, but the simplest and potentially most useful method, based on the sample partial correlation, seems to have been overlooked, its distribution only having been investigated in some simple parametric instances. The present note shows that an easy to apply permutation test based on the sample partial correlation with nonparametrically estimated marginal regressions has good large and small sample properties.

math.ST↗
arXiv2026

Instance-Log-Optimality of Portfolio-Based E-Processes and their Sequential Hypothesis Tests

We consider the problem of sequential hypothesis testing using $e$-processes. For a rich class of composite testing problems---which include bounded mean testing, equal mean testing for bounded random tuples, and some key ingredients of two-sample and independence testing as special cases---we show that any $e$-process satisfying a certain sublinear regret bound is asymptotically and almost surely instance-log-optimal for a composite alternative. This is a strong notion of optimality that has not previously been established for the aforementioned problems, and we provide explicit test supermartingales and $e$-processes satisfying this notion in a more general case. Furthermore, we derive matching lower and upper bounds on the expected rejection time in the high-confidence regime for the resulting sequential tests in all of these cases. The proofs of these results make weak, algorithm-agnostic moment assumptions and rely on a proof technique involving the aforementioned regret and a family of numeraire portfolios. Finally, we discuss how all of these theorems hold in a distribution-uniform sense, a notion of log-optimality that is stronger still and seems to be new to the literature.

math.ST↗
arXiv2026

Common Drivers in Sparsely Interacting Hawkes Processes

We study a multivariate Hawkes process as a model for time-continuous relational event networks. The model does not assume the network to be known, it includes covariates, and it allows for both common drivers, parameters common to all the actors in the network, and also local parameters specific for each actor. We derive rates of convergence for all of the model parameters when both the number of actors and the time horizon tends to infinity. To prevent an exploding network, sparseness is assumed. We also discuss numerical aspects.

math.ST↗