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RANDOM FIELDS AND GEOMETRY published with Springer in 2007, but rather a companion volume, still under production, that gives a simpler version of the theory of the first book as well as lots of applications. You can find the original Random Fields and Geometry on the Springer site. Meanwhile, enjoy what is available of the second volume, and keep in mind… (More)

We are interested in the geometric properties of real-valued Gaussian random fields defined on manifolds. Our manifolds, M , are of class C and the random fields f are smooth. Our interest in these fields focuses on their excursion sets, f−1[u,+∞), and their geometric properties. Specifically, we derive the expected Euler characteristic E[χ(f−1[u,+∞))] of… (More)

We study the accuracy of the expected Euler characteristic approximation to the distribution of the maximum of a smooth, centered, unit variance Gaussian process f . Using a point process representation of the error, valid for arbitrary smooth processes, we show that the error is in general exponentially smaller than any of the terms in the approximation.… (More)

- Robert J. Adler, Omer Bobrowski, Mathew S. Borman, Eliran Subag, Shmuel Weinberger
- 2010

We discuss and review recent developments in the area of applied algebraic topology, such as persistent homology and barcodes. In particular, we discuss how these are related to understanding more about manifold learning from random point cloud data, the algebraic structure of simplicial complexes determined by random vertices, and, in most detail, the… (More)

The main topics of this workshop lay at the point where Probability meets Geometry, specifically the study of the random geometry and topology generated by smooth random functions. While these problems have their roots in various applications of image and shape analysis in a wide variety of disciplines, their main mathematical content lies in probability… (More)

We describe how to take a stable ARMA time series through the various stages of model identi cation parameter estimation and diag nostic checking and accompany the discussion with a goodly number of large scale simulations that show which methods do and do not work and where some of the pitfalls and problems associated with stable time series modelling lie

- Assaf J. Zeevi, Ron Meir, Robert J. Adler
- NIPS
- 1996

We consider the problem of prediction of stationary time series, using the architecture known as mixtures of experts (MEM). Here we suggest a mixture which blends several autoregressive models. This study focuses on some theoretical foundations of the prediction problem in this context. More precisely, it is demonstrated that this model is a universal… (More)

- Robert J. Adler
- 2008

This is a brief review, in relatively nontechnical terms, of recent rather technical advances in the theory of random field geometry. These advances have provided a collection of explicit new formulae describing mean values of a variety of geometric characteristics of excursion sets of random fields, such as their volume, surface area and Euler… (More)

- Robert J. Adler, Jose H. Blanchet, Jingchen Liu
- 2008 Winter Simulation Conference
- 2008

We are interested in computing tail probabilities for the maxima of Gaussian random fields. In this paper, we discuss two special cases: random fields defined over a finite number of distinct point and fields with finite Karhunen-Loève expansions. For the first case we propose an importance sampling estimator which yields asymptotically zero relative… (More)

over high levels u. For a large class of such random fields we compute the u → ∞ asymptotic joint distribution of the numbers of critical points, of various types, of X in Au, conditional on Au being non-empty. This allows us, for example, to obtain the asymptotic conditional distribution of the Euler characteristic of the excursion set. In a significant… (More)