Modified Linear Projection for Large Spatial Data Sets

Recent developments in engineering techniques for spatial data collection such as geographic information systems have resulted in an increasing need for methods to analyze large spatial data sets. These sorts of data sets can be found in various fields of the natural and social sciences. However, model fitting and spatial prediction using these large spatial data sets are impractically time-consuming, because of the necessary matrix inversions. Various methods have been developed to deal with this problem, including a reduced rank approach and a sparse matrix approximation. In this paper, we propose a modification to an existing reduced rank approach to capture both the large- and small-scale spatial variations effectively. We have used simulated examples and an empirical data analysis to demonstrate that our proposed approach consistently performs well when compared with other methods. In particular, the performance of our new method does not depend on the dependence properties of the spatial covariance functions.Comment: 29 pages, 5 figures, 4 table

A Computationally Efficient Projection-Based Approach for Spatial Generalized Linear Mixed Models

Inference for spatial generalized linear mixed models (SGLMMs) for high-dimensional non-Gaussian spatial data is computationally intensive. The computational challenge is due to the high-dimensional random effects and because Markov chain Monte Carlo (MCMC) algorithms for these models tend to be slow mixing. Moreover, spatial confounding inflates the variance of fixed effect (regression coefficient) estimates. Our approach addresses both the computational and confounding issues by replacing the high-dimensional spatial random effects with a reduced-dimensional representation based on random projections. Standard MCMC algorithms mix well and the reduced-dimensional setting speeds up computations per iteration. We show, via simulated examples, that Bayesian inference for this reduced-dimensional approach works well both in terms of inference as well as prediction, our methods also compare favorably to existing "reduced-rank" approaches. We also apply our methods to two real world data examples, one on bird count data and the other classifying rock types

Scanamorphos: a map-making software for Herschel and similar scanning bolometer arrays

Scanamorphos is one of the public softwares available to post-process scan observations performed with the Herschel photometer arrays. This post-processing mainly consists in subtracting the total low-frequency noise (both its thermal and non-thermal components), masking high-frequency artefacts such as cosmic ray hits, and projecting the data onto a map. Although it was developed for Herschel, it is also applicable with minimal adjustment to scan observations made with some other imaging arrays subjected to low-frequency noise, provided they entail sufficient redundancy; it was successfully applied to P-Artemis, an instrument operating on the APEX telescope. Contrary to matrix-inversion softwares and high-pass filters, Scanamorphos does not assume any particular noise model, and does not apply any Fourier-space filtering to the data, but is an empirical tool using purely the redundancy built in the observations -- taking advantage of the fact that each portion of the sky is sampled at multiple times by multiple bolometers. It is an interactive software in the sense that the user is allowed to optionally visualize and control results at each intermediate step, but the processing is fully automated. This paper describes the principles and algorithm of Scanamorphos and presents several examples of application.Comment: This is the final version as accepted by PASP (on July 27, 2013). A copy with much better-quality figures is available on http://www2.iap.fr/users/roussel/herschel