Nonlinear Multivariate Spatial Modeling Using NLPCA and Pair‐Copulas

A novel geostatistical modeling approach is developed to model nonlinear multivariate spatial dependence using nonlinear principal component analysis (NLPCA) and pair‐copulas. In spatial studies, multivariate measurements are frequently collected at each location. The dependence between such measurements can be complex. In this article, a multivariate geostatistical model is developed that can capture both nonlinear spatial dependence across locations and nonlinear dependence between measurements at a particular location. Nonlinear multivariate dependence between spatial variables is removed using NLPCA. Subsequently, a pair‐copula based model is fitted to each transformed variable to model the univariate nonlinear spatial dependencies. NLPCA and pair‐copulas, within the proposed model, are compared with stepwise conditional transformation (SCT) and conventional kriging. The results show that, for the two case studies presented, the proposed model that utilizes NLPCA and pair‐copulas reproduces nonlinear multivariate structures and univariate distributions better than existing methods based on SCT and kriging.     

Settlement Form and Evolution in the Central Highlands of Scotland,ca. 1100–1900

Since 1996, archaeologists from Glasgow University have been involved in a research project on the north shores of Loch Tay in the Central Highlands of Scotland. This work—known as the Ben Lawers Historic Landscape Project—was specifically focused on medieval and later settlement remains. For the purposes of this paper, the results of the archaeological work are contrasted with work from similar sites elsewhere in Scotland. The sweeping changes in tenurial, social and cultural spheres, known as the Improvements, of the eighteenth and nineteenth centuries are considered in relation to the preceding six hundred years.     

Book reviews

The Geography of Europe's Futures. Ian Masser, Ove Sviden and Michael Wegener, London, Belhaven Press, 1992, 225 pp., £12.99, ISBN 1 85293 231/2 7/5.

Cities and Regions in the New Europe. Mick Dunford and Grigoris Kafkalas (Eds), London, Belhaven Press, 1992, 339 pp., £42.00, ISBN: 1 85293 221 X.

Regional Development and Contemporary Industrial Response: Extending Flexible Specialisation. Huib Ernste and Verena Meier (Eds), London, Belhaven Press, 1992, 256 pp., £35.00, ISBN: 1 85293 214 7.

Understanding Information: Business, Technology and Geography. K. Robins (Ed.), London, Belhaven Press, 1992, 207 pp., £37.50, ISBN: 1 85293 109 4.

Humanising the City? Social Contexts of Urban life at the Turn of the Millennium. Anthony P. Cohen and Katsuyoshi Fukui (Eds), Edinburgh, Edinburgh University Press, 228 pp., £29.50 hb., ISBN 0 7486 0388 3.     

Book reviews

Regions Reconsidered: Economic Networks, Innovation and Local Department in Industrial Countries. Edward Bergman, Gunter Maier and Franz Tödtling (Eds), London: Mansell Publishing Limited, 1991, 312pp.

Travel Sickness: The Need for a Sustainable Transport Policy for Britain. J. Roberts, J. Cleary, K. Hamilton and J. Hanna (Eds), London: Lawrence and Wishart, 1992, 358pp.

Endogenous Development and Southern Europe. G. Garofoli (Ed.), Aldershot: Avebury Press, 1992, ISBN 1 85628 1310, 250pp., £37.50.