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Physical Sciences and Mathematics Commons™
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Full-Text Articles in Physical Sciences and Mathematics
Random Set Theory And Problems Of Modeling, Noel A. Cressie, G M. Laslett
Random Set Theory And Problems Of Modeling, Noel A. Cressie, G M. Laslett
Professor Noel Cressie
The three- or four-dimensional world in which we live is full of objects to be measured and summarized. Very often a parsimonious finite collection of measurements is enough for scientific investigation into an object’s genesis and evolution. There is a growing need, however, to describe and model objects through their form as well as their size. The purpose of this article is to show the potentials and limitations of a probabilistic and statistical approach. Collections of objects (the data) are assimilated to a random set (the model), whose parameters provide description and/or explanation.
Some Diagnostics For Markov Random Fields, Noel A. Cressie, Prasenjit Kapat
Some Diagnostics For Markov Random Fields, Noel A. Cressie, Prasenjit Kapat
Professor Noel Cressie
The development of diagnostics to check the fit of a proposed Markov random field (MRP) to data is a very important problem in spatial statistics. In this article, the consequences of fitting a given MRF to spatial data are visualized using diagnostic plots. The Gaussian MRF known as the conditional autoregressive model is featured. Various types of departures of the data from the fitted MRF model are calculated, allowing locally influential observations to be highlighted using the MRF-Neighborhoods plot. Through a global summary statistic and the Model-Comparison plot, we compare MRF models that differ both in terms of the neighborhood …