Spatiotemporal Random Fields in Exposure Analysis and Assessment
What follows is a play which involves the philosophers St. Thomas Aquinas, Francis Bacon and August Comte (hence we will call it the ABC play). These philosophers promoted ideas that may help us understand important aspects of the random field concept. Aquinas (1225–1274) argued for a system of philosophy that is based on a combination of mystic Aristotelian faith and natural reason. Bacon (1561–1626) introduced the concept of scientific method that emphasizes experimentation and observations. Finally, Comte (1798–1857) promoted the view that one should focus on the connections between observable facts in order to make hypotheses and develop theories. In our theatrical play, Aquinas goes into an isolated room and generates a sequence of numbers. Our prior (initial) knowledge regarding the mechanism that Aquinas used to generate his data was that he tossed a die repeatedly (we assumed here that while God may not play dice, his Saints do!) and recorded the outcome, but the outcome itself is --of course-- unknown to us. Based on this limited knowledge we are asked to guess what the sequence looks like.
KeywordsRandom Field Covariance Function Covariance Model Hurst Exponent Invasion Percolation
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