In this book, we are concerned with multiscale methods and models. The term multiscale broadly refers to processes, algorithms, and data that can be structured by scale. A well-known example of a multiscale stochastic process is a fractal (e.g., Mandelbrot, 1999). An example of a multiscale algorithm is the fast wavelet transform (e.g., Vidakovic, 1999; Mallat, 1999). An example of multiscale data is a time series dataset that happens to be observable at different sampling frequencies. One could check the price of a stock once a year, daily, hourly, or every minute. The fluctuations in the annual prices will generally have rather different behavior than the hourly fluctuations, and one may want to model both sorts of behavior simultaneously.
KeywordsSingle Photon Emission Compute Tomography Multiscale Model Coarse Scale Markov Chain Monte Carlo Method Multiscale Method
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