Download e-book for kindle: Multiscale Modeling: A Bayesian Perspective (Springer Series by Marco A.R. Ferreira, Herbert K.H. Lee

By Marco A.R. Ferreira, Herbert K.H. Lee

ISBN-10: 0387708979

ISBN-13: 9780387708973

ISBN-10: 0387708987

ISBN-13: 9780387708980

This hugely necessary booklet comprises technique for the research of information that come up from multiscale approaches. It brings jointly a couple of contemporary advancements and makes them available to a much wider viewers. Taking a Bayesian strategy permits complete accounting of uncertainty, and likewise addresses the fragile factor of uncertainty at a number of scales. those tools can deal with various quantities of past wisdom at diversified scales, as usually happens in practice.

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Additional resources for Multiscale Modeling: A Bayesian Perspective (Springer Series in Statistics)

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Finer levels use kernels of smaller width on a larger number of background grid points. 4) l=0 i=1 l=0 where xl (s) is the lth resolution process, and each of these processes is generated from a convolution of kernels kl on an appropriate resolution background process wl . As before, a mean term or mean function can be added in as well. If the process is observed on multiple scales, then the terms accumulate only to the scale being modeled. 5) q=0 i=1 where yl (tj ) is an observation of the process at the lth scale, j ∈ {1, .

The function ψ may be used to generate by translation and scaling operations a whole family of wavelets. For this reason, ψ is called the mother wavelet. 1) where u ∈ R and s ∈ R+ . Depending on whether s < 1 or s > 1, then ψs0 will be a contracted or an expanded version of ψ, respectively. The simplest and maybe most well-known wavelet is the Haar wavelet (Haar, 1910). 5 ≤ t < 1, ⎩ 0, otherwise. Due to its blockiness, the Haar wavelet is not appropriate to approximate smooth functions. Fortunately, there are many other families of wavelets.

CL−1 . Moreover, a full Bayesian analysis may require MCMC-based methods. This type of analysis takes into account all sources of uncertainty and can be extended to more complex situations, such as, for example, nonequally spaced regression and hierarchical functional analysis. For a nice introduction to MCMC methods for wavelets, see M¨ uller and Vidakovic (1999b). In practice, very often a lack of prior knowledge about the function f will prevent the elicitation of priors for the hyperparameters.

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Multiscale Modeling: A Bayesian Perspective (Springer Series in Statistics) by Marco A.R. Ferreira, Herbert K.H. Lee

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