Download Multiscale Modeling: A Bayesian Perspective (Springer Series by Marco A.R. Ferreira, Herbert K.H. Lee PDF

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

This hugely helpful booklet comprises method for the research of information that come up from multiscale strategies. It brings jointly a few contemporary advancements and makes them obtainable to a much wider viewers. Taking a Bayesian strategy permits complete accounting of uncertainty, and in addition addresses the fragile factor of uncertainty at a number of scales. those tools can deal with various quantities of past wisdom at assorted scales, as frequently happens in practice.

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If a mean parameter is included, it can either be given a flat prior or the same prior as the background process (which helps to simplify the computations). As with the single-resolution convolution model, the background process can be fit via either REML or MCMC, and the full posterior including unknown parameters can be found with MCMC methods (Higdon, 2002). edu/~herbie/multiscale). This code can serve as a template and is easily modified for a variety of more complex situations. 0 * ** * * *** ** * * * * ** ** * * * * * * * * * * * * * * ** *** * * * * * ** * * * * ** ** * * * * * * * ** * ** * * * * * * * * * * * 10 10 20 30 40 s Fig.

Finally, the model can be made more robust by using Student-t errors (Vidakovic, 1998; Clyde and George, 2000). Vannucci and Corradi (1999a) have presented a recursive approach to computing the covariances between the empirical wavelet coefficients within and across scales. Based on the empirical wavelet coefficients’ covariance structure, Vannucci and Corradi (1999a,b) have proposed a joint prior distribution for the wavelet coefficients. In a related approach, Vidakovic and M¨ uller (1995) have proposed a joint prior distribution for the wavelet coefficients that assumes independence across scales and dependence within scales.

5 Bayesian Nonparametric Regression with Wavelets 47 that the estimator is the posterior median; as a result, some wavelet coefficients may be estimated as equal to zero. As this may lead to signal representations based on a few wavelet coefficients different from zero, this may be particularly useful when the objective is to compress the signal. , see Vidakovic, 1998). As the specification of the priors for the hyperparameters is not an easy task in wavelet nonparametric regression, Abramovich et al.

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