20,795 research outputs found
A Bayesian information criterion for singular models
We consider approximate Bayesian model choice for model selection problems
that involve models whose Fisher-information matrices may fail to be invertible
along other competing submodels. Such singular models do not obey the
regularity conditions underlying the derivation of Schwarz's Bayesian
information criterion (BIC) and the penalty structure in BIC generally does not
reflect the frequentist large-sample behavior of their marginal likelihood.
While large-sample theory for the marginal likelihood of singular models has
been developed recently, the resulting approximations depend on the true
parameter value and lead to a paradox of circular reasoning. Guided by examples
such as determining the number of components of mixture models, the number of
factors in latent factor models or the rank in reduced-rank regression, we
propose a resolution to this paradox and give a practical extension of BIC for
singular model selection problems
Wavelet analysis and scaling properties of time series
We propose a wavelet based method for the characterization of the scaling
behavior of non-stationary time series. It makes use of the built-in ability of
the wavelets for capturing the trends in a data set, in variable window sizes.
Discrete wavelets from the Daubechies family are used to illustrate the
efficacy of this procedure. After studying binomial multifractal time series
with the present and earlier approaches of detrending for comparison, we
analyze the time series of averaged spin density in the 2D Ising model at the
critical temperature, along with several experimental data sets possessing
multi-fractal behavior.Comment: 4 pages, 4 figures. Accepted for publication in PR
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