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Full-Text Articles in Statistics and Probability
Complexity Reduction In State-Based Modeling, Martin Zwick
Complexity Reduction In State-Based Modeling, Martin Zwick
Systems Science Faculty Publications and Presentations
For a system described by a relation among qualitative variables (or quantitative variables "binned" into symbolic states), expressed either set-theoretically or as a multivariate joint probability distribution, complexity reduction (compression of representation) is normally achieved by modeling the system with projections of the overall relation. To illustrate, if ABCD is a four variable relation, then models ABC:BCD or AB:BC:CD:DA, specified by two triadic or four dyadic relations, respectively, represent simplifications of the ABCD relation. Simplifications which are lossless are always preferred over the original full relation, while simplifications which lose constraint are still preferred if the reduction of complexity more …
Additive Nonparametric Regression With Autocorrelated Errors, Michael S. Smith, C Wong, Robert Kohn
Additive Nonparametric Regression With Autocorrelated Errors, Michael S. Smith, C Wong, Robert Kohn
Michael Stanley Smith
A Bayesian approach is presented for nonparametric estimation of an additive regression model with autocorrelated errors. Each of the potentially nonlinear components is modelled as a regression spline using many knots, while the errors are modelled by a high order stationary autoregressive process parameterised in terms of its autocorrelations. The distribution of significant knots and partial autocorrelations is accounted for using subset selection. Our approach also allows the selection of a suitable transformation of the dependent variable. All aspects of the model are estimated simultaneously using Markov chain Monte Carlo. It is shown empirically that the proposed approach works well …