Finite-sample system identification: An overview and a new correlation method

Finite-sample system identification algorithms can be used to build guaranteed confidence regions for unknown model parameters under mild statistical assumptions. It has been shown that in many circumstances these rigorously built regions are comparable in size and shape to those that could be built by resorting to the asymptotic theory. The latter sets are, however, not guaranteed for finite samples and can sometimes lead to misleading results. The general principles behind finite-sample methods make them virtually applicable to a large variety of even nonlinear systems. While these principles are simple enough, a rigorous treatment of the attendant technical issues makes the corresponding theory complex and not easy to access. This is believed to be one of the reasons why these methods have not yet received widespread acceptance by the identification community and this letter is meant to provide an easy access point to finite-sample system identification by presenting the fundamental ideas underlying these methods in a simplified manner. We then review three (classes of) methods that have been proposed so far-1) Leave-out Sign-dominant Correlation Regions (LSCR); 2) Sign-Perturbed Sums (SPS); 3) Perturbed Dataset Methods (PDMs). By identifying some difficulties inherent in these methods, we also propose in this letter a new sign-perturbation method based on correlation which overcome some of these difficulties

Asymptotic properties of SPS confidence regions

Sign-Perturbed Sums (SPS) is a system identification method that constructs non-asymptotic confidence regions for the parameters of linear regression models under mild statistical assumptions. One of its main features is that, for any finite number of data points and any user-specified probability, the constructed confidence region contains the true system parameter with exactly the user-chosen probability. In this paper we examine the size and the shape of the confidence regions, and we show that the regions are strongly consistent, i.e., they almost surely shrink around the true parameter as the number of data points increases. Furthermore, the confidence region is contained in a marginally inflated version of the confidence ellipsoid obtained from the asymptotic system identification theory. The results are also illustrated by a simulation example

Undermodelling Detection with Sign-Perturbed Sums

Sign-Perturbed Sums (SPS) is a finite sample system identification method that can build exact confidence regions for the unknown parameters of linear systems under mild statistical assumptions. Theoretical studies of the SPS method have assumed so far that the order of the system model is known to the user. In this paper we discuss the implications of this assumption for the applicability of the SPS method, and we propose an extension that, under mild assumptions, i) still delivers guaranteed confidence regions when the model order is correct, and ii) it is guaranteed to detect, in the long run, if the model order is wrong

Seiberg-Witten-Floer homology of a surface times a circle for non-torsion spin-c structures

We determine the Seiberg-Witten-Floer homology groups of the three-manifold which is the product of a surface of genus $g \geq 1$ times the circle, together with its ring structure, for spin-c structures which are non-trivial on the three-manifold. We give applications to computing Seiberg-Witten invariants of four-manifolds which are connected sums along surfaces and also we reprove the higher type adjunction inequalities previously obtained by Oszv\'ath and Szab\'o.Comment: 26 pages, no figures, Latex2e, to appear in Math. Nac

Numerical calculation of linear modes in stellar disks

We present a method for solving the two-dimensional linearized collisionless Boltzmann equation using Fourier expansion along the orbits. It resembles very much solutions present in the literature, but it differs by the fact that everything is performed in coordinate space instead of using action-angle variables. We show that this approach, though less elegant, is both feasible and straightforward. This approach is then incorporated in a matrix method in order to calculate self-consistent modes, using a set of potential-density pairs which is obtained numerically. We investigated the stability of some unperturbed disks having an almost flat rotation curve, an exponential disk and a non-zero velocity dispersion. The influence of the velocity dispersion, halo mass and anisotropy on the stability is further discussed.Comment: 12 pages LaTeX format, uses laa.tex (enclosed), 16 PostScript figures. tarred, gzipped, uuencoded. Postscript version available at ftp://naos.rug.ac.be/pub/LINMOD2.ps.Z Accepted for publication in A &

Base pair opening within B-DNA: free energy pathways for GC and AT pairs from umbrella sampling simulations.

The conformational pathways and the free energy variations for base opening into the major and minor grooves of a B-DNA duplex are studied using umbrella sampling molecular dynamics simulations. We compare both GC and AT base pair opening within a double-stranded d(GAGAGAGAGAGAG). d(CTCTCTCTCTCTC) oligomer, and we are also able to study the impact of opening on the conformational and dynamic properties of DNA and on the surrounding solvent. The results indicate a two-stage opening process with an initial coupling of the movements of the bases within the perturbed base pair. Major and minor groove pathways are energetically comparable in the case of the pyrimidine bases, but the major groove pathway is favored for the larger purine bases. Base opening is coupled to changes in specific backbone dihedrals and certain helical distortions, including untwisting and bending, although all these effects are dependent on the particular base involved. Partial opening also leads to well defined water bridging sites, which may play a role in stabilizing the perturbed base pairs

Asymptotic properties of SPS confidence regions

Sign-Perturbed Sums (SPS) is a system identification method that constructs non-asymptotic confidence regions for the parameters of linear regression models under mild statistical assumptions. One of its main features is that, for any finite number of data points and any user-specified probability, the constructed confidence region contains the true system parameter with exactly the user-chosen probability. In this paper we examine the size and the shape of the confidence regions, and we show that the regions are strongly consistent, i.e., they almost surely shrink around the true parameter as the number of data points increases. Furthermore, the confidence region is contained in a marginally inflated version of the confidence ellipsoid obtained from the asymptotic system identification theory. The results are also illustrated by a simulation example