Classical vs. Bayesian methods for linear system identification: point estimators and confidence sets

This paper compares classical parametric methods with recently developed Bayesian methods for system identification. A Full Bayes solution is considered together with one of the standard approximations based on the Empirical Bayes paradigm. Results regarding point estimators for the impulse response as well as for confidence regions are reported.Comment: number of pages = 8, number of figures =

Perturbed Datasets Methods for Hypothesis Testing and Structure of Corresponding Confidence Sets

Hypothesis testing methods that do not rely on exact distribution assumptions have been emerging lately. The method of sign-perturbed sums (SPS) is capable of characterizing confidence regions with exact confidence levels for linear regression and linear dynamical systems parameter estimation problems if the noise distribution is symmetric. This paper describes a general family of hypothesis testing methods that have an exact user chosen confidence level based on finite sample count and without relying on an assumed noise distribution. It is shown that the SPS method belongs to this family and we provide another hypothesis test for the case where the symmetry assumption is replaced with exchangeability. In the case of linear regression problems it is shown that the confidence regions are connected, bounded and possibly non-convex sets in both cases. To highlight the importance of understanding the structure of confidence regions corresponding to such hypothesis tests it is shown that confidence sets for linear dynamical systems parameter estimates generated using the SPS method can have non-connected parts, which have far reaching consequences

Applicability of a Representation for the Martin's Real-Part Formula in Model-Independent Analyses

Using a novel representation for the Martin's real-part formula without the full scaling property, an almost model-independent description of the proton-proton differential cross section data at high energies (19.4 GeV - 62.5 GeV) is obtained. In the impact parameter and eikonal frameworks, the extracted inelastic overlap function presents a peripheral effect (tail) above 2 fm and the extracted opacity function is characterized by a zero (change of sign) in the momentum transfer space, confirming results from previous model-independent analyses. Analytical parametrization for these empirical results are introduced and discussed. The importance of investigations on the inverse problems in high-energy elastic hadron scattering is stressed and the relevance of the proposed representation is commented. A short critical review on the use of Martin's formula is also presented.Comment: Two comments and one reference added at the end of Subsec. 3.3; 23 pages, 9 figures; to be published in Int. J. Mod. Phys.

Carving model-free inference

In many large-scale experiments, the investigator begins with pilot data to look for promising findings. As fresh data becomes available at a later point of time, or from a different source, she is left with the question of how to use the full data to infer for the selected findings. Compensating for the overoptimism from selection, carving permits a reuse of pilot data for valid inference. The principles of carving are quite appealing in practice: instead of throwing away the pilot samples, carving simply discards the information consumed at the time of selection. However, the theoretical justification for carving is strongly tied to parametric models, an example being the ubiquitous gaussian model. In this paper we develop asymptotic guarantees to substantiate the use of carving beyond gaussian generating models. In simulations and in an application on gene expression data, we find that carving delivers valid and tight confidence intervals in model-free settings.Comment: 50 pages, 2 figures, 7 Table

Locally stationary long memory estimation

There exists a wide literature on modelling strongly dependent time series using a longmemory parameter d, including more recent work on semiparametric wavelet estimation. As a generalization of these latter approaches, in this work we allow the long-memory parameter d to be varying over time. We embed our approach into the framework of locally stationary processes. We show weak consistency and a central limit theorem for our log-regression wavelet estimator of the time-dependent d in a Gaussian context. Both simulations and a real data example complete our work on providing a fairly general approach