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The Bayesian and Akaike information criteria aim at finding a good balance between under- and over-fitting. They are extensively used every day by practitioners. Yet we contend they suffer from at least two afflictions: their penalty…
Information of interest can often only be extracted from data by model fitting. When the functional form of such a model can not be deduced from first principles, one has to make a choice between different possible models. A common approach…
The Akaike information criterion (AIC) has been used as a statistical criterion to compare the appropriateness of different dark energy candidate models underlying a particular data set. Under suitable conditions, the AIC is an indirect…
Recent astronomical observations indicate that the Universe is presently almost flat and undergoing a period of accelerated expansion. Basing on Einstein's general relativity all these observations can be explained by the hypothesis of a…
In the information-based paradigm of inference, model selection is performed by selecting the candidate model with the best estimated predictive performance. The success of this approach depends on the accuracy of the estimate of the…
Fourier power spectra and phases of a signal from a large number of radiating sources orbiting around a black hole are investigated. It is assumed that the individual sources (bright spots) are located in an accretion disc and their…
We discuss different methods for phenomenological approximations of signals with (generally) irregularly spaced arguments. Such signals may be classified as periodic, multi-periodic, quasi-periodic (cyclic), burst-type and flicker-type (see…
In this paper, we address a model selection problem for ergodic jump diffusion processes based on high-frequency samples. We evaluate the expected genuine log-likelihood function and derive an Akaike-type information criterion based on the…
We report our theoretical and experimental investigations into errors in quantum state estimation, putting a special emphasis on their asymptotic behavior. Tomographic measurements and maximum likelihood estimation are used for estimating…
In statistical modeling area, the Akaike information criterion AIC, is a widely known and extensively used tool for model choice. The {\phi}-divergence test statistic is a recently developed tool for statistical model selection. The…
To determine the exact shape of the luminosity function (LF) of galaxies is one of the central problems in galactic astronomy and observational cosmology. The most popular method to estimate the LF is maximum likelihood, which is clearly…
High-frequency quasiperiodic oscillations of the X-ray flux comming from black-hole binaries have the potential to provide precise estimates of the mass and the spin of the central black hole, if an adequate model for them was available.…
Regression models fitted to data can be assessed on their goodness of fit, though models with many parameters should be disfavored to prevent over-fitting. Statisticians' tools for this are little known to physical scientists. These include…
In this paper we introduce a new feature selection algorithm to remove the irrelevant or redundant features in the data sets. In this algorithm the importance of a feature is based on its fitting to the Catastrophe model. Akaike information…
We present a statistical perspective on boosting. Special emphasis is given to estimating potentially complex parametric or nonparametric models, including generalized linear and additive models as well as regression models for survival…
The study of X-ray time-lag spectra in active galactic nuclei (AGN) is currently an active research area, since it has the potential to illuminate the physics and geometry of the innermost region (i.e. close to the putative super-massive…
The theoretical foundation for a number of model selection criteria is established in the context of inhomogeneous point processes and under various asymptotic settings: infill, increasing domain, and combinations of these. For…
Using various latest cosmological datasets including Type-Ia supernovae, cosmic microwave background radiation, baryon acoustic oscillations, and estimations of the Hubble parameter, we test some dark energy models with parameterized…
In this article we propose a general class of risk measures which can be used for data based evaluation of parametric models. The loss function is defined as generalized quadratic distance between the true density and the proposed model.…
Bayesian model averaging is a practical method for dealing with uncertainty due to model specification. Use of this technique requires the estimation of model probability weights. In this work, we revisit the derivation of estimators for…