Optimal predictive model selection

Often the goal of model selection is to choose a model for future prediction, and it is natural to measure the accuracy of a future prediction by squared error loss. Under the Bayesian approach, it is commonly perceived that the optimal predictive model is the model with highest posterior probability, but this is not necessarily the case. In this paper we show that, for selection among normal linear models, the optimal predictive model is often the median probability model, which is defined as the model consisting of those variables which have overall posterior probability greater than or equal to 1/2 of being in a model. The median probability model often differs from the highest probability model

The Median Probability Model and Correlated Variables

The median probability model (MPM) Barbieri and Berger (2004) is defined as the model consisting of those variables whose marginal posterior probability of inclusion is at least 0.5. The MPM rule yields the best single model for prediction in orthogonal and nested correlated designs. This result was originally conceived under a specific class of priors, such as the point mass mixtures of non-informative and g-type priors. The MPM rule, however, has become so very popular that it is now being deployed for a wider variety of priors and under correlated designs, where the properties of MPM are not yet completely understood. The main thrust of this work is to shed light on properties of MPM in these contexts by (a) characterizing situations when MPM is still safe under correlated designs, (b) providing significant generalizations of MPM to a broader class of priors (such as continuous spike-and-slab priors). We also provide new supporting evidence for the suitability of g-priors, as opposed to independent product priors, using new predictive matching arguments. Furthermore, we emphasize the importance of prior model probabilities and highlight the merits of non-uniform prior probability assignments using the notion of model aggregates

Radiative corrections to the background of μ→eγ\mu\to e\gamma decay

Radiative muon decay in the kinematics similar to the neutrinoless decay $\mu\to e\gamma$ is considered. Radiative corrections due to 1-loop virtual photons and emission of additional soft or hard photons are taken into account. Analytical expressions and numerical estimations are presented.Comment: 11 pages, LaTeX, misprints in Eqs.(9,12,14) fixe

U(2) and Maximal Mixing of nu_{mu}

A U(2) flavor symmetry can successfully describe the charged fermion masses and mixings, and supress SUSY FCNC processes, making it a viable candidate for a theory of flavor. We show that a direct application of this U(2) flavor symmetry automatically predicts a mixing of 45 degrees for nu_mu to nu_s, where nu_s is a light, right-handed state. The introduction of an additional flavor symmetry acting on the right-handed neutrinos makes the model phenomenologically viable, explaining the solar neutrino deficit as well as the atmospheric neutrino anomaly, while giving a potential hot dark matter candidate and retaining the theory's predictivity in the quark sector.Comment: 20 pages, 1 figur

Electric Dipole moments of charged leptons and lepton flavor violating interactions in the general two Higgs Doublet model

We calculate the electric dipole moment of electron using the experimental result of muon electric dipole moment and upper limit of the BR(\mu --> e\gamma) in the framework of the general two Higgs doublet model. Our prediction is 10^{-32} e-cm, which lies in the experimental current limits. Further, we obtain constraints for the Yukawa couplings \bar{\xi}^{D}_{N,\tau e} and \bar{\xi}^{D}_{N,\tau\mu}. Finally we present an expression which connects the BR(\tau\to \mu\gamma) and the electric dipole moment of \tau-lepton and study the relation between these physical quantities.Comment: 8 pages, 4 Figures (required epsf sty

Gamma-ray burst jet propagation, development of angular structure, and the luminosity function

The fate and observable properties of gamma-ray burst jets depend crucially on their interaction with the progenitor material that surrounds the central engine. We present a semi-analytical model of such interaction, which builds upon several previous analytical and numerical works, aimed at predicting the angular distribution of jet and cocoon energy and Lorentz factor after breakout, given the properties of the ambient material and of the jet at launch. Using this model, we construct synthetic populations of structured jets, assuming either a collapsar (for long gamma-ray bursts -- LGRBs) or a binary neutron star merger (for short gamma-ray bursts -- SGRBs) as progenitor. We assume all progenitors to be identical, and we allow little variability in the jet properties at launch: our populations therefore feature a quasi-universal structure. These populations are able to reproduce the main features of the observed LGRB and SGRB luminosity functions, although several uncertainties and caveats remain to be addressed.Comment: 15 pages, 12 figures. Revised version, submitted to A&A (several new figures and expanded discussion. Conclusions unchanged). Comments and suggestions are welcome

Carbon based double layer capacitors with aprotic electrolyte solutions: the possible role of intercalation/insertion processes

The extraordinary stability and cycle life performance of today's electrochemical double-layer capacitors (EDLCs) are generally ascribed to the fact that charge storage in activated carbon (AC) is based on pure double-layer charging. In contrast, Faradaic charge-transfer reactions like those occurring in batteries are often connected with dimensional changes, which can affect the cycle life of these storage devices. Here we report the charge-induced height change of an AC electrode in an aprotic electrolyte solution, 1mol/l (C2H5)4NBF4 (TEABF4) in acetonitrile. The results are compared with those obtained for a graphite electrode in the same electrolyte. For both electrodes, we observe an expansion/contraction of several percent for a potential window of ±2V vs. the immersion potential (ip). For the EDLC electrode, significant expansion starts at about 1V remote from the ip and hence is well within the normal EDLC operation range. For the graphite electrode, the height changes are unambiguously caused by intercalation/deintercalation of both anions and cations. The close analogies between the graphite and the EDLC electrode suggest that ion intercalation or insertion processes might play a major role for charge storage, self discharge, cyclability, and the voltage limitation of EDLC

Flavour physics from an approximate U(2)^3 symmetry

The quark sector of the Standard Model exhibits an approximate U(2)^3 flavour symmetry. This symmetry, broken in specific directions dictated by minimality, can explain the success of the Cabibbo-Kobayashi-Maskawa picture of flavour mixing and CP violation, confirmed by the data so far, while allowing for observable deviations from it, as expected in most models of ElectroWeak Symmetry Breaking. Building on previous work in the specific context of supersymmetry, we analyze the expected effects and we quantify the current bounds in a general Effective Field Theory framework. As a further relevant example we then show how the U(2)^3 symmetry and its breaking can be implemented in a generic composite Higgs model and we make a first analysis of its peculiar consequences. We also discuss how some partial extension of U(2)^3 to the lepton sector can arise, both in general and in composite Higgs models. An optimistic though conceivable interpretation of the considerations developed in this paper gives reasons to think that new physics searches in the flavour sector may be about to explore an interesting realm of phenomena.Comment: 29 pages, 5 figure

Two-Loop Large-mtm_t Electroweak Corrections to K→πννˉK\to\pi\nu\bar\nu for Arbitrary Higgs Boson Mass

We consider for the first time the leading large top mass corrections, arising at higher order in electroweak interactions, to the rare decays $K\to\pi\nu\bar\nu$ and the related modes $B\to X_s\nu\bar\nu$ and $B\to l^+l^-$. Higher order effects of similar type have previously been calculated in the large-$m_t$ limit for key observables of precision electroweak physics at Z-factories. Here we obtain the corresponding corrections of order ${\cal O}(G^2_F m^4_t)$ at the amplitude level for short-distance dominated rare meson decays. This allows us to quantify the importance of higher order electroweak effects for these processes, which can be reliably computed and have very small uncertainties from strong interactions. Simultaneously it becomes possible to remove, to some extent, ambiguities in the definition of electroweak parameters describing the strength of FCNC interactions. The corrections we discuss are at the level of a few percent.Comment: 11 pages, LaTeX, 1 eps-figur