Nonlinear sequential designs for logistic item response theory models with applications to computerized adaptive tests

Computerized adaptive testing is becoming increasingly popular due to advancement of modern computer technology. It differs from the conventional standardized testing in that the selection of test items is tailored to individual examinee's ability level. Arising from this selection strategy is a nonlinear sequential design problem. We study, in this paper, the sequential design problem in the context of the logistic item response theory models. We show that the adaptive design obtained by maximizing the item information leads to a consistent and asymptotically normal ability estimator in the case of the Rasch model. Modifications to the maximum information approach are proposed for the two- and three-parameter logistic models. Similar asymptotic properties are established for the modified designs and the resulting estimator. Examples are also given in the case of the two-parameter logistic model to show that without such modifications, the maximum likelihood estimator of the ability parameter may not be consistent.Comment: Published in at http://dx.doi.org/10.1214/08-AOS614 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Higgs-μ\mu-τ\tau Coupling at High and Low Energy Colliders

There is no tree-level flavor changing neutral current (FCNC) in the standard model (SM) which contains only one Higgs doublet. If more Higgs doublets are introduced for various reasons, the tree level FCNC would be inevitable except extra symmetry was imposed. Therefore FCNC processes are the excellent probes for the physics beyond the SM (BSM). In this paper, we studied the lepton flavor violated (LFV) decay processes $h\rightarrow\mu\tau$ and $\tau\rightarrow\mu\gamma$ induced by Higgs-$\mu$-$\tau$ vertex. For $\tau\rightarrow\mu\gamma$, its branching ratio is also related to the $ht\bar{t}$, $h\tau^+\tau^-$ and $hW^+W^-$ vertices. We categorized the BSM into two scenarios for the Higgs coupling strengths near or away from SM. For the latter scenario, we took the spontaneously broken two Higgs doublet model (Lee model) as an example. We considered the constraints by recent data from LHC and B factories, and found that the measurements gave weak constraints. At LHC Run II, $h\rightarrow\mu\tau$ will be confirmed or set stricter limit on its branching ratio. Accordingly, $\textrm{Br}(\tau\rightarrow\mu\gamma)\lesssim\mathcal{O}(10^{-10}-10^{-8})$ for general chosen parameters. For the positive case, $\tau\rightarrow\mu\gamma$ can be discovered with $\mathcal{O}(10^{10})$ $\tau$ pair samples at SuperB factory, Super $\tau$-charm factory and new Z-factory. The future measurements for $\textrm{Br}(h\rightarrow\mu\tau)$ and $\textrm{Br}(\tau\rightarrow\mu\gamma)$ will be used to distinguish these two scenarios or set strict constraints on the correlations among different Higgs couplings, please see Table II in the text for details.Comment: 18 pages, 10 figures, 2 table; more references added; more discussions about cancellation in the amplitude added accoeding to the referee's suggestion

Localization of U(1)U(1) gauge vector field on flat branes with five-dimension (asymptotic) AdS5_{5} spacetime

In order to localize $U(1)$ gauge vector field on Randall-Sundrum-like braneworld model with infinite extra dimension, we propose a new kind of non-minimal coupling between the $U(1)$ gauge field and the gravity. We propose three kinds of coupling methods and they all support the localization of zero mode. In addition, one of them can support the localization of massive modes. Moreover, the massive tachyonic modes can be excluded. And our method can be used not only in the thin braneword models but also in the thick ones.Comment: Added acknowledgments to the refree. Appeared on JHE