Dependency and false discovery rate: Asymptotics

Some effort has been undertaken over the last decade to provide conditions for the control of the false discovery rate by the linear step-up procedure (LSU) for testing $n$ hypotheses when test statistics are dependent. In this paper we investigate the expected error rate (EER) and the false discovery rate (FDR) in some extreme parameter configurations when $n$ tends to infinity for test statistics being exchangeable under null hypotheses. All results are derived in terms of $p$-values. In a general setup we present a series of results concerning the interrelation of Simes' rejection curve and the (limiting) empirical distribution function of the $p$-values. Main objects under investigation are largest (limiting) crossing points between these functions, which play a key role in deriving explicit formulas for EER and FDR. As specific examples we investigate equi-correlated normal and $t$-variables in more detail and compute the limiting EER and FDR theoretically and numerically. A surprising limit behavior occurs if these models tend to independence.Comment: Published in at http://dx.doi.org/10.1214/009053607000000046 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Thermally activated interface motion in a disordered ferromagnet

We investigate interface motion in disordered ferromagnets by means of Monte Carlo simulations. For small temperatures and driving fields a so-called creep regime is found and the interface velocity obeys an Arrhenius law. We analyze the corresponding energy barrier as well as the field and temperature dependence of the prefactor.Comment: accepted for publication in Computer Physics Communication

On the false discovery rate and an asymptotically optimal rejection curve

In this paper we introduce and investigate a new rejection curve for asymptotic control of the false discovery rate (FDR) in multiple hypotheses testing problems. We first give a heuristic motivation for this new curve and propose some procedures related to it. Then we introduce a set of possible assumptions and give a unifying short proof of FDR control for procedures based on Simes' critical values, whereby certain types of dependency are allowed. This methodology of proof is then applied to other fixed rejection curves including the proposed new curve. Among others, we investigate the problem of finding least favorable parameter configurations such that the FDR becomes largest. We then derive a series of results concerning asymptotic FDR control for procedures based on the new curve and discuss several example procedures in more detail. A main result will be an asymptotic optimality statement for various procedures based on the new curve in the class of fixed rejection curves. Finally, we briefly discuss strict FDR control for a finite number of hypotheses.Comment: Published in at http://dx.doi.org/10.1214/07-AOS569 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Dynamic effect of overhangs and islands at the depinning transition in two-dimensional magnets

With the Monte Carlo methods, we systematically investigate the short-time dynamics of domain-wall motion in the two-dimensional random-field Ising model with a driving field ?DRFIM?. We accurately determine the depinning transition field and critical exponents. Through two different definitions of the domain interface, we examine the dynamics of overhangs and islands. At the depinning transition, the dynamic effect of overhangs and islands reaches maximum. We argue that this should be an important mechanism leading the DRFIM model to a different universality class from the Edwards-Wilkinson equation with quenched disorderComment: 9 pages, 6 figure

Interface Motion in Disordered Ferromagnets

We consider numerically the depinning transition in the random-field Ising model. Our analysis reveals that the three and four dimensional model displays a simple scaling behavior whereas the five dimensional scaling behavior is affected by logarithmic corrections. This suggests that d=5 is the upper critical dimension of the depinning transition in the random-field Ising model. Furthermore, we investigate the so-called creep regime (small driving fields and temperatures) where the interface velocity is given by an Arrhenius law.Comment: some misprints correcte

Deformation texture of aluminium – A grain interaction simulation approach

We present plane strain simulations about the dependence of orientational in-grain subdivision and crystallographic deformation textures in aluminium polycrystals on grain interaction. The predictions are compared to experiments. For the simulations we use a crystal plasticity finite element and different polycrystal homogenization models. One set of finite element simulations is conducted by statistically varying the arrangement of the grains in a polycrystal. Each grain contains 8 integration points and has different neighbor grains in each simulation. The reorientation paths of the 8 integration points in each grain are sampled for the different polycrystal arrangements. For quantifying the influence of the grain neighborhood on subdivision and texture we use a mean orientation concept for the calculation of the orientation spread among the 8 originally identical in-grain orientation points after plastic straining. The results are compared to Taylor-Bishop-Hill-type and Sachs-type models which consider grain interaction on a statistical basis. The progress report reveals five important points about grain interaction. First, the consideration of local grain neighborhood has a significant influence on the reorientation of a grain (up to 20% in terms of its end orientation and its orientation density), but its own initial orientation is more important for its reorientation behavior than its grain neighborhood. Second, the sharpness of the deformation texture is affected by grain interaction leading to an overall weaker texture when compared to results obtained without interaction. Third, the in-grain subdivision of formerly homogeneous grains occurring during straining is strongly dependent on their initial orientation. [...

Creep motion in a random-field Ising model

We analyze numerically a moving interface in the random-field Ising model which is driven by a magnetic field. Without thermal fluctuations the system displays a depinning phase transition, i.e., the interface is pinned below a certain critical value of the driving field. For finite temperatures the interface moves even for driving fields below the critical value. In this so-called creep regime the dependence of the interface velocity on the temperature is expected to obey an Arrhenius law. We investigate the details of this Arrhenius behavior in two and three dimensions and compare our results with predictions obtained from renormalization group approaches.Comment: 6 pages, 11 figures, accepted for publication in Phys. Rev.