Beyond first-order asymptotics for Cox regression

To go beyond standard first-order asymptotics for Cox regression, we develop parametric bootstrap and second-order methods. In general, computation of $P$-values beyond first order requires more model specification than is required for the likelihood function. It is problematic to specify a censoring mechanism to be taken very seriously in detail, and it appears that conditioning on censoring is not a viable alternative to that. We circumvent this matter by employing a reference censoring model, matching the extent and timing of observed censoring. Our primary proposal is a parametric bootstrap method utilizing this reference censoring model to simulate inferential repetitions of the experiment. It is shown that the most important part of improvement on first-order methods - that pertaining to fitting nuisance parameters - is insensitive to the assumed censoring model. This is supported by numerical comparisons of our proposal to parametric bootstrap methods based on usual random censoring models, which are far more unattractive to implement. As an alternative to our primary proposal, we provide a second-order method requiring less computing effort while providing more insight into the nature of improvement on first-order methods. However, the parametric bootstrap method is more transparent, and hence is our primary proposal. Indications are that first-order partial likelihood methods are usually adequate in practice, so we are not advocating routine use of the proposed methods. It is however useful to see how best to check on first-order approximations, or improve on them, when this is expressly desired.Comment: Published at http://dx.doi.org/10.3150/13-BEJ572 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Protein Design is NP-hard

Biologists working in the area of computational protein design have never doubted the seriousness of the algorithmic challenges that face them in attempting in silico sequence selection. It turns out that in the language of the computer science community, this discrete optimization problem is NP-hard. The purpose of this paper is to explain the context of this observation, to provide a simple illustrative proof and to discuss the implications for future progress on algorithms for computational protein design

Bodies of constant stress experiencing forces of orbital flight

Bodies of constant stress experiencing orbital flight centrifugal and gravitational force

Pseudacris clarkii

Number of Pages: 3Integrative BiologyGeological Science

Analysis of Adjoint Error Correction for Superconvergent Functional Estimates

Earlier work introduced the notion of adjoint error correction for obtaining superconvergent estimates of functional outputs from approximate PDE solutions. This idea is based on a posteriori error analysis suggesting that the leading order error term in the functional estimate can be removed by using an adjoint PDE solution to reveal the sensitivity of the functional to the residual error in the original PDE solution. The present work provides a priori error analysis that correctly predicts the behaviour of the remaining leading order error term. Furthermore, the discussion is extended from the case of homogeneous boundary conditions and bulk functionals, to encompass the possibilities of inhomogeneous boundary conditions and boundary functionals. Numerical illustrations are provided for both linear and nonlinear problems.\ud \ud This research was supported by EPSRC under grant GR/K91149, and by NASA/Ames Cooperative Agreement No. NCC 2-5431

Stop Co-Annihilation in the Minimal Supersymmetric Standard Model Revisited

We re-examine the stop co-annihilation scenario of the Minimal Supersymmetric Standard Model, wherein a bino-like lightest supersymmetric particle has a thermal relic density set by co-annihilations with a scalar partner of the top quark in the early universe. We concentrate on the case where only the top partner sector is relevant for the cosmology, and other particles are heavy. We discuss the cosmology with focus on low energy parameters and an emphasis on the implications of the measured Higgs boson mass and its properties. We find that the irreducible direct detection signal correlated with this cosmology is generically well below projected experimental sensitivity, and in most cases lies below the neutrino background. A larger, detectable, direct detection rate is possible, but is unrelated to the co-annihilation cosmology. LHC searches for compressed spectra are crucial for probing this scenario