Nonparametric Bayesian hazard rate models based on penalized splines

Extensions of the traditional Cox proportional hazard model, concerning the following features are often desirable in applications: Simultaneous nonparametric estimation of baseline hazard and usual fixed covariate effects, modelling and detection of time-varying covariate effects and nonlinear functional forms of metrical covariates, and inclusion of frailty components. In this paper, we develop Bayesian multiplicative hazard rate models for survival and event history data that can deal with these issues in a flexible and unified framework. Some simpler models, such as piecewise exponential models with a smoothed baseline hazard, are covered as special cases. Embedded in the counting process approach, nonparametric estimation of unknown nonlinear functional effects of time or covariates is based on Bayesian penalized splines. Inference is fully Bayesian and uses recent MCMC sampling schemes. Smoothing parameters are an integral part of the model and are estimated automatically. We investigate performance of our approach through simulation studies, and illustrate it with a real data application

Bayesian mapping of brain regions using compound Markov random field priors

Human brain mapping, i.e. the detection of functional regions and their connections, has experienced enormous progress through the use of functional magnetic resonance imaging (fMRI). The massive spatio-temporal data sets generated by this imaging technique impose challenging problems for statistical analysis. Many approaches focus on adequate modeling of the temporal component. Spatial aspects are often considered only in a separate postprocessing step, if at all, or modeling is based on Gaussian random fields. A weakness of Gaussian spatial smoothing is possible underestimation of activation peaks or blurring of sharp transitions between activated and non-activated regions. In this paper we suggest Bayesian spatio-temporal models, where spatial adaptivity is improved through inhomogeneous or compound Markov random field priors. Inference is based on an approximate MCMC technique. Performance of our approach is investigated through a simulation study, including a comparison to models based on Gaussian as well as more robust spatial priors in terms of pixelwise and global MSEs. Finally we demonstrate its use by an application to fMRI data from a visual stimulation experiment for assessing activation in visual cortical areas

Adaptive Gaussian Markov Random Fields with Applications in Human Brain Mapping

Functional magnetic resonance imaging (fMRI) has become the standard technology in human brain mapping. Analyses of the massive spatio-temporal fMRI data sets often focus on parametric or nonparametric modeling of the temporal component, while spatial smoothing is based on Gaussian kernels or random fields. A weakness of Gaussian spatial smoothing is underestimation of activation peaks or blurring of high-curvature transitions between activated and non-activated brain regions. In this paper, we introduce a class of inhomogeneous Markov random fields (MRF) with spatially adaptive interaction weights in a space-varying coefficient model for fMRI data. For given weights, the random field is conditionally Gaussian, but marginally it is non-Gaussian. Fully Bayesian inference, including estimation of weights and variance parameters, is carried out through efficient MCMC simulation. An application to fMRI data from a visual stimulation experiment demonstrates the performance of our approach in comparison to Gaussian and robustified non-Gaussian Markov random field models

Geoadditive Survival Models: A Supplement

This technical report supplements the paper Geoadditive Survival Models (Hennerfeind, Brezger and Fahrmeir, 2005, Revised for JASA). In particular, we describe the simulation study of this paper in greater detail, present additional results for the application, and provide a complete proof of Theorem 1, Corollary 1, as well as the lemmata and corollaries in the appendix

Transiently enhanced interlayer tunneling in optically driven high-Tc superconductors

Recent pump-probe experiments reported an enhancement of superconducting transport along the c axis of underdoped YBa2Cu3O6+δ (YBCO), induced by a midinfrared optical pump pulse tuned to a specific lattice vibration. To understand this transient nonequilibrium state, we develop a pump-probe formalism for a stack of Josephson junctions, and we consider the tunneling strengths in the presence of modulation with an ultrashort optical pulse. We demonstrate that a transient enhancement of the Josephson coupling can be obtained for pulsed excitation and that this can be even larger than in a continuously driven steady state. Especially interesting is the conclusion that the effect is largest when the material is parametrically driven at a frequency immediately above the plasma frequency, in agreement with what is found experimentally. For bilayer Josephson junctions, an enhancement similar to that experimentally is predicted below the critical temperature Tc. This model reproduces the essential features of the enhancement measured below Tc. To reproduce the experimental results above Tc, we will explore extensions of this model, such as in-plane and amplitude fluctuations, elsewhere.Deutsche Forschungsgemeinschaft; SFB 925; EXC 1074; Joachim Herz StiftungFirst author draf

Geoadditive survival models

Survival data often contain geographical or spatial information, such as the residence of individuals. We propose geoadditive survival models for analyzing spatial effects jointly with possibly nonlinear effects of other covariates. Within a unified Bayesian framework, our approach extends the classical Cox model to a more general multiplicative hazard rate model, augmenting the common linear predictor with a spatial component and nonparametric terms for nonlinear effects of time and metrical covariates. Markov random fields and penalized regression splines are used as basic building blocks. Inference is fully Bayesian and uses computationally efficient MCMC sampling schemes. Smoothing parameters are an integral part of the model and are estimated automatically. Perfomance is investigated through simulation studies. We apply our approach to data from a case study in London and Essex that aims to estimate the effect of area of residence and further covariates on waiting times to coronary artery bypass graft (CABG)

Geoadditive survival models

Survival data often contain small-area geographical or spatial information, such as the residence of individuals. In many cases the impact of such spatial effects on hazard rates is of considerable substantive interest. Therefore, extensions of known survival or hazard rate models to spatial models have been suggested recently. Mostly, a spatial component is added to the usual linear predictor of the Cox model. We propose flexible continuous-time geoadditive models, extending the Cox model with respect to several aspects often needed in applications: The common linear predictor is generalized to an additive predictor, including nonparametric components for the log-baseline hazard, time-varying effects and possibly nonlinear effects of continuous covariates or further time scales, and a spatial component for geographical effects. In addition, uncorrelated frailty effects or nonlinear two-way interactions can be incorporated. Inference is developed within a unified fully Bayesian framework. We prefer to use penalized regression splines and Markov random fields as basic building blocks, but geostatistical (kriging) models are also considered. Posterior analysis uses computationally efficient MCMC sampling schemes. Smoothing parameters are an integral part of the model and are estimated automatically. Propriety of posteriors is shown under fairly general conditions, and practical performance is investigated through simulation studies. We apply our approach to data from a case study in London and Essex that aims to estimate the effect of area of residence and further covariates on waiting times to coronary artery bypass graft (CABG). Results provide clear evidence of nonlinear time-varying effects, and considerable spatial variability of waiting times to bypass graft

The Hadwiger theorem on convex functions. I

A complete classification of all continuous, epi-translation and rotation invariant valuations on the space of super-coercive convex functions on ${\mathbb R}^n$ is established. The valuations obtained are functional versions of the classical intrinsic volumes. For their definition, singular Hessian valuations are introduced

Using a nested single-model large ensemble to assess the internal variability of the North Atlantic Oscillation and its climatic implications for central Europe

Central European weather and climate are closely related to atmospheric mass advection triggered by the North Atlantic Oscillation (NAO), which is a relevant index for quantifying internal climate variability on multi-annual timescales. It remains unclear, however, how large-scale circulation variability affects local climate characteristics when downscaled using a regional climate model. In this study, 50 members of a single-model initial-condition large ensemble (LE) of a nested regional climate model are analyzed for a NAO-climate relationship. The overall goal of the study is to assess whether the range of NAO internal variability is represented consistently between the driving global climate model (GCM;the Canadian Earth System Model version 2 - CanESM2) and the nested regional climate model (RCM;the Canadian Regional Climate Model version 5 - CRCM5). Responses of mean surface air temperature and total precipitation to changes in the NAO index value are examined in a central European domain in both CanESM2-LE and CRCM5-LE via Pearson correlation coefficients and the change per unit index change for historical (1981-2010) and future (2070-2099) winters. Results show that statistically robust NAO patterns are found in the CanESM2-LE under current forcing conditions. NAO flow pattern reproductions in the CanESM2-LE trigger responses in the high-resolution CRCM5-LE that are comparable to reanalysis data. NAO-response relationships weaken in the future period, but their intermember spread shows no significant change. The results stress the value of single-model ensembles for the evaluation of internal variability by pointing out the large differences of NAO-response relationships among individual members. They also strengthen the validity of the nested ensemble for further impact modeling using RCM data only, since important large-scale teleconnections present in the driving data propagate properly to the fine-scale dynamics in the RCM

Probing optically silent superfluid stripes in cuprates

Unconventional superconductivity in the cuprates emerges from, or coexists with, other types of electronic order. However, these orders are sometimes invisible because of their symmetry. For example, the possible existence of superfluid charge stripes in the normal state of single layer cuprates cannot be validated with infrared optics, because interlayer tunneling fluctuations vanish on average. Similarly, it is not easy to establish if charge orders are responsible for dynamical decoupling of the superconducting layers over broad ranges of doping and temperatures. Here, we show that TeraHertz pulses can excite nonlinear tunneling currents between linearly de-coupled charge-ordered planes. A giant TeraHertz third harmonic signal is observed in La1.885Ba0.115CuO4 far above Tc=13 K and up to the charge ordering temperature TCO = 55 K. We model these results by considering large order-parameter-phase oscillations in a pair density wave condensate, and show how nonlinear mixing of optically silent tunneling modes can drive large dipole-carrying super-current oscillations. Our results provide compelling experimental support for the presence of hidden superfluid order in the normal state of cuprates. These experiments also underscore the power of nonlinear TeraHertz optics as a sensitive probe of frustrated excitations in quantum solids.Comment: 9 pages main text, 5 figures, 12 page supplementar