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"Fahrmeir, L"
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Spatial quantitative analysis of fluorescently labeled nuclear structures: Problems, methods, pitfalls
The vast majority of microscopic data in biology of the cell nucleus is currently collected using fluorescence microscopy, and most of these data are subsequently subjected to quantitative analysis. The analysis process unites a number of steps, from image acquisition to statistics, and at each of these steps decisions must be made that may crucially affect the conclusions of the whole study. This often presents a really serious problem because the researcher is typically a biologist, while the decisions to be taken require expertise in the fields of physics, computer image analysis, and statistics. The researcher has to choose between multiple options for data collection, numerous programs for preprocessing and processing of images, and a number of statistical approaches. Written for biologists, this article discusses some of the typical problems and errors that should be avoided. The article was prepared by a team uniting expertise in biology, microscopy, image analysis, and statistics. It considers the options a researcher has at the stages of data acquisition (choice of the microscope and acquisition settings), preprocessing (filtering, intensity normalization, deconvolution), image processing (radial distribution, clustering, co-localization, shape and orientation of objects), and statistical analysis.
Journal Article
Spike-and-Slab Priors for Function Selection in Structured Additive Regression Models
Structured additive regression (STAR) provides a general framework for complex Gaussian and non-Gaussian regression models, with predictors comprising arbitrary combinations of nonlinear functions and surfaces, spatial effects, varying coefficients, random effects, and further regression terms. The large flexibility of STAR makes function selection a challenging and important task, aiming at (1) selecting the relevant covariates, (2) choosing an appropriate and parsimonious representation of the impact of covariates on the predictor, and (3) determining the required interactions. We propose a spike-and-slab prior structure for function selection that allows to include or exclude single coefficients as well as blocks of coefficients representing specific model terms. A novel multiplicative parameter expansion is required to obtain good mixing and convergence properties in a Markov chain Monte Carlo simulation approach and is shown to induce desirable shrinkage properties. In simulation studies and with (real) benchmark classification data, we investigate sensitivity to hyperparameter settings and compare performance to competitors. The flexibility and applicability of our approach are demonstrated in an additive piecewise exponential model with time-varying effects for right-censored survival times of intensive care patients with sepsis. Geoadditive and additive mixed logit model applications are discussed in an extensive online supplement.
Journal Article
Fiber Tracking from DTI Using Linear State Space Models: Detectability of the Pyramidal Tract
Diffusiontensor imaging (DTI) is an emerging and promising tool to provide information about the course of white matter fiber tracts in the human brain. Based on specific acquisition schemes, diffusion tensor data resemble local fiber orientations allowing for a reconstruction of the fiber bundles. Current techniques to calculate fascicles range from simple heuristic tracking solutions to Bayesian and differential equations approaches. Most methods are based only on local diffusion information, often resulting in bending or kinking fiber paths in voxels with reduced diffusion properties. In this article we present a new tracking approach based on linear state space models encompassing an inherent smoothness criterion to avoid too wiggly tracked fiber bundles. The new technique will be described formally and tested on simulated and real data. The performance tests are focused on the pyramidal tract, where we employed a test–retest study and a group comparison in healthy subjects. Anatomical course was confirmed in a patient with selective degeneration of the pyramidal tract. The potential of the presented technique for improved neurosurgical planning is demonstrated by visualization of a tumor-induced displacement of the motor pathways. The paper closes with a thorough discussion of perspectives and limitations of the new tracking approach.
Journal Article
Adaptive Gaussian Markov random fields with applications in human brain mapping
Functional magnetic resonance imaging has become a standard technology in human brain mapping. Analyses of the massive spatiotemporal functional magnetic resonance imaging data sets often focus on parametric or non-parametric modelling of the temporal component, whereas 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 regions of the brain. To improve spatial adaptivity, we introduce a class of inhomogeneous Markov random fields with stochastic interaction weights in a space-varying coefficient model. 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, can be carried out through efficient Markov chain Monte Carlo simulation. Although motivated by the analysis of functional magnetic resonance imaging data, the methodological development is general and can also be used for spatial smoothing and regression analysis of areal data on irregular lattices. An application to stylized artificial data and to real functional magnetic resonance imaging data from a visual stimulation experiment demonstrates the performance of our approach in comparison with Gaussian and robustified non-Gaussian Markov random-field models.
Journal Article
Bayesian Spatiotemporal Inference in Functional Magnetic Resonance Imaging
Mapping of the human brain by means of functional magnetic resonance imaging (fMRI) is an emerging field in cognitive and clinical neuroscience. Current techniques to detect activated areas of the brain mostly proceed in two steps. First, conventional methods of correlation, regression, and time series analysis are used to assess activation by a separate, pixelwise comparison of the fMRI signal time courses to the reference function of a presented stimulus. Spatial aspects caused by correlations between neighboring pixels are considered in a separate second step, if at all. The aim of this article is to present hierarchical Bayesian approaches that allow one to simultaneously incorporate temporal and spatial dependencies between pixels directly in the model formulation. For reasons of computational feasibility, models have to be comparatively parsimonious, without oversimplifying. We introduce parametric and semiparametric spatial and spatiotemporal models that proved appropriate and illustrate their performance applied to visual fMRI data.
Journal Article
External forcing of earthquake swarms at Alpine regions: example from a seismic meteorological network at Mt. Hochstaufen SE-Bavaria
In the last few years, it has been shown that above-average rainfall and the following diffusion of excess water into subsurface structures is able to trigger earthquake swarms in the uppermost brittle portion of the Earth's crust. However, there is still an ongoing debate on whether the crust already needs to be in a critical-to-failure state or whether it is sufficient that water is transported rapidly within channels and veins of karst or similar geological formations to the underlying, earthquake-generating layers. Also unknown is the role of other forcing mechanisms, possible co-variables and probably necessary tectonic loading in the triggering process of earthquakes. Because of these problems, we do not use an explicit physical model but instead analyze the meteorological and geophysical data via sophisticated statistical models. \\\newline We are interested in the influence of a more complete set of possible forcing parameters, including the influence of synthetic earth tides, on the occurrence of earthquake swarms. In this context, regression models are the adequate tool, since the calculation of simple correlations can be confounded by the other variables. Since our outcome variable (the number of quakes) is a count, we use Poisson regression models that include the plausible assumption of a Poisson distribution for the counts. For this study, we use nearly continuous recordings of a seismic and meteorological network in the years 2002–2008 at Mt. Hochstaufen in SE-Bavaria. Our non-linear regression model reveals correlations between external forces and the triggering of earthquakes. In addition to the still dominant influence of rainfall, theoretical estimated tidal tilt show some weak influence on the swarm generation. However, the influence of the modeled trend functions shows that rain is by far not the most important forcing mechanism present in the data.
Journal Article
Some asymptotic results on generalized penalized spline smoothing
The paper discusses asymptotic properties of penalized spline smoothing if the spline basis increases with the sample size. The proof is provided in a generalized smoothing model allowing for non-normal responses. The results are extended in two ways. First, assuming the spline coefficients to be a priori normally distributed links the smoothing framework to generalized linear mixed models. We consider the asymptotic rates such that the Laplace approximation is justified and the resulting fits in the mixed model correspond to penalized spline estimates. Secondly, we make use of a fully Bayesian viewpoint by imposing an a priori distribution on all parameters and coefficients. We argue that with the postulated rates at which the spline basis dimension increases with the sample size the posterior distribution of the spline coefficients is approximately normal. The validity of this result is investigated in finite samples by comparing Markov chain Monte Carlo results with their asymptotic approximation in a simulation study.
Journal Article
Bayesian Modeling of the Hemodynamic Response Function in BOLD fMRI
In functional magnetic resonance imaging (fMRI), modeling the complex link between neuronal activity and its hemodynamic response via the neurovascular coupling requires an elaborate and sensitive response model. Methods based on physiologic assumptions as well as direct, descriptive models have been proposed. The focus of this study is placed on such a direct approach that allows for a robust pixelwise determination of hemodynamic characteristics, such as time to peak or the poststimulus undershoot. A Bayesian procedure is presented that can easily be adapted to different hemodynamic properties in question and can be estimated without numerical problems known from nonlinear optimization algorithms. The usefulness of the model is demonstrated by thorough analyzes of the poststimulus undershoot in visual and acoustic stimulation paradigms. Further, we show the capability of this approach to improve analysis of fMRI data in altered hemodynamic conditions.
Journal Article
PENALIZED STRUCTURED ADDITIVE REGRESSION FOR SPACE-TIME DATA: A BAYESIAN PERSPECTIVE
We propose extensions of penalized spline generalized additive models for analyzing space-time regression data and study them from a Bayesian perspective. Non-linear effects of continuous covariates and time trends are modelled through Bayesian versions of penalized splines, while correlated spatial effects follow a Markov random field prior. This allows to treat all functions and effects within a unified general framework by assigning appropriate priors with different forms and degrees of smoothness. Inference can be performed either with full (FB) or empirical Bayes (EB) posterior analysis. FB inference using MCMC techniques is a slight extension of previous work. For EB inference, a computationally efficient solution is developed on the basis of a generalized linear mixed model representation. The second approach can be viewed as posterior mode estimation and is closely related to penalized likelihood estimation in a frequentist setting. Variance components, corresponding to inverse smoothing parameters, are then estimated by marginal likelihood. We carefully compare both inferential procedures in simulation studies and illustrate them through data applications. The methodology is available in the open domain statistical package BayesX and as an S-plus/R function.
Journal Article