Podcasts about gaussian markov

Dynamic imaging series acquired in medical and biological research are often analyzed with the help of compartment models. Compartment models provide a parametric, nonlinear function of interpretable, kinetic parameters describing how some concentration of interest evolves over time. Aiming to estimate the kinetic parameters, this leads to a nonlinear regression problem. In many applications, the number of compartments needed in the model is not known from biological considerations but should be inferred from the data along with the kinetic parameters. As data from medical and biological experiments are often available in the form of images, the spatial data structure of the images has to be taken into account. This thesis addresses the problem of parameter estimation and model selection in compartment models. Besides a penalized maximum likelihood based approach, several Bayesian approaches-including a hierarchical model with Gaussian Markov random field priors and a model state approach with flexible model dimension-are proposed and evaluated to accomplish this task. Existing methods are extended for parameter estimation and model selection in more complex compartment models. However, in nonlinear regression and, in particular, for more complex compartment models, redundancy issues may arise. This thesis analyzes difficulties arising due to redundancy issues and proposes several approaches to alleviate those redundancy issues by regularizing the parameter space. The potential of the proposed estimation and model selection approaches is evaluated in simulation studies as well as for two in vivo imaging applications: a dynamic contrast enhanced magnetic resonance imaging (DCE-MRI) study on breast cancer and a study on the binding behavior of molecules in living cell nuclei observed in a fluorescence recovery after photobleaching (FRAP) experiment.

We develop contrasting spatio-temporal models for two weather variables: solar radiation and rainfall. For solar radiation the aim is to assess the performance of area networks of photo-voltaic cells. Although radiation measured at a sufficiently fine temporal scale has a bimodal marginal distribution (Glasbey, 2001), averages of 10-minute or longer duration can be transformed to be approximately Gaussian, and we fit a spatio-temporal auto-regressive moving average (STARMA) process (Glasbey and Allcroft, 2007). For rainfall, the aim is to disaggregate to a finer spatial scale than that observed. To overcome the difficulty that the marginal distribution of hourly rainfall has a singularity at zero and so is highly non-Gaussian, we apply a monotonic transformation. This defines a latent Gaussian variable, with zero rainfall corresponding to censored values below a threshold, which we model using a spatio-temporal Gaussian Markov random field (Allcroft and Glasbey, 2003). For both models, computations are simplified by approximating space by a torus and using Fourier transforms. Allcroft, D.J. and Glasbey, C.A. (2003). A latent Gaussian Markov random field model for spatio-temporal rainfall disaggregation. Applied Statistics, 52, 487-498. Glasbey CA (2001). Nonlinear autoregressive time series with multivariate Gaussian mixtures as marginal distributions. Applied Statistics, 50, 143-154. Glasbey, C.A. and Allcroft, D.J. (2007). A STARMA model for solar radiation. Available at http://www.bioss.sari.ac.uk/staff/chris.html : http://www.bioss.sari.ac.uk/staff/chris.html Chris Glasbey - Biomathematics and Statistics Scotland Bande son disponible au format mp3 Durée : 51 mn

Models for infectious disease surveillance counts have to take into account the specific characteristics of this type of data. While showing a regular, often seasonal, pattern over long time periods, there are occasional irregularities or outbreaks. A model which is a compromise between mechanistic models and empirical models is proposed. A key idea is to distinguish between an endemic and an epidemic component, which allows to separate the regular pattern from the irregularities and outbreaks. This is of particular advantage for outbreak detection in public health surveillance. While the endemic component is parameter-driven, the epidemic component is based on observationdriven approaches, including an autoregression on past observations. A particular challenge of infectious disease counts is the modelling of the outbreaks and irregularities in the data. We model the autoregressive parameter of the epidemic component by a Bayesian changepoint model, which shows an adaptive amount of smoothing, and is able to model the jumps and fast increases as well as the smooth decreases in the data. While the model can be used as a generic approach for infectious disease counts, it is particularly suited for outbreak detection in public health surveillance. Furthermore, the predictive qualities of the Bayesian changepoint model allow for short term predictions of the number of disease cases, which are of particular public health interest. A sequential update using a particle filter is provided, that can be used for a prospective analysis of the changepoint model conditioning on fixed values for the other parameters, which is of particular advantage for public health surveillance. A suitable multivariate extension is provided, that is able to explain the interactions between units, e.g. age groups or spatial regions. An application to influenza and meningococcal disease data shows that the occasional outbreaks of meningococcal disease can largely be explained by the influence of influenza on meningococcal disease. The risk of a future meningococcal disease outbreak caused by influenza can be predicted. The comparison of the different models, including a model based on Gaussian Markov random fields shows that the inclusion of the epidemic component as well as a time varying epidemic parameter improves the fit and the predictive qualities of the model.

In geographical epidemiology, disease counts are typically available in discrete spatial units and at discrete time-points. For example, surveillance data on infectious diseases usually consists of weekly counts of new infections in pre-defined geographical areas. Similarly, but on a different time-scale, cancer registries typically report yearly incidence or mortality counts in administrative regions. A major methodological challenge lies in building realistic models for space-time interactions on discrete irregular spatial graphs. In this paper, we will discuss an observation-driven approach, where past observed counts in neighbouring areas enter directly as explanatory variables, in contrast to the parameter-driven approach through latent Gaussian Markov random fields (Rue and Held, 2005) with spatio-temporal structure. The main focus will lie on the demonstration of the spread of influenza in Germany, obtained through the design and simulation of a spatial extension of the classical SIR model (Hufnagel et al., 2004).

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.

This thesis is concerned with the analysis of spatial and temporal structures of epidemiological data using modern Bayes techniques. Mainly autoregressive distributions as Gaussian Markov random fields or random walks are used as smoothing priors. Such extensive models can be estimated using MCMC methods only. Some effective algorithms are introduced to get estimates in acceptable time. Especially for space time interactions such algorithms are essential. As example spatial Bayesian models are applied for wildlife disease incidence data. Discrete and continous frameworks for spatial analysis are compared on a data set on infant mortality cases. Age-period-cohort models are discussed in detail and an extension for spatial data is presented. Finally a stochastic model for space time data on infectious diseases is described.

We propose a full model-based framework for a statistical analysis of incidence or mortality count data stratified by age, period and space, with specific inclusion of additional cohort effects. The setup will be fully Bayesian based on a series of Gaussian Markov random field priors for each of the components. Additional space-time interactions will be either modelled as space-period or space-cohort effects. Statistical inference is based on efficient algorithms to block update Gaussian Markov random fields, which have recently been proposed in the literature. We illustrate our approach in an analysis of stomach cancer data in West Germany.

Gaussian Markov random field (GMRF) models are commonly used to model spatial correlation in disease mapping applications. For Bayesian inference by MCMC, so far mainly single-site updating algorithms have been considered. However, convergence and mixing properties of such algorithms can be extremely bad due to strong dependencies of parameters in the posterior distribution. In this paper, we propose various block sampling algorithms in order to improve the MCMC performance. The methodology is rather general, allows for non-standard full conditionals, and can be applied in a modular fashion in a large number of different scenarios. For illustration we consider three different models: two formulations for spatial modelling of a single disease (with and without additional unstructured parameters respectively), and one formulation for the joint analysis of two diseases. We apply the proposed algorithms to two datasets known from the literature. The results indicate that the largest benefits are obtained if parameters and the corresponding hyperparameter are updated jointly in one large block. In certain situations, even updating of all or nearly all parameters in one block may be necessary. Implementation of such block algorithms is surprisingly easy using methods for fast sampling of Gaussian Markov random fields (Rue, 2000). By comparison, estimates of the relative risk and related quantities, such as the posterior probability of an exceedence relative risk, based on single-site updating, can be rather misleading, even for very long runs. Our results may have wider relevance for efficient MCMC simulation in hierarchical models with Markov random field components.