Collaborative Research Center (SFB) 386: Statistical Analysis of discrete structures - Applications in Biometrics and Econometrics, University of Munich (LMU) https://hdl.handle.net/10419/157 2026-09-14T01:48:09Z 2026-09-14T01:48:09Z Dargatz, Christiane https://hdl.handle.net/10419/31042 2023-12-18T02:28:41Z 2007-01-01T00:00:00Z

Title: A diffusion approximation for an epidemic model Authors: Dargatz, Christiane Abstract: Influenza is one of the most common and severe diseases worldwide. Devastating epidemics actuated by a new subtype of the influenza A virus occur again and again with the most important example given by the Spanish Flu in 1918/19 with more than 27 million deaths. For the development of pandemic plans it is essential to understand the character of the dissemination of the disease. We employ an extended SIR model for a probabilistic analysis of the spatio-temporal spread of influenza in Germany. The inhomogeneous mixing of the population is taken into account by the introduction of a network of subregions, connected according to Germany's commuter and domestic air traffic. The infection dynamics is described by a multivariate diffusion process, the discussion of which is a major part of this report. We furthermore present likelihood-based estimates of the model parameters.

2007-01-01T00:00:00Z Heim, Susanne https://hdl.handle.net/10419/31074 2023-11-30T02:33:59Z 2007-01-01T00:00:00Z

Title: Wavelets for diffusion tensor imaging Authors: Heim, Susanne Abstract: In this paper, wavelet basis functions are investigated for their suitability for processing and analysing diffusion tensor imaging (DTI) data. First, wavelet theory is introduced and explained by means of 1d and 2d examples (Section 1.1 - 1.3). General thresholding techniques, which serve as regularization concepts for wavelet based models, are presented in Section 1.4. Regularization of DTI data can be performed at two stages, either immediately after acquisition (Wirestam et al., 2006) or after tensor estimation. The latter stage of denoising is outlined in Section 6 together with the incorporation of the positive definiteness constraint using log-Cholesky parametrization. In Section 3, the procedure is examined in a simulation study and compared to standard processing and the space-varying coefficient model (SVCM) based on B-spines (Heim et al., 2007). In addition, a real data example is presented and discussed. Finally, an approach is proposed how a space-varying coefficient model could fairly be adapted to wavelet basis functions. The theoretical parts are based on books of Gencay et al. (2002, Chap. 1, 4-6), Härdle et al. (1998), Ogden (1997) and Jansen (2001) if not stated otherwise. For an introduction to diffusion tensor imaging refer to Heim et al. (2007, Chap. 2).

2007-01-01T00:00:00Z Fahrmeir, Ludwig Kneib, Thomas https://hdl.handle.net/10419/31017 2023-11-03T02:01:17Z 2006-01-01T00:00:00Z

Title: Propriety of posteriors in structured additive regression models: theory and empirical evidence Authors: Fahrmeir, Ludwig; Kneib, Thomas Abstract: Structured additive regression comprises many semiparametric regression models such as generalized additive (mixed) models, geoadditive models, and hazard regression models within a unified framework. In a Bayesian formulation, nonparametric functions, spatial effects and further model components are specified in terms of multivariate Gaussian priors for high-dimensional vectors of regression coefficients. For several model terms, such as penalised splines or Markov random fields, these Gaussian prior distributions involve rank-deficient precision matrices, yielding partially improper priors. Moreover, hyperpriors for the variances (corresponding to inverse smoothing parameters) may also be specified as improper, e.g. corresponding to Jeffery's prior or a flat prior for the standard deviation. Hence, propriety of the joint posterior is a crucial issue for full Bayesian inference in particular if based on Markov chain Monte Carlo simulations. We establish theoretical results providing sufficient (and sometimes necessary) conditions for propriety and provide empirical evidence through several accompanying simulation studies.

2006-01-01T00:00:00Z Czado, Claudia Pflüger, Carolin https://hdl.handle.net/10419/31011 2023-11-03T02:02:41Z 2006-01-01T00:00:00Z

Title: Modeling dependencies between rating categories and their effects on prediction in a credit risk portfolio Authors: Czado, Claudia; Pflüger, Carolin Abstract: The internal-ratings based Basel II approach increases the need for the development of more realistic default probability models. In this paper we follow the approach taken in McNeil and Wendin (2006) by constructing generalized linear mixed models for estimating default probabilities from annual data on companies with different credit ratings. The models considered, in contrast to McNeil and Wendin (2006), allow parsimonious parametric models to capture simultaneously dependencies of the default probabilities on time and credit ratings. Macro-economic variables can also be included. Estimation of all model parameters are facilitated with a Bayesian approach using Markov Chain Monte Carlo methods. Special em- phasis is given to the investigation of predictive capabilities of the models considered. In particular predictable model specifications are used. The empirical study using default data from Standard and Poor gives evidence that the correlation between credit ratings further apart decreases and is higher than the one induced by the autoregressive time dynamics.

2006-01-01T00:00:00Z