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Quasi-periodic signals, which look like sine waves with variable frequency and amplitude, are common in nature and society. Examples that will be analyzed in this paper are sounds of crickets, counts of sunspots, movements of ocean currents, and brightness of variable stars. Euler’s formula for the complex logarithm, combined with smoothly changing real and imaginary components, provides a powerful...
Although the literature on varying coefficient models (VCMs) is vast, we believe that there remains room to make these models more widely accessible and provide a unified and practical implementation for a variety of complex data settings. The adaptive nature and strength of P-spline VCMs allow a full range of models: from simple to additive structures, from standard to generalized linear models,...
The paper describes the link between penalized spline smoothing and Linear Mixed Models and how these two models form a practical and theoretically interesting partnership. As offspring of this partnership one can not only estimate the smoothing parameter in a Maximum Likelihood framework but also utilize the Mixed Model technology to derive numerically handy solutions to more general questions and...
The paper is concerned with Bayesian analysis under prior-data conflict, i.e. the situation when observed data are rather unexpected under the prior (and the sample size is not large enough to eliminate the influence of the prior). Two approaches for Bayesian linear regression modeling based on conjugate priors are considered in detail, namely the standard approach also described in Fahrmeir et al...
Modern statistics has developed numerous methods for linear and nonlinear regression models, but the correct treatment of model uncertainty is still a difficult task. One approach is model selection, where, usually in a stepwise procedure, an optimal model is searched with respect to some (asymptotic) criterion such as AIC or BIC. A draw back of this approach is, that the reported post model selection...
Model criticism and comparison of Bayesian hierarchical models is often based on posterior or leave-one-out cross-validatory predictive checks. Cross-validatory checks are usually preferred because posterior predictive checks are difficult to assess and tend to be too conservative. However, techniques for statistical inference in such models often try to avoid full (manual) leave-one-out cross-validation,...
The paper introduces two new data augmentation algorithms for sampling the parameters of a binary or multinomial logit model from their posterior distribution within a Bayesian framework. The new samplers are based on rewriting the underlying random utility model in such away that only differences of utilities are involved. As a consequence, the error term in the logit model has a logistic distribution...
We develop generalized semiparametric regression models for exponential family and hazard regression where multiple covariates are measured with error and the functional form of their effects remains unspecified. The main building blocks in our approach are Bayesian penalized splines and Markov chain Monte Carlo simulation techniques. These enable a modular and numerically efficient implementation...
In this paper, we use geoadditive semiparametric regression models to study the determinants of chronic undernutrition of boys and girls in India in 1998/99. A particular focus of our paper is to explain the strong regional pattern in undernutrition and sex differences in determinants of undernutrition. We find that determinants associated with competition for household resources and cultural factors...
Spatially structured additivemodels offer the flexibility to estimate regression relationships for spatially and temporally correlated data. Here, we focus on the estimation of conditional deer browsing probabilities in the National Park “Bayerischer Wald”. The models are fitted using a componentwise boosting algorithm. Smooth and non-smooth base learners for the spatial component of the models are...
A likelihood-based boosting approach for fitting generalized linear mixed models is presented. In contrast to common procedures it can be used in highdimensional settings where a large number of potentially influential explanatory variables is available. Constructed as a componentwise boosting method it is able to perform variable selection with the complexity of the resulting estimator being determined...
The measurement of the attitude towards statistics and the relationship between the attitude towards statistics and several socio-demographic and educational factors was investigated in a survey on over 600 students of the Ludgwig-Maximilians-Universität (LMU). The attitude towards statistics was measured by means of the Affect and Cognitive Competence scales of the Survey of Attitudes Towards Statistics...
Graphical models are a powerful tool to analyze multivariate data sets that allow to reveal direct and indirect relationships and to visualize the association structure in a graph. As with any statistical analysis, however, the obtained results partly reflect the uncertainty being inherent in any type of data and depend on the selected variables to be included in the analysis, the coding of these...
Astrategy for testing differential conditional independence structures (CIS) between two graphs is introduced. The graphs have the same set of nodes and are estimated from data sampled under two different conditions. The test uses the entire pathplot in a Lasso regression as the information on how a node connects with the remaining nodes in the graph. The interpretation of the paths as random...
Dependence modelling and estimation is a key issue in the assessment of financial risk. It is common knowledge meanwhile that the multivariate normal model with linear correlation as its natural dependence measure is by no means an ideal model. We suggest a large class of models and a dependence function, which allows us to capture the complete extreme dependence structure of a portfolio. We also...
Ordinal stochastic volatility (OSV) models were recently developed and fitted by Müller & Czado (2009) to account for the discreteness of financial price changes, while allowing for stochastic volatility (SV). The model allows for exogenous factors both on the mean and volatility level. A Bayesian approach using Markov Chain Monte Carlo (MCMC) is followed to facilitate estimation in these parameter...
Over the last couple of years we could observe a strong growth of copula based credit portfolio models. So far the major interest has revolved the ability of certain copula families to map specific phenomena such as default clustering or the evolution of prices (e.g., credit derivatives prices). Still few questions have been posed regarding copula selection. This is surprising as the problem of estimating...
The integer autoregressive model of order p can be employed for the analysis of discrete–valued time series data. It can be shown, under some conditions, that its correlation structure is identical to that of the usual autoregressive process. The model is usually fitted by the method of least squares. However, consider an alternative estimation scheme, which is based on minimizing the least squares...
The Gaussian stochastic volatility model is extended to allow for periodic autoregressions (PAR) in both the level and log-volatility process. Each PAR is represented as a first order vector autoregression for a longitudinal vector of length equal to the period. The periodic stochastic volatility model is therefore expressed as a multivariate stochastic volatility model. Bayesian posterior inference...
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