Generalized structured additive regression based on Bayesian P-splines

Generalized additive models (GAM) for modelling nonlinear effects of continuous covariates are now well established tools for the applied statistician. In this paper we develop Bayesian GAM's and extensions to generalized structured additive regression based on one or two dimensional P-splines as the main building block. The approach extends previous work by Lang und Brezger (2003) for Gaussian responses. Inference relies on Markov chain Monte Carlo (MCMC) simulation techniques, and is either based on iteratively weighted least squares (IWLS) proposals or on latent utility representations of (multi)categorical regression models. Our approach covers the most common univariate response distributions, e.g. the Binomial, Poisson or Gamma distribution, as well as multicategorical responses. For the first time, we present Bayesian semiparametric inference for the widely used multinomial logit models. As we will demonstrate through two applications on the forest health status of trees and a space-time analysis of health insurance data, the approach allows realistic modelling of complex problems. We consider the enormous flexibility and extendability of our approach as a main advantage of Bayesian inference based on MCMC techniques compared to more traditional approaches. Software for the methodology presented in the paper is provided within the public domain package BayesX

Women, Work, and Motherhood: Changing Employment Penalties for Motherhood in West Germany after 1945 -- A Comparative Analysis of Cohorts Born in 1934-1971

This paper deals with the effects of entry into motherhood on women's employment dynamics. Our analysis is based on the complete lifetime working- and income histories of a 1% sample of all persons born between 1934 and 1971 and employed in West Germany sometime between 1975 and 1995. We use the records of women who were employed before the birth of their first child. We apply a semi-parametric hierarchical Bayesian modeling approach simultaneously including several time scales and further covariates whose effects we estimate by MCMC techniques. We investigate short-term consequences of entry into motherhood and their changes over different birth cohorts and thereby take into account the employment histories before the birth of the first child. We conduct two models differentiating between the simple return to the labor market and the return for at least a certain period in order to measure subsequent employment stability. Our results indicate that a higher extent of employment experience, a stronger attachment to the labor market and an employment in white collar jobs reduces the employment penalty for mothers after the birth of their first child

Penalized additive regression for space-time data: a Bayesian perspective

We propose extensions of penalized spline generalized additive models for analysing 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 own 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 smoothing parameters, are then estimated by using marginal likelihood. We carefully compare both inferential procedures in simulation studies and illustrate them through real data applications. The methodology is available in the open domain statistical package BayesX and as an S-plus/R function

A Laplace Transform Method for Molecular Mass Distribution Calculation from Rheometric Data

Polydisperse linear polymer melts can be microscopically described by the tube model and fractal reptation dynamics, while on the macroscopic side the generalized Maxwell model is capable of correctly displaying most of the rheological behavior. In this paper, a Laplace transform method is derived and different macroscopic starting points for molecular mass distribution calculation are compared to a classical light scattering evaluation. The underlying assumptions comprise the modern understanding on polymer dynamics in entangled systems but can be stated in a mathematically generalized way. The resulting method is very easy to use due to its mathematical structure and it is capable of calculating multimodal molecular mass distributions of linear polymer melts

BayesX: Analysing Bayesian structured additive regression models

There has been much recent interest in Bayesian inference for generalized additive and related models. The increasing popularity of Bayesian methods for these and other model classes is mainly caused by the introduction of Markov chain Monte Carlo (MCMC) simulation techniques which allow the estimation of very complex and realistic models. This paper describes the capabilities of the public domain software BayesX for estimating complex regression models with structured additive predictor. The program extends the capabilities of existing software for semiparametric regression. Many model classes well known from the literature are special cases of the models supported by BayesX. Examples are Generalized Additive (Mixed) Models, Dynamic Models, Varying Coefficient Models, Geoadditive Models, Geographically Weighted Regression and models for space-time regression. BayesX supports the most common distributions for the response variable. For univariate responses these are Gaussian, Binomial, Poisson, Gamma and negative Binomial. For multicategorical responses, both multinomial logit and probit models for unordered categories of the response as well as cumulative threshold models for ordered categories may be estimated. Moreover, BayesX allows the estimation of complex continuous time survival and hazardrate models

Remote Stratigraphic Analysis: Combined TM and AIS Results in the Wind River/bighorn Basin Area, Wyoming

An in-progress study demonstrates the utility of airborne imaging spectrometer (AIS) data for unraveling the stratigraphic evolution of a North American, western interior foreland basin. AIS data are used to determine the stratigraphic distribution of mineralogical facies that are diagnostic of specific depositional environments. After wavelength and amplitude calibration using natural ground targets with known spectral characteristics, AIS data identify calcite, dolomite, gypsum and montmorillonite-bearing strata in the Permian-Cretaceous sequence. Combined AIS and TM results illustrate the feasibility of spectral stratigraphy, remote analysis of stratigraphic sequences