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

Genetic analysis reveals the complex structure of HIV-1 transmission within defined risk groups

We explored the epidemic history of HIV-1 subtype B in the United Kingdom using statistical methods that infer the population history of pathogens from sampled gene sequence data. Phylogenetic analysis of HIV-1 pol gene sequences from Britain showed at least six large transmission chains, indicating a genetically variable, but epidemiologically homogeneous, epidemic among men having sex with men. Through coalescent-based analysis we showed that these chains arose through separate introductions of subtype B strains into the United Kingdom in the early-to-mid 1980s. After an initial period of exponential growth, the rate of spread generally slowed in the early 1990s, which is more likely to correlate with behaviour change than with reduced infectiousness resulting from highly active antiretroviral therapy. Our results provide new insights into the complexity of HIV-1 epidemics that must be considered when developing HIV monitoring and prevention initiatives