A two-component model for counts of infectious diseases

We propose a stochastic model for the analysis of time series of disease counts as collected in typical surveillance systems on notifiable infectious diseases. The model is based on a Poisson or negative binomial observation model with two components: a parameter-driven component relates the disease incidence to latent parameters describing endemic seasonal patterns, which are typical for infectious disease surveillance data. An observation-driven or epidemic component is modeled with an autoregression on the number of cases at the previous time points. The autoregressive parameter is allowed to change over time according to a Bayesian changepoint model with unknown number of changepoints. Parameter estimates are obtained through the Bayesian model averaging using Markov chain Monte Carlo techniques. We illustrate our approach through analysis of simulated data and real notification data obtained from the German infectious disease surveillance system, administered by the Robert Koch Institute in Berlin. Software to fit the proposed model can be obtained from http://www.statistik.lmu.de/ approximately mhofmann/twins.     

Model selection and parameter estimation for ion channel recordings with an application to the K + outward-rectifier in barley leaf

We present a statistical method, and its accompanying algorithms, for the selection of a mathematical model of the gating mechanism of an ion channel and for the estimation of the parameters of this model. The method assumes a hidden Markov model that incorporates filtering, colored noise and state-dependent white excess noise for the recorded data. The model selection and parameter estimation are performed via a Bayesian approach using Markov chain Monte Carlo. The method is illustrated by its application to single-channel recordings of the K⁺ outward-rectifier in barley leaf.Acknowledgement The authors thank Sake Vogelzang, Bert van Duijn and Bert de Boer for their helpful advice and useful comments and suggestions.     

Bayesian phylogenetic model selection using reversible jump Markov chain Monte Carlo

A common problem in molecular phylogenetics is choosing a model of DNA substitution that does a good job of explaining the DNA sequence alignment without introducing superfluous parameters. A number of methods have been used to choose among a small set of candidate substitution models, such as the likelihood ratio test, the Akaike Information Criterion (AIC), the Bayesian Information Criterion (BIC), and Bayes factors. Current implementations of any of these criteria suffer from the limitation that only a small set of models are examined, or that the test does not allow easy comparison of non-nested models. In this article, we expand the pool of candidate substitution models to include all possible time-reversible models. This set includes seven models that have already been described. We show how Bayes factors can be calculated for these models using reversible jump Markov chain Monte Carlo, and apply the method to 16 DNA sequence alignments. For each data set, we compare the model with the best Bayes factor to the best models chosen using AIC and BIC. We find that the best model under any of these criteria is not necessarily the most complicated one; models with an intermediate number of substitution types typically do best. Moreover, almost all of the models that are chosen as best do not constrain a transition rate to be the same as a transversion rate, suggesting that it is the transition/transversion rate bias that plays the largest role in determining which models are selected. Importantly, the reversible jump Markov chain Monte Carlo algorithm described here allows estimation of phylogeny (and other phylogenetic model parameters) to be performed while accounting for uncertainty in the model of DNA substitution.     

Population-Based Reversible Jump Markov Chain Monte Carlo

We present an extension of population-based Markov chain MonteCarlo to the transdimensional case. A major challenge is thatof simulating from high- and transdimensional target measures.In such cases, Markov chain Monte Carlo methods may not adequatelytraverse the support of the target; the simulation results willbe unreliable. We develop population methods to deal with suchproblems, and give a result proving the uniform ergodicity ofthese population algorithms, under mild assumptions. This resultis used to demonstrate the superiority, in terms of convergencerate, of a population transition kernel over a reversible jumpsampler for a Bayesian variable selection problem. We also givean example of a population algorithm for a Bayesian multivariatemixture model with an unknown number of components. This isapplied to gene expression data of 1000 data points in six dimensionsand it is demonstrated that our algorithm outperforms some competingMarkov chain samplers. In this example, we show how to combinethe methods of parallel chains (Geyer, 1991), tempering (Geyer& Thompson, 1995), snooker algorithms (Gilks et al., 1994),constrained sampling and delayed rejection (Green & Mira,2001).     

Template mixture models for direct cortical electrical interference data

This paper introduces a statistical approach for high-level spatial analysis when there is little prior information about the shape or location of the region of interest in the underlying image and limited spatial resolution of the available data. Our work was motivated by a functional brain mapping technique called direct cortical electrical interference (DCEI) that gives binary observations at multiple sites throughout the brain. We estimate an underlying, binary spatial response function using a mixture of an unknown number of simple geometrical shapes (e.g. circles) with unknown centers and sizes to be estimated. Inference is made using reversible jump Markov chain Monte Carlo. The approach is illustrated with simulated examples and a real example with DCEI data.     

Bayesian Updating of Model-Based Risk Estimates Using Imperfect Public Health Surveillance Data

Model-based estimation of the human health risks resulting from exposure to environmental contaminants can be an important tool for structuring public health policy. Due to uncertainties in the modeling process, the outcomes of these assessments are usually probabilistic representations of a range of possible risks. In some cases, health surveillance data are available for the assessment population over all or a subset of the risk projection period and this additional information can be used to augment the model-based estimates. We use a Bayesian approach to update model-based estimates of health risks based on available health outcome data. Updated uncertainty distributions for risk estimates are derived using Monte Carlo sampling, which allows flexibility to model realistic situations including measurement error in the observable outcomes. We illustrate the approach by using imperfect public health surveillance data on lung cancer deaths to update model-based lung cancer mortality risk estimates in a population exposed to ionizing radiation from a uranium processing facility.