Bayesian Geostatistical Design

This paper describes the use of model-based geostatistics for choosing the optimal set of sampling locations, collectively called the design, for a geostatistical analysis. Two types of design situations are considered. These are retrospective design, which concerns the addition of sampling locations to, or deletion of locations from, an existing design, and prospective design, which consists of choosing optimal positions for a new set of sampling locations. We propose a Bayesian design criterion which focuses on the goal of efficient spatial prediction whilst allowing for the fact that model parameter values are unknown. The results show that in this situation a wide range of inter-point distances should be included in the design, and the widely used regular design is therefore not the optimal choice.

Bayesian Hidden Markov Modeling of Array CGH Data

Genomic alterations have been linked to the development and progression of cancer. The technique of Comparative Genomic Hybridization (CGH) yields data consisting of fluorescence intensity ratios of test and reference DNA samples. The intensity ratios provide information about the number of copies in DNA. Practical issues such as the contamination of tumor cells in tissue specimens and normalization errors necessitate the use of statistics for learning about the genomic alterations from array-CGH data. As increasing amounts of array CGH data become available, there is a growing need for automated algorithms for characterizing genomic profiles. Specifically, there is a need for algorithms that can identify gains and losses in the number of copies based on statistical considerations, rather than merely detect trends in the data. We adopt a Bayesian approach, relying on the hidden Markov model to account for the inherent dependence in the intensity ratios. Posterior inferences are made about gains and losses in copy number. Localized amplifications (associated with oncogene mutations) and deletions (associated with mutations of tumor suppressors) are identified using posterior probabilities. Global trends such as extended regions of altered copy number are detected. Since the posterior distribution is analytically intractable, we implement a Metropolis-within-Gibbs algorithm for efficient simulation-based inference. Publicly available data on pancreatic adenocarcinoma, glioblastoma multiforme and breast cancer are analyzed, and comparisons are made with some widely-used algorithms to illustrate the reliability and success of the technique.

A BAYESIAN SHRINKAGE MODEL FOR INCOMPLETE LONGITUDINAL BINARY DATA WITH APPLICATION TO THE BREAST CANCER PREVENTION TRIAL

We consider inference in randomized studies, in which repeatedly measured outcomes may be informatively missing due to drop out. In this setting, it is well known that full data estimands are not identified unless unverified assumptions are imposed. We assume a non-future dependence model for the drop-out mechanism and posit an exponential tilt model that links non-identifiable and identifiable distributions. This model is indexed by non-identified parameters, which are assumed to have an informative prior distribution, elicited from subject-matter experts. Under this model, full data estimands are shown to be expressed as functionals of the distribution of the observed data. To avoid the curse of dimensionality, we model the distribution of the observed data using a Bayesian shrinkage model. In a simulation study, we compare our approach to a fully parametric and a fully saturated model for the distribution of the observed data. Our methodology is motivated and applied to data from the Breast Cancer Prevention Trial.