Stochastic Models Based on Molecular Hybridization Theory for Short Oligonucleotide Microarrays

High density oligonucleotide expression arrays are a widely used tool for the measurement of gene expression on a large scale. Affymetrix GeneChip arrays appear to dominate this market. These arrays use short oligonucleotides to probe for genes in an RNA sample. Due to optical noise, non-specific hybridization, probe-specific effects, and measurement error, ad-hoc measures of expression, that summarize probe intensities, can lead to imprecise and inaccurate results. Various researchers have demonstrated that expression measures based on simple statistical models can provide great improvements over the ad-hoc procedure offered by Affymetrix. Recently, physical models based on molecular hybridization theory, have been proposed as useful tools for prediction of, for example, non-specific hybridization. These physical models show great potential in terms of improving existing expression measures. In this paper we demonstrate that the system producing the measured intensities is too complex to be fully described with these relatively simple physical models and we propose empirically motivated stochastic models that compliment the above mentioned molecular hybridization theory to provide a comprehensive description of the data. We discuss how the proposed model can be used to obtain improved measures of expression useful for the data analysts.

Reduced Bayesian Hierarchical Models: Estimating Health Effects of Simultaneous Exposure to Multiple Pollutants

Quantifying the health effects associated with simultaneous exposure to many air pollutants is now a research priority of the US EPA. Bayesian hierarchical models (BHM) have been extensively used in multisite time series studies of air pollution and health to estimate health effects of a single pollutant adjusted for potential confounding of other pollutants and other time-varying factors. However, when the scientific goal is to estimate the impacts of many pollutants jointly, a straightforward application of BHM is challenged by the need to specify a random-effect distribution on a high-dimensional vector of nuisance parameters, which often do not have an easy interpretation. In this paper we introduce a new BHM formulation, which we call "reduced BHM", aimed at analyzing clustered data sets in the presence of a large number of random effects that are not of primary scientific interest. At the first stage of the reduced BHM, we calculate the integrated likelihood of the parameter of interest (e.g. excess number of deaths attributed to simultaneous exposure to high levels of many pollutants). At the second stage, we specify a flexible random-effect distribution directly on the parameter of interest. The reduced BHM overcomes many of the challenges in the specification and implementation of full BHM in the context of a large number of nuisance parameters. In simulation studies we show that the reduced BHM performs comparably to the full BHM in many scenarios, and even performs better in some cases. Methods are applied to estimate location-specific and overall relative risks of cardiovascular hospital admissions associated with simultaneous exposure to elevated levels of particulate matter and ozone in 51 US counties during the period 1999-2005.

Mechanical Properties of Plant Underground Storage Organs and Implications for Dietary Models of Early Hominins

The diet of early human ancestors has received renewed theoretical interest since the discovery of elevated d13C values in the enamel of Australopithecus africanus and Paranthropus robustus. As a result, the hominin diet is hypothesized to have included C4 grass or the tissues of animals which themselves consumed C4 grass. On mechanical grounds, such a diet is incompatible with the dental morphology and dental microwear of early hominins. Most inferences, particularly for Paranthropus, favor a diet of hard or mechanically resistant foods. This discrepancy has invigorated the longstanding hypothesis that hominins consumed plant underground storage organs (USOs). Plant USOs are attractive candidate foods because many bulbous grasses and cormous sedges use C4 photosynthesis. Yet mechanical data for USOs—or any putative hominin food—are scarcely known. To fill this empirical void we measured the mechanical properties of USOs from 98 plant species from across sub-Saharan Africa. We found that rhizomes were the most resistant to deformation and fracture, followed by tubers, corms, and bulbs. An important result of this study is that corms exhibited low toughness values (mean = 265.0 J m-2) and relatively high Young’s modulus values (mean = 4.9 MPa). This combination of properties fits many descriptions of the hominin diet as consisting of hard-brittle objects. When compared to corms, bulbs are tougher (mean = 325.0 J m-2) and less stiff (mean = 2.5 MPa). Again, this combination of traits resembles dietary inferences, especially for Australopithecus, which is predicted to have consumed soft-tough foods. Lastly, we observed the roasting behavior of Hadza hunter-gatherers and measured the effects of roasting on the toughness on undomesticated tubers. Our results support assumptions that roasting lessens the work of mastication, and, by inference, the cost of digestion. Together these findings provide the first mechanical basis for discussing the adaptive advantages of roasting tubers and the plausibility of USOs in the diet of early hominins.

Efficiency of the Sieved-NPMLE in CAR-Missing Data Models

We consider nonparametric missing data models for which the censoring mechanism satisfies coarsening at random and which allow complete observations on the variable X of interest. W show that beyond some empirical process conditions the only essential condition for efficiency of an NPMLE of the distribution of X is that the regions associated with incomplete observations on X contain enough complete observations. This is heuristically explained by describing the EM-algorithm. We provide identifiably of the self-consistency equation and efficiency of the NPMLE in order to make this statement rigorous. The usual kind of differentiability conditions in the proof are avoided by using an identity which holds for the NPMLE of linear parameters in convex models. We provide a bivariate censoring application in which the condition and hence the NPMLE fails, but where other estimators, not based on the NPMLE principle, are highly inefficient. It is shown how to slightly reduce the data so that the conditions hold for the reduced data. The conditions are verified for the univariate censoring, double censored, and Ibragimov-Has'minski models.