Screening for Differentially Expressed Genes: Are Multilevel Models Helpful?

Screening for changes in gene expression across biological conditions using microarrays is now a common tool in biology. Efficient use of these data for identifying important biological hypotheses is inherently a statistical problem. In this paper we present a broad Bayesian multilevel framework for developing computationally fast shrinkage-based screening tools for this purpose. Our scheme makes it easy to adapt the choice of statistics to the goals of the analysis and to the genomic distributions of signal and noise. We empirically investigate the extent to which these shrinkage-based statistics improve performance, and the conditions under which such improvements takes place. Our evaluation uses both extensive simulations and controlled biological experiments. The experimental data include a so-called spike-in experiment, in which the target biological signal is known, and a two-sample experiment, which illustrates the typical conditions in which the methods studied are applied. Our results emphasize two important practical concerns that are not receiving sufficient attention in applied work in this area. First, while shrinkage strategies based on multilevel models are able to improve selection performance, they require careful verification of the assumptions on the relationship between signal and noise. Incorrect specification of this relationship can negatively affect a selection procedure. Because this inter-gene relationship is generally identifiable in genomic experiments, we suggest a simple diagnostic plot to assist model checking. Secondly, no statistic performs optimally across two common categories of experimental goals: selecting genes with large changes, and selecting genes with reliably measured changes. Therefore, careful consideration of analysis goals is critical in the choice of the approach taken

The effect of public funding on research output: the New Zealand Marsden Fund

The Marsden Fund is the premiere funding mechanism for blue skies research in New Zealand. In 2014, $56 million was awarded to 101 research projects chosen from among 1222 applications from researchers at universities, Crown Research Institutes and independent research organizations. This funding mechanism is similar to those in other countries, such as the European Research Council. This research measures the effect of funding receipt from the New Zealand Marsden Fund using a unique dataset of funded and unfunded proposals that includes the evaluation scores assigned to all proposals. This allows us to control statistically for potential bias driven by the Fund’s efforts to fund projects that are expected to be successful, and also to measure the efficacy of the selection process itself. We find that Marsden Funding does increase the scientific output of the funded researchers, but that there is no evidence that the final selection process is able to meaningfully predict the likely success of different proposals

A Numerical Slow Manifold Approach to Model Reduction for Optimal Control of Multiple Time Scale ODE

Time scale separation is a natural property of many control systems that can be ex- ploited, theoretically and numerically. We present a numerical scheme to solve optimal control problems with considerable time scale separation that is based on a model reduction approach that does not need the system to be explicitly stated in singularly perturbed form. We present examples that highlight the advantages and disadvantages of the method