Meta-Analysis of Mid-p-Values: Some New Results based on the Convex Order.

The mid-p-value is a proposed improvement on the ordinary p-value for the case where the test statistic is partially or completely discrete. In this case, the ordinary p-value is conservative, meaning that its null distribution is larger than a uniform distribution on the unit interval, in the usual stochastic order. The mid-p-value is not conservative. However, its null distribution is dominated by the uniform distribution in a different stochastic order, called the convex order. The property leads us to discover some new finite-sample and asymptotic bounds on functions of mid-p-values, which can be used to combine results from different hypothesis tests conservatively, yet more powerfully, using mid-p-values rather than p-values. Our methodology is demonstrated on real data from a cyber-security application.

A Bayesian cluster analysis method for single-molecule localization microscopy data.

Cell function is regulated by the spatiotemporal organization of the signaling machinery, and a key facet of this is molecular clustering. Here, we present a protocol for the analysis of clustering in data generated by 2D single-molecule localization microscopy (SMLM)-for example, photoactivated localization microscopy (PALM) or stochastic optical reconstruction microscopy (STORM). Three features of such data can cause standard cluster analysis approaches to be ineffective: (i) the data take the form of a list of points rather than a pixel array; (ii) there is a non-negligible unclustered background density of points that must be accounted for; and (iii) each localization has an associated uncertainty in regard to its position. These issues are overcome using a Bayesian, model-based approach. Many possible cluster configurations are proposed and scored against a generative model, which assumes Gaussian clusters overlaid on a completely spatially random (CSR) background, before every point is scrambled by its localization precision. We present the process of generating simulated and experimental data that are suitable to our algorithm, the analysis itself, and the extraction and interpretation of key cluster descriptors such as the number of clusters, cluster radii and the number of localizations per cluster. Variations in these descriptors can be interpreted as arising from changes in the organization of the cellular nanoarchitecture. The protocol requires no specific programming ability, and the processing time for one data set, typically containing 30 regions of interest, is ∼18 h; user input takes ∼1 h.

Bayesian cluster identification in single-molecule localization microscopy data.

Single-molecule localization-based super-resolution microscopy techniques such as photoactivated localization microscopy (PALM) and stochastic optical reconstruction microscopy (STORM) produce pointillist data sets of molecular coordinates. Although many algorithms exist for the identification and localization of molecules from raw image data, methods for analyzing the resulting point patterns for properties such as clustering have remained relatively under-studied. Here we present a model-based Bayesian approach to evaluate molecular cluster assignment proposals, generated in this study by analysis based on Ripley's K function. The method takes full account of the individual localization precisions calculated for each emitter. We validate the approach using simulated data, as well as experimental data on the clustering behavior of CD3ζ, a subunit of the CD3 T cell receptor complex, in resting and activated primary human T cells.

Dynamic Bayesian clustering.

Clusters of time series data may change location and memberships over time; in gene expression data, this occurs as groups of genes or samples respond differently to stimuli or experimental conditions at different times. In order to uncover this underlying temporal structure, we consider dynamic clusters with time-dependent parameters which split and merge over time, enabling cluster memberships to change. These interesting time-dependent structures are useful in understanding the development of organisms or complex organs, and could not be identified using traditional clustering methods. In cell cycle data, these time-dependent structure may provide links between genes and stages of the cell cycle, whilst in developmental data sets they may highlight key developmental transitions.

Dissecting the fission yeast regulatory network reveals phase-specific control elements of its cell cycle.

BACKGROUND: Fission yeast Schizosaccharomyces pombe and budding yeast Saccharomyces cerevisiae are among the original model organisms in the study of the cell-division cycle. Unlike budding yeast, no large-scale regulatory network has been constructed for fission yeast. It has only been partially characterized. As a result, important regulatory cascades in budding yeast have no known or complete counterpart in fission yeast. RESULTS: By integrating genome-wide data from multiple time course cell cycle microarray experiments we reconstructed a gene regulatory network. Based on the network, we discovered in addition to previously known regulatory hubs in M phase, a new putative regulatory hub in the form of the HMG box transcription factor SPBC19G7.04. Further, we inferred periodic activities of several less known transcription factors over the course of the cell cycle, identified over 500 putative regulatory targets and detected many new phase-specific and conserved cis-regulatory motifs. In particular, we show that SPBC19G7.04 has highly significant periodic activity that peaks in early M phase, which is coordinated with the late G2 activity of the forkhead transcription factor fkh2. Finally, using an enhanced Bayesian algorithm to co-cluster the expression data, we obtained 31 clusters of co-regulated genes 1) which constitute regulatory modules from different phases of the cell cycle, 2) whose phase order is coherent across the 10 time course experiments, and 3) which lead to identification of phase-specific control elements at both the transcriptional and post-transcriptional levels in S. pombe. In particular, the ribosome biogenesis clusters expressed in G2 phase reveal new, highly conserved RNA motifs. CONCLUSION: Using a systems-level analysis of the phase-specific nature of the S. pombe cell cycle gene regulation, we have provided new testable evidence for post-transcriptional regulation in the G2 phase of the fission yeast cell cycle. Based on this comprehensive gene regulatory network, we demonstrated how one can generate and investigate plausible hypotheses on fission yeast cell cycle regulation which can potentially be explored experimentally.

Bayesian coclustering of Anopheles gene expression time series: study of immune defense response to multiple experimental challenges.

We present a method for Bayesian model-based hierarchical coclustering of gene expression data and use it to study the temporal transcription responses of an Anopheles gambiae cell line upon challenge with multiple microbial elicitors. The method fits statistical regression models to the gene expression time series for each experiment and performs coclustering on the genes by optimizing a joint probability model, characterizing gene coregulation between multiple experiments. We compute the model using a two-stage Expectation-Maximization-type algorithm, first fixing the cross-experiment covariance structure and using efficient Bayesian hierarchical clustering to obtain a locally optimal clustering of the gene expression profiles and then, conditional on that clustering, carrying out Bayesian inference on the cross-experiment covariance using Markov chain Monte Carlo simulation to obtain an expectation. For the problem of model choice, we use a cross-validatory approach to decide between individual experiment modeling and varying levels of coclustering. Our method successfully generates tightly coregulated clusters of genes that are implicated in related processes and therefore can be used for analysis of global transcript responses to various stimuli and prediction of gene functions.

Finding groups in gene expression data.

The vast potential of the genomic insight offered by microarray technologies has led to their widespread use since they were introduced a decade ago. Application areas include gene function discovery, disease diagnosis, and inferring regulatory networks. Microarray experiments enable large-scale, high-throughput investigations of gene activity and have thus provided the data analyst with a distinctive, high-dimensional field of study. Many questions in this field relate to finding subgroups of data profiles which are very similar. A popular type of exploratory tool for finding subgroups is cluster analysis, and many different flavors of algorithms have been used and indeed tailored for microarray data. Cluster analysis, however, implies a partitioning of the entire data set, and this does not always match the objective. Sometimes pattern discovery or bump hunting tools are more appropriate. This paper reviews these various tools for finding interesting subgroups.