Stepwise Signal Extraction via Marginal Likelihood

Time-varying dynamic network model for dynamic resting state functional connectivity in fMRI and MEG imaging

Dynamic resting state functional connectivity (RSFC) characterizes fluctuations that occur over time in functional brain networks. Existing methods to extract dynamic RSFCs, such as sliding-window and clustering methods that are inherently non-adaptive, have various limitations such as high-dimensionality, an inability to reconstruct brain signals, insufficiency of data for reliable estimation, insensitivity to rapid changes in dynamics, and a lack of generalizability across multiply functional imaging modalities. To overcome these deficiencies, we develop a novel and unifying time-varying dynamic network (TVDN) framework for examining dynamic resting state functional connectivity. TVDN includes a generative model that describes the relation between a low-dimensional dynamic RSFC and the brain signals, and an inference algorithm that automatically and adaptively learns the low-dimensional manifold of dynamic RSFC and detects dynamic state transitions in data. TVDN is applicable to multiple modalities of functional neuroimaging such as fMRI and MEG/EEG. The estimated low-dimensional dynamic RSFCs manifold directly links to the frequency content of brain signals. Hence we can evaluate TVDN performance by examining whether learnt features can reconstruct observed brain signals. We conduct comprehensive simulations to evaluate TVDN under hypothetical settings. We then demonstrate the application of TVDN with real fMRI and MEG data, and compare the results with existing benchmarks. Results demonstrate that TVDN is able to correctly capture the dynamics of brain activity and more robustly detect brain state switching both in resting state fMRI and MEG data.

Testing for dependence on tree structures

Tree-like structures are abundant in the empirical sciences as they can summarize high-dimensional data and show latent structure among many samples in a single framework. Prominent examples include phylogenetic trees or hierarchical clustering derived from genetic data. Currently, users employ ad hoc methods to test for association between a given tree and a response variable, which reduces reproducibility and robustness. In this paper, we introduce treeSeg, a simple to use and widely applicable methodology with high power for testing between all levels of hierarchy for a given tree and the response while accounting for the overall false positive rate. Our method allows for precise uncertainty quantification and therefore, increases interpretability and reproducibility of such studies across many fields of science.

Tree structures, showing hierarchical relationships and the latent structures between samples, are ubiquitous in genomic and biomedical sciences. A common question in many studies is whether there is an association between a response variable measured on each sample and the latent group structure represented by some given tree. Currently, this is addressed on an ad hoc basis, usually requiring the user to decide on an appropriate number of clusters to prune out of the tree to be tested against the response variable. Here, we present a statistical method with statistical guarantees that tests for association between the response variable and a fixed tree structure across all levels of the tree hierarchy with high power while accounting for the overall false positive error rate. This enhances the robustness and reproducibility of such findings.

Statistics and Related Topics in Single-Molecule Biophysics

Since the universal acceptance of atoms and molecules as the fundamental constituents of matter in the early twentieth century, molecular physics, chemistry and molecular biology have all experienced major theoretical breakthroughs. To be able to actually "see" biological macromolecules, one at a time in action, one has to wait until the 1970s. Since then the field of single-molecule biophysics has witnessed extensive growth both in experiments and theory. A distinct feature of single-molecule biophysics is that the motions and interactions of molecules and the transformation of molecular species are necessarily described in the language of stochastic processes, whether one investigates equilibrium or nonequilibrium living behavior. For laboratory measurements following a biological process, if it is sampled over time on individual participating molecules, then the analysis of experimental data naturally calls for the inference of stochastic processes. The theoretical and experimental developments of single-molecule biophysics thus present interesting questions and unique opportunity for applied statisticians and probabilists. In this article, we review some important statistical developments in connection to single-molecule biophysics, emphasizing the application of stochastic-process theory and the statistical questions arising from modeling and analyzing experimental data.