Andrew Holbrook

Geodesic Lagrangian Monte Carlo over the space of positive definite matrices: with application to Bayesian spectral density estimation

ABSTRACT We present geodesic Lagrangian Monte Carlo, an extension of Hamiltonian Monte Carlo for sampling from posterior distributions defined on general Riemannian manifolds. We apply this new algorithm to Bayesian inference on symmetric or Hermitian positive definite (PD) matrices. To do so, we exploit the Riemannian structure induced by Cartans canonical metric. The geodesics that correspond to this metric are available in closed-form and – within the context of Lagrangian Monte Carlo – provide a principled way to travel around the space of PD matrices. Our method improves Bayesian inference on such matrices by allowing for a broad range of priors, so we are not limited to conjugate priors only. In the context of spectral density estimation, we use the (non-conjugate) complex reference prior as an example modelling option made available by the algorithm. Results based on simulated and real-world multivariate time series are presented in this context, and future directions are outlined.

Attitudes toward Potential Participant Registries

Difficult participant recruitment is a consistent barrier to successful medical research. Potential participant registries represent an increasingly common intervention to overcome this barrier. A variety of models for registries exist, but few data are available to instruct their design and implementation. To provide such data, we surveyed 110 cognitively normal research participants enrolled in a longitudinal study of aging and dementia. Seventy-four (67%) individuals participated in the study. Most (78%, CI: 0.67, 0.87) participants were likely to enroll in a registry. Willingness to participate was reduced for registries that required enrollment through the Internet using a password (26%, CI: 0.16, 0.36) or through email (38%, CI: 0.27, 0.49). Respondents acknowledged their expectations that researchers share information about their health and risk for disease and their concerns that their data could be shared with for-profit companies. We found no difference in respondent preferences for registries that shared contact information with researchers, compared to honest broker models that take extra precautions to protect registrant confidentiality (28% versus 30%; p = 0.46). Compared to those preferring a shared information model, respondents who preferred the honest broker model or who lacked model preference voiced increased concerns about sharing registrant data, especially with for-profit organizations. These results suggest that the design of potential participant registries may impact the population enrolled, and hence the population that will eventually be enrolled in clinical studies. Investigators operating registries may need to offer particular assurances about data security to maximize registry enrollment but also must carefully manage participant expectations.

The ANTs Longitudinal Cortical Thickness Pipeline

Longitudinal studies of development and disease in the human brain have motivated the acquisition of large neuroimaging data sets and the concomitant development of robust methodological and statistical tools for quantifying neurostructural changes. Longitudinal-specific strategies for acquisition and processing have potentially significant benefits including more consistent estimates of intra-subject measurements while retaining predictive power. In this work, we introduce the open-source Advanced Normalization Tools (ANTs) registration-based cortical thickness longitudinal processing pipeline and its application to the first phase of the Alzheimer’s Disease Neuroimaging Initiative (ADNI-1) comprising over 600 subjects with multiple time points from baseline to 36 months. We demonstrate in these data that the single-subject template construction and same orientation processing results in a simultaneous minimization of residual variability and maximization of between-subject variability immediately estimable from a longitudinal mixed-effects modeling strategy. It is known from the statistical literature that optimizing these dual criteria leads to greater scientific interpretability in terms of tighter confidence intervals in calculated mean trends, smaller prediction intervals, and narrower confidence intervals for determining cross-sectional effects. This strategy is evaluated over the entire cortex, as defined by the Desikan-Killiany-Tourville labeling protocol, where comparisons are made with the cross-sectional and longitudinal FreeSurfer processing streams. Subsequent linear mixed effects modeling for identifying diagnostic groupings within the ADNI cohort is provided as supporting evidence for the utility of the proposed ANTs longitudinal framework which provides unbiased structural neuroimage processing and competitive to superior power for longitudinal structural change detection.

A Bayesian supervised dual-dimensionality reduction model for simultaneous decoding of LFP and spike train signals: Bayesian neural decoding

Neuroscientists are increasingly collecting multimodal data during experiments and observational studies. Different data modalities-such as EEG, fMRI, LFP, and spike trains-offer different views of the complex systems contributing to neural phenomena. Here, we focus on joint modeling of LFP and spike train data, and present a novel Bayesian method for neural decoding to infer behavioral and experimental conditions. This model performs supervised dual-dimensionality reduction: it learns low-dimensional representations of two different sources of information that not only explain variation in the input data itself, but also predict extra-neuronal outcomes. Despite being one probabilistic unit, the model consists of multiple modules: exponential PCA and wavelet PCA are used for dimensionality reduction in the spike train and LFP modules, respectively; these modules simultaneously interface with a Bayesian binary regression module. We demonstrate how this model may be used for prediction, parametric inference, and identification of influential predictors. In prediction, the hierarchical model outperforms other models trained on LFP alone, spike train alone, and combined LFP and spike train data. We compare two methods for modeling the loading matrix and find them to perform similarly. Finally, model parameters and their posterior distributions yield scientific insights.

LATERAL ENTORHINAL CORTICAL THINNING PREDICTS COGNITIVE DECLINE IN THE ADNI SAMPLE

MC than in NC, and increased with more progressed EYO and higher dementia rating scale (CDR) scores in the MC subjects. For the factor analysis of cortical thickness, 3 factors explained 56% of the variance. Within the MC group, we observed a significant interaction between sTREM2 x EYO onto the factor scores of predominantly frontal cortical thickness (beta1⁄4 0.11, p1⁄4 0.03). Inspection of figure 1 shows that a positive association between higher sTREM2 and cortical thickness started to emerge after the estimated symptom onset. No associations were observed in NC. Conclusions:TREM2 increases during the course of AD. However, higher TREM2 is associated with greater frontal cortical thickness during more advanced stages, potentially due to compensatory processes in the frontal lobe or due to TREM2-mediated phagocytotic and non-inflammatory immune response to apoptotic processes.