Gaussian Process Kernels for Cross-Spectrum Analysis in Electrophysiological Time Series

Multi-output Gaussian processes provide a convenient framework for multi-task problems. An illustrative and motivating example of a multi-task problem is multi-region electrophysiological time-series data, where experimentalists are interested in both power and phase coherence between channels. Recently, the spectral mixture (SM) kernel was proposed to model the spectral density of a single task in a Gaussian process framework. This work develops a novel covariance kernel for multiple outputs, called the cross-spectral mixture (CSM) kernel. This new, flexible kernel represents both the power and phase relationship between multiple observation channels. The expressive capabilities of the CSM kernel are demonstrated through implementation of 1) a Bayesian hidden Markov model, where the emission distribution is a multi-output Gaussian process with a CSM covariance kernel, and 2) a Gaussian process factor analysis model, where factor scores represent the utilization of cross-spectral neural circuits. Results are presented for measured multi-region electrophysiological data.

Cervical cancer precursors and hormonal contraceptive use in HIV-positive women: application of a causal model and semi-parametric estimation methods.

OBJECTIVE: To demonstrate the application of causal inference methods to observational data in the obstetrics and gynecology field, particularly causal modeling and semi-parametric estimation. BACKGROUND: Human immunodeficiency virus (HIV)-positive women are at increased risk for cervical cancer and its treatable precursors. Determining whether potential risk factors such as hormonal contraception are true causes is critical for informing public health strategies as longevity increases among HIV-positive women in developing countries. METHODS: We developed a causal model of the factors related to combined oral contraceptive (COC) use and cervical intraepithelial neoplasia 2 or greater (CIN2+) and modified the model to fit the observed data, drawn from women in a cervical cancer screening program at HIV clinics in Kenya. Assumptions required for substantiation of a causal relationship were assessed. We estimated the population-level association using semi-parametric methods: g-computation, inverse probability of treatment weighting, and targeted maximum likelihood estimation. RESULTS: We identified 2 plausible causal paths from COC use to CIN2+: via HPV infection and via increased disease progression. Study data enabled estimation of the latter only with strong assumptions of no unmeasured confounding. Of 2,519 women under 50 screened per protocol, 219 (8.7%) were diagnosed with CIN2+. Marginal modeling suggested a 2.9% (95% confidence interval 0.1%, 6.9%) increase in prevalence of CIN2+ if all women under 50 were exposed to COC; the significance of this association was sensitive to method of estimation and exposure misclassification. CONCLUSION: Use of causal modeling enabled clear representation of the causal relationship of interest and the assumptions required to estimate that relationship from the observed data. Semi-parametric estimation methods provided flexibility and reduced reliance on correct model form. Although selected results suggest an increased prevalence of CIN2+ associated with COC, evidence is insufficient to conclude causality. Priority areas for future studies to better satisfy causal criteria are identified.

Nonparametric estimation of structural models for high-frequency currency market data

Empirical modeling of high-frequency currency market data reveals substantial evidence for nonnormality, stochastic volatility, and other nonlinearities. This paper investigates whether an equilibrium monetary model can account for nonlinearities in weekly data. The model incorporates time-nonseparable preferences and a transaction cost technology. Simulated sample paths are generated using Marcet's parameterized expectations procedure. The paper also develops a new method for estimation of structural economic models. The method forces the model to match (under a GMM criterion) the score function of a nonparametric estimate of the conditional density of observed data. The estimation uses weekly U.S.-German currency market data, 1975-90. © 1995.

Weighted and two-stage least squares estimation of semiparametric truncated regression models

This paper provides a root-n consistent, asymptotically normal weighted least squares estimator of the coefficients in a truncated regression model. The distribution of the errors is unknown and permits general forms of unknown heteroskedasticity. Also provided is an instrumental variables based two-stage least squares estimator for this model, which can be used when some regressors are endogenous, mismeasured, or otherwise correlated with the errors. A simulation study indicates that the new estimators perform well in finite samples. Our limiting distribution theory includes a new asymptotic trimming result addressing the boundary bias in first-stage density estimation without knowledge of the support boundary. © 2007 Cambridge University Press.

Estimation of in-canopy ammonia sources and sinks in a fertilized Zea mays field.

An analytical model was developed to describe in-canopy vertical distribution of ammonia (NH(3)) sources and sinks and vertical fluxes in a fertilized agricultural setting using measured in-canopy mean NH(3) concentration and wind speed profiles. This model was applied to quantify in-canopy air-surface exchange rates and above-canopy NH(3) fluxes in a fertilized corn (Zea mays) field. Modeled air-canopy NH(3) fluxes agreed well with independent above-canopy flux estimates. Based on the model results, the urea fertilized soil surface was a consistent source of NH(3) one month following the fertilizer application, whereas the vegetation canopy was typically a net NH(3) sink with the lower portion of the canopy being a constant sink. The model results suggested that the canopy was a sink for some 70% of the estimated soil NH(3) emissions. A logical conclusion is that parametrization of within-canopy processes in air quality models are necessary to explore the impact of agricultural field level management practices on regional air quality. Moreover, there are agronomic and environmental benefits to timing liquid fertilizer applications as close to canopy closure as possible. Finally, given the large within-canopy mean NH(3) concentration gradients in such agricultural settings, a discussion about the suitability of the proposed model is also presented.

A Dynamic Directional Model for Effective Brain Connectivity using Electrocorticographic (ECoG) Time Series.

We introduce a dynamic directional model (DDM) for studying brain effective connectivity based on intracranial electrocorticographic (ECoG) time series. The DDM consists of two parts: a set of differential equations describing neuronal activity of brain components (state equations), and observation equations linking the underlying neuronal states to observed data. When applied to functional MRI or EEG data, DDMs usually have complex formulations and thus can accommodate only a few regions, due to limitations in spatial resolution and/or temporal resolution of these imaging modalities. In contrast, we formulate our model in the context of ECoG data. The combined high temporal and spatial resolution of ECoG data result in a much simpler DDM, allowing investigation of complex connections between many regions. To identify functionally segregated sub-networks, a form of biologically economical brain networks, we propose the Potts model for the DDM parameters. The neuronal states of brain components are represented by cubic spline bases and the parameters are estimated by minimizing a log-likelihood criterion that combines the state and observation equations. The Potts model is converted to the Potts penalty in the penalized regression approach to achieve sparsity in parameter estimation, for which a fast iterative algorithm is developed. The methods are applied to an auditory ECoG dataset.

Safety-critical medical device development using the UPP2SF model translation tool

Software-based control of life-critical embedded systems has become increasingly complex, and to a large extent has come to determine the safety of the human being. For example, implantable cardiac pacemakers have over 80,000 lines of code which are responsible for maintaining the heart within safe operating limits. As firmware-related recalls accounted for over 41% of the 600,000 devices recalled in the last decade, there is a need for rigorous model-driven design tools to generate verified code from verified software models. To this effect, we have developed the UPP2SF model-translation tool, which facilitates automatic conversion of verified models (in UPPAAL) to models that may be simulated and tested (in Simulink/Stateflow). We describe the translation rules that ensure correct model conversion, applicable to a large class of models. We demonstrate how UPP2SF is used in themodel-driven design of a pacemaker whosemodel is (a) designed and verified in UPPAAL (using timed automata), (b) automatically translated to Stateflow for simulation-based testing, and then (c) automatically generated into modular code for hardware-level integration testing of timing-related errors. In addition, we show how UPP2SF may be used for worst-case execution time estimation early in the design stage. Using UPP2SF, we demonstrate the value of integrated end-to-end modeling, verification, code-generation and testing process for complex software-controlled embedded systems. © 2014 ACM.