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Register a new userA functional-data approach to the Argo data
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Added by
Drew Yarger
Publication date
2020
fields
Mathematical Statistics
and research's language is
English
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The Argo data is a modern oceanography dataset that provides unprecedented global coverage of temperature and salinity measurements in the upper 2,000 meters of depth of the ocean. We study the Argo data from the perspective of functional data analysis (FDA). We develop spatio-temporal functional kriging methodology for mean and covariance estimation to predict temperature and salinity at a fixed location as a smooth function of depth. By combining tools from FDA and spatial statistics, including smoothing splines, local regression, and multivariate spatial modeling and prediction, our approach provides advantages over current methodology that consider pointwise estimation at fixed depths. Our approach naturally leverages the irregularly-sampled data in space, time, and depth to fit a space-time functional model for temperature and salinity. The developed framework provides new tools to address fundamental scientific problems involving the entire upper water column of the oceans such as the estimation of ocean heat content, stratification, and thermohaline oscillation. For example, we show that our functional approach yields more accurate ocean heat content estimates than ones based on discrete integral approximations in pressure. Further, using the derivative function estimates, we obtain a new product of a global map of the mixed layer depth, a key component in the study of heat absorption and nutrient circulation in the oceans. The derivative estimates also reveal evidence for density
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Positron Emission Tomography (PET) is an imaging technique which can be used to investigate chemical changes in human biological processes such as cancer development or neurochemical reactions. Most dynamic PET scans are currently analyzed based on the assumption that linear first order kinetics can be used to adequately describe the system under observation. However, there has recently been strong evidence that this is not the case. In order to provide an analysis of PET data which is free from this compartmental assumption, we propose a nonparametric deconvolution and analysis model for dynamic PET data based on functional principal component analysis. This yields flexibility in the possible deconvolved functions while still performing well when a linear compartmental model setup is the true data generating mechanism. As the deconvolution needs to be performed on only a relative small number of basis functions rather than voxel by voxel in the entire 3-D volume, the methodology is both robust to typical brain imaging noise levels while also being computationally efficient. The new methodology is investigated through simulations in both 1-D functions and 2-D images and also applied to a neuroimaging study whose goal is the quantification of opioid receptor concentration in the brain.
Evolutionary models of languages are usually considered to take the form of trees. With the development of so-called tree constraints the plausibility of the tree model assumptions can be addressed by checking whether the moments of observed variables lie within regions consistent with trees. In our linguistic application, the data set comprises acoustic samples (audio recordings) from speakers of five Romance languages or dialects. We wish to assess these functional data for compatibility with a hereditary tree model at the language level. A novel combination of canonical function analysis (CFA) with a separable covariance structure provides a method for generating a representative basis for the data. This resulting basis is formed of components which emphasize language differences whilst maintaining the integrity of the observational language-groupings. A previously unexploited Gaussian tree constraint is then applied to component-by-component projections of the data to investigate adherence to an evolutionary tree. The results indicate that while a tree model is unlikely to be suitable for modeling all aspects of the acoustic linguistic data, certain features of the spoken Romance languages highlighted by the separable-CFA basis may indeed be suitably modeled as a tree.
Accurate real-time tracking of influenza outbreaks helps public health officials make timely and meaningful decisions that could save lives. We propose an influenza tracking model, ARGO (AutoRegression with GOogle search data), that uses publicly available online search data. In addition to having a rigorous statistical foundation, ARGO outperforms all previously available Google-search-based tracking models, including the latest version of Google Flu Trends, even though it uses only low-quality search data as input from publicly available Google Trends and Google Correlate websites. ARGO not only incorporates the seasonality in influenza epidemics but also captures changes in peoples online search behavior over time. ARGO is also flexible, self-correcting, robust, and scalable, making it a potentially powerful tool that can be used for real-time tracking of other social events at multiple temporal and spatial resolutions.
One of the classic concerns in statistics is determining if two samples come from thesame population, i.e. homogeneity testing. In this paper, we propose a homogeneitytest in the context of Functional Data Analysis, adopting an idea from multivariatedata analysis: the data depth plot (DD-plot). This DD-plot is a generalization of theunivariate Q-Q plot (quantile-quantile plot). We propose some statistics based onthese DD-plots, and we use bootstrapping techniques to estimate their distributions.We estimate the finite-sample size and power of our test via simulation, obtainingbetter results than other homogeneity test proposed in the literature. Finally, weillustrate the procedure in samples of real heterogeneous data and get consistent results.
Functional magnetic resonance imaging (fMRI) has provided invaluable insight into our understanding of human behavior. However, large inter-individual differences in both brain anatomy and functional localization after anatomical alignment remain a major limitation in conducting group analyses and performing population-level inference. This paper addresses this problem by developing and validating a new computational technique for reducing misalignment across individuals in functional brain systems by spatially transforming each subjects functional data to a common reference map. Our proposed Bayesian functional registration approach allows us to assess differences in brain function across subjects and individual differences in activation topology. It combines intensity-based and feature-based information into an integrated framework and allows inference to be performed on the transformation via the posterior samples. We evaluate the method in a simulation study and apply it to data from a study of thermal pain. We find that the proposed approach provides increased sensitivity for group-level inference.
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