RESUMEN
Bayesian methods provide direct inference in functional data analysis applications without reliance on bootstrap techniques. A major tool in functional data applications is the functional principal component analysis which decomposes the data around a common mean function and identifies leading directions of variation. Bayesian functional principal components analysis (BFPCA) provides uncertainty quantification on the estimated functional model components via the posterior samples obtained. We propose central posterior envelopes (CPEs) for BFPCA based on functional depth as a descriptive visualization tool to summarize variation in the posterior samples of the estimated functional model components, contributing to uncertainty quantification in BFPCA. The proposed BFPCA relies on a latent factor model and targets model parameters within a mixed effects modeling framework using modified multiplicative gamma process shrinkage priors on the variance components. Functional depth provides a center-outward order to a sample of functions. We utilize modified band depth and modified volume depth for ordering of a sample of functions and surfaces, respectively, to derive at CPEs of the mean and eigenfunctions within the BFPCA framework. The proposed CPEs are showcased in extensive simulations. Finally, the proposed CPEs are applied to the analysis of a sample of power spectral densities (PSD) from resting state electroencephalography (EEG) where they lead to novel insights on diagnostic group differences among children diagnosed with autism spectrum disorder and their typically developing peers across age.
RESUMEN
Advances in remote sensing technology can help estimate biodiversity at large spatial extents. To assess whether we could use hyperspectral visible near-infrared (VNIR) spectra to estimate species diversity, we examined the correlations between species diversity and spectral diversity in early-successional abandoned agricultural fields in the Ridge and Valley ecoregion of north-central Virginia at the Blandy Experimental Farm. We established plant community plots and collected vegetation surveys and ground-level hyperspectral data from 350 to 1,025 nm wavelengths. We related spectral diversity (standard deviations across spectra) with species diversity (Shannon-Weiner index) and evaluated whether these correlations differed among spectral regions throughout the visible and near-infrared wavelength regions, and across different spectral transformation techniques. We found positive correlations in the visible regions using band depth data, positive correlations in the near-infrared region using first derivatives of spectra, and weak to no correlations in the red-edge region using either of the two spectral transformation techniques. To investigate the role of pigment variability in these correlations, we estimated chlorophyll, carotenoid, and anthocyanin concentrations of five dominant species in the plots using spectral vegetation indices. Although interspecific variability in pigment levels exceeded intraspecific variability, chlorophyll was more varied within species than carotenoids and anthocyanins, contributing to the lack of correlation between species diversity and spectral diversity in the red-edge region. Interspecific differences in pigment levels, however, made it possible to differentiate these species remotely, contributing to the species-spectral diversity correlations. VNIR spectra can be used to estimate species diversity, but the relationships depend on the spectral region examined and the spectral transformation technique used.
RESUMEN
Many model-based methods have been developed over the last several decades for analysis of electroencephalograms (EEGs) in order to understand electrical neural data. In this work, we propose to use the functional boxplot (FBP) to analyze log periodograms of EEG time series data in the spectral domain. The functional bloxplot approach produces a median curve-which is not equivalent to connecting medians obtained from frequency-specific boxplots. In addition, this approach identifies a functional median, summarizes variability, and detects potential outliers. By extending FBPs analysis from one-dimensional curves to surfaces, surface boxplots are also used to explore the variation of the spectral power for the alpha (8-12 Hz) and beta (16-32 Hz) frequency bands across the brain cortical surface. By using rank-based nonparametric tests, we also investigate the stationarity of EEG traces across an exam acquired during resting-state by comparing the spectrum during the early vs. late phases of a single resting-state EEG exam.
RESUMEN
In this paper, we introduce a surface boxplot as a tool for visualization and exploratory analysis of samples of images. First, we use the notion of volume depth to order the images viewed as surfaces. In particular, we define the median image. We use an exact and fast algorithm for the ranking of the images. This allows us to detect potential outlying images that often contain interesting features not present in most of the images. Second, we build a graphical tool to visualize the surface boxplot and its various characteristics. A graph and histogram of the volume depth values allow us to identify images of interest. The code is available in the supporting information of this paper. We apply our surface boxplot to a sample of brain images and to a sample of climate model outputs.
RESUMEN
This study aims at comparing the capability of different sensors to detect land cover materials within an historical urban center. The main objective is to evaluate the added value of hyperspectral sensors in mapping a complex urban context. In this study we used: (a) the ALI and Hyperion satellite data, (b) the LANDSAT ETM+ satellite data, (c) MIVIS airborne data and (d) the high spatial resolution IKONOS imagery as reference. The Venice city center shows a complex urban land cover and therefore was chosen for testing the spectral and spatial characteristics of different sensors in mapping the urban tissue. For this purpose, an object-oriented approach and different common classification methods were used. Moreover, spectra of the main anthropogenic surfaces (i.e. roofing and paving materials) were collected during the field campaigns conducted on the study area. They were exploited for applying band-depth and sub-pixel analyses to subsets of Hyperion and MIVIS hyperspectral imagery. The results show that satellite data with a 30m spatial resolution (ALI, LANDSAT ETM+ and HYPERION) are able to identify only the main urban land cover materials.