Family-based clusters of cognitive test performance in familial schizophrenia

BACKGROUND: Cognitive traits derived from neuropsychological test data are considered to be potential endophenotypes of schizophrenia. Previously, these traits have been found to form a valid basis for clustering samples of schizophrenia patients into homogeneous subgroups. We set out to identify such clusters, but apart from previous studies, we included both schizophrenia patients and family members into the cluster analysis. The aim of the study was to detect family clusters with similar cognitive test performance. METHODS: Test scores from 54 randomly selected families comprising at least two siblings with schizophrenia spectrum disorders, and at least two unaffected family members were included in a complete-linkage cluster analysis with interactive data visualization. RESULTS: A well-performing, an impaired, and an intermediate family cluster emerged from the analysis. While the neuropsychological test scores differed significantly between the clusters, only minor differences were observed in the clinical variables. CONCLUSIONS: The visually aided clustering algorithm was successful in identifying family clusters comprising both schizophrenia patients and their relatives. The present classification method may serve as a basis for selecting phenotypically more homogeneous groups of families in subsequent genetic analyses

Modeling probability density through ultraspherical polynomial transformations

Abstract We present a method for fitting parametric probability density models using an integrated square error criterion on a continuum of weighted Lebesgue spaces formed by ultraspherical polynomials. This approach is inherently suitable for creating mixture model representations of complex distributions and allows fully autonomous cluster analysis of high-dimensional datasets. The method is also suitable for extremely large sets, allowing post facto model selection and analysis even in the absence of the original data. Furthermore, the fitting procedure only requires the parametric model to be pointwise evaluable, making it trivial to fit user-defined models through a generic algorithm

Multivariate posterior singular spectrum analysis

Abstract A generalized, multivariate version of the Posterior Singular Spectrum Analysis (PSSA) method is described for the identification of credible features in multivariate time series. We combine Bayesian posterior modeling with multivariate SSA (MSSA) and infer the MSSA signal components with a credibility analysis of the posterior sample. The performance of multivariate PSSA (MPSSA) is compared to the single-variate PSSA with an artificial example and the potential of MPSSA is demonstrated with real data using NAO and SOI climate index series

A scale space approach for exploring structure in spherical data

Abstract A novel scale space approach, SphereSiZer, is proposed for exploring structure in spherical data, that is, directional data on the unit sphere of the three-dimensional Euclidean space. The method finds statistically significant gradients of the smooths of the probability density function underlying the observed data. Bootstrap is used to establish significance and inference is summarized with planar maps of contour plots of smooths of the data, overlaid with arrows that indicate the directions and magnitudes of the significant gradients. An effective way to explore such maps is a movie where each frame corresponds to a fixed level of smoothing, that is, a particular spatial scale on the sphere. The SphereSiZer is demonstrated using simulated data as well as two real-data examples. The first example examines the distribution of infant head normal vector directions. The presence of local maxima in the normal vector distribution may indicate head deformity, such as severe flatness or asymmetry. The second example considers the distribution of earthquakes in the Northern Hemisphere

Rejoinder:rejoinder to statistical scale space methods

Rejoinder Rejoinder to Statistical Scale Space Methods. Holmström, L., and Pasanen, L. (2017) Statistical Scale Space Methods. International Statistical Review, 85: 1–30. doi: 10.1111/insr.12155

Scale space multiresolution correlation analysis for time series data

Abstract We propose a new scale space method for the discovery of structure in the correlation between two time series. The method considers the possibility that correlation may not be constant in time and that it might have different features when viewed at different time scales. The time series are first decomposed into additive components corresponding to their features in different time scales. Temporal changes in correlation between pairs of such components are then explored by using weighted correlation within a sliding time window of varying length. Bayesian, sampling-based inference is used to establish the credibility of the correlation structures thus found and the results of analyses are summarized in scale space feature maps. The performance of the method is demonstrated using one artificial and two real data sets. The results underline the usefulness of the scale space approach when the correlation between the time series exhibit time-varying structure in different scales

Statistical scale space methods

Summary The goal of statistical scale space analysis is to extract scale-dependent features from noisy data. The data could be for example an observed time series or digital image in which case features in either different temporal or spatial scales would be sought. Since the 1990s, a number of statistical approaches to scale space analysis have been developed, most of them using smoothing to capture scales in the data, but other interpretations of scale have also been proposed. We review the various statistical scale space methods proposed and mention some of their applications

Estimation of level set trees using adaptive partitions

Abstract We present methods for the estimation of level sets, a level set tree, and a volume function of a multivariate density function. The methods are such that the computation is feasible and estimation is statistically efficient in moderate dimensional cases (d≈8) and for moderate sample sizes (n≈ 50,000). We apply kernel estimation together with an adaptive partition of the sample space. We illustrate how level set trees can be applied in cluster analysis and in flow cytometry

A scale space approach for estimating the characteristic feature sizes in hierarchical signals

Abstract The temporal and spatial data analysed in, for example, ecology or climatology, are often hierarchically structured, carrying information in different scales. An important goal of data analysis is then to decompose the observed signal into distinctive hierarchical levels and to determine the size of the features that each level represents. Using differences of smooths, scale space multiresolution analysis decomposes a signal into additive components associated with different levels of scales present in the data. The smoothing levels used to compute the differences are determined by the local minima of the norm of the so‐called scale‐derivative of the signal. While this procedure accomplishes the first goal, the hierarchical decomposition of the signal, it does not achieve the second goal, the determination of the actual size of the features corresponding to each hierarchical level. Here, we show that the maximum of the scale‐derivative norm of an extracted hierarchical component can be used to estimate its characteristic feature size. The feasibility of the method is demonstrated using an artificial image and a time series of a drought index, based on climate reconstructions from long tree ring chronologies

At what scales and why does forest structure vary in naturally dynamic boreal forests?:an analysis of forest landscapes on two continents

Abstract Identifying the scales of variation in forest structures and the underlying processes are fundamental for understanding forest dynamics. Here, we studied these scale-dependencies in forest structure in naturally dynamic boreal forests on two continents. We identified the spatial scales at which forest structures varied, and analyzed how the scales of variation and the underlying drivers differed among the regions and at particular scales. We studied three 2 km × 2 km landscapes in northeastern Finland and two in eastern Canada. We estimated canopy cover in contiguous 0.1-ha cells from aerial photographs and used scale-derivative analysis to identify characteristic scales of variation in the canopy cover data. We analyzed the patterns of variation at these scales using Bayesian scale space analysis. We identified structural variation at three spatial scales in each landscape. Among landscapes, the largest scale of variation showed the greatest variability (20.1–321.4 ha), related to topography, soil variability, and long-term disturbance history. Superimposed on this large-scale variation, forest structure varied at similar scales (1.3–2.8 ha) in all landscapes. This variation correlated with recent disturbances, soil variability, and topographic position. We also detected intense variation at the smallest scale analyzed (0.1 ha, grain of our data), partly driven by recent disturbances. The distinct scales of variation indicated hierarchical structure in the landscapes studied. Except for the large-scale variation, these scales were remarkably similar among the landscapes. This suggests that boreal forests may display characteristic scales of variation that occur somewhat independent of the tree species characteristics or the disturbance regime