Academic literature on the topic 'Nested separable covariances'

In this paper, the issue of direction of arrival (DOA) estimation is discussed, and a partial angular sparse representation (SR)-based method using a sparse separate nested acoustic vector sensor (SSN-AVS) array is developed. Traditional AVS array is improved by separating the pressure sensor array and velocity sensor array into two different sparse array geometries with nested relationship. This improved array geometry can achieve large degrees of freedom (DOF) after the extended vectorization of the cross-covariance matrix, and only partial SR of the angle is required by exploiting the cyclic phase ambiguity caused by the large inter-element spacing of the virtual array. Joint sparse recovery is developed to amend the grid offset and unitary transformation is utilized to transform the complex atoms into real-valued ones. After sparse recovery, the sparse vector can simultaneously provide high-resolution but ambiguous angle estimation and unambiguous reference angle estimation embedded in the AVS array, and they are combined to obtain unique and high-resolution DOA estimation. Compared to other state-of-the-art DOA estimation methods using the AVS array, the proposed algorithm can provide better DOA estimation performance while requiring lower complexity. Multiple simulation results verify the effectiveness of the approach.

Statistical analysis of data from repeated measures experiments with missing factor combinations encounters multiple complications. Data from asynchronous cyclic drought experiments incorporate unequal numbers of drought cycles for different sources and provide an example of data both with repeated measures and missing factor combinations. Repeated measures data are problematic because typical analyses with PROC GLM do not allow the researcher to compare candidate covariance structures. In contrast, PROC MIXED allows comparison of covariance structures and several options for modeling serial correlation and variance heterogeneity. When there are missing factor combinations, the cross-classified model traditionally used for synchronized trials is inappropriate. For asynchronous data, some least squares means estimates for treatment and source main effects, and treatment by source interaction effects are inestimable. The objectives of this paper were to use an asynchronous drought cycle data set to 1) model an appropriate covariance structure using mixed models, and 2) compare the cross-classified fixed effects model to drought cycle nested within source models. We used a data set of midday water potential measurements taken during a cyclic drought study of 15 half-siblings of bigtooth maples (Acer grandidentatum Nutt.) indigenous to Arizona, New Mexico, Texas, and Utah. Data were analyzed using SAS PROC MIXED software. Information criteria lead to the selection of a model incorporating separate compound symmetric covariance structures for the two irrigation treatment groups. When using nested models in the fixed portion of the model, there are no missing factors because drought cycle is not treated as a crossed experimental factor. Nested models provided meaningful F tests and estimated all the least squares means, but the cross-classified model did not. Furthermore, the nested models adequately compared the treatment effect of sources subjected to asynchronous drought events. We conclude that researchers wishing to analyze data from asynchronous drought trials must consider using mixed models with nested fixed effects.

Multilevel organization of morphometric data (cells are “nested” within patients) requires special methods for studying correlations between karyometric features. The most distinct feature of these methods is that separate correlation (covariance) matrices are produced for every level in the hierarchy. In karyometric research, the cell‐level (i.e., within‐tumor) correlations seem to be of major interest. Beside their biological importance, these correlation coefficients (CC) are compulsory when dimensionality reduction is required. Using MLwiN, a dedicated program for multilevel modeling, we show how to use multivariate multilevel models (MMM) to obtain and interpret CC in each of the levels. A comparison with two usual, “single‐level” statistics shows that MMM represent the only way to obtain correct cell‐level correlation coefficients. The summary statistics method (take average values across each patient) produces patient‐level CC only, and the “pooling” method (merge all cells together and ignore patients as units of analysis) yields incorrect CC at all. We conclude that multilevel modeling is an indispensable tool for studying correlations between morphometric variables.

We test the hypotheses that 1) growth hormone (GH)-releasing peptide-2 (G) synergizes with l-arginine (A), a compound putatively achieving selective somatostatin withdrawal and 2) gender modulates this synergy on GH secretion. To these ends, 18 young healthy volunteers (9 men and 9 early follicular phase women) each received separate morning intravenous infusions of saline (S) or A (30 g over 30 min) or G (1 μg/kg) or both, in randomly assigned order. Blood was sampled at 10-min intervals for later chemiluminescence assay of serum GH concentrations. Analysis of covariance revealed that the preinjection (basal) serum GH concentrations significantly determined secretagogue responsiveness and that sex ( P = 0.02) and stimulus type ( P < 0.001) determined the slope of this relationship. Nested ANOVA applied to log-transformed measures of GH release showed that gender determines 1) basal rates of GH secretion, 2) the magnitude of the GH secretory response to A, 3) the rapidity of attaining the GH maximum, and 4) the magnitude or fold (but not absolute) elevation in GH secretion above preinjection basal, as driven by the combination of A and G. In contrast, the emergence of the G and A synergy is sex independent. We conclude that gender modulates key facets of basal and A/G-stimulated GH secretion in young adults.

Abstract Research has long documented the psycho-social sequelae experienced by those who have been treated for and survived cancer. Depression, affect and other indicators of mood state have been an important focus of that research However, there is little research on racial differences in depression and affect outcomes or the specific cancer and age-related factors that predict them. The research to be presented is based on a 10 year, six wave NCI funded study of 471 older adult (age 60+), long-term cancer survivors randomly selected from the tumor registry of a comprehensive cancer treatment center. Key outcome measures were depression (CES-D) scale) and both positive and negative affect (PANAS). Covariance analyses and nested OLS Regression were used to identify Black-white differences these outcomes and the relative importance of both cancer and non-cancer predictors. Blacks reported lower levels of depression and negative affect when compared to whites. In a separate regression analysis of the black sub-sample, continuing cancer-related symptoms were by far the strongest predictors (beta =.16) of negative affect. In the white sub-sample, while cancer-related symptoms continued to be a significant predictor (beta=.16), non-cancer symptoms were substantially more important (beta=. 22). These results will hopefully help practitioners to have a better understanding of the nuanced racialized experiences and mental health among cancer survivors, and how these may impact after-care for older adult cancer survivors.

The area under the receiver operating characteristic curve (AUC) is widely used in evaluating diagnostic performance for many clinical tasks. It is still challenging to evaluate the reading performance of distinguishing between positive and negative regions of interest (ROIs) in the nested-data problem, where multiple ROIs are nested within the cases. To address this issue, we identify two kinds of AUC estimators, within-cases AUC and between-cases AUC. We focus on the between-cases AUC estimator, since our main research interest is in patient-level diagnostic performance rather than location-level performance (the ability to separate ROIs with and without disease within each patient). Another reason is that as the case number increases, the number of between-cases paired ROIs is much larger than the number of within-cases ROIs. We provide estimators for the variance of the between-cases AUC and for the covariance when there are two readers. We derive and prove the above estimators’ theoretical values based on a simulation model and characterize their behavior using Monte Carlo simulation results. We also provide a real-data example. Moreover, we connect the distribution-based simulation model with the simulation model based on the linear mixed-effect model, which helps better understand the sources of variation in the simulated dataset.

AbstractFisheries scientists compare processes among species to estimate species productivity, management reference points, and climate sensitivities. Ecologists have developed “phylogenetic comparative methods” (PCMs) to address these questions, but there is surprisingly little application of PCM within fisheries science. Here, I bridge this gap by introducing PCM (including Brownian motion, Ornstein–Uhlenbeck, and Pagel's kappa and lambda models for species covariance), thereby showing that PCM generalizes the nested taxonomic random effects that are commonly used in fisheries science. I next summarize phylogenetic structural equation models (PSEMs), which extend the linear models that are commonly used in fisheries. Finally, I re‐analyse a high‐quality database used to predict mortality rates from longevity and/or growth parameters. I specifically propose a PSEM that reverts to a longevity‐based prediction when longevity information is available but uses phylogenetic corrected growth parameters otherwise. Using this single PSEM replaces the common practice of fitting and predicting using separate linear models depending upon what data are available for a given species. Cross‐validation suggests that the relationship between log‐mortality rate and longevity does not vary based on phylogeny, and therefore, linear models and PSEM both explain 82% of variance when longevity is available. When longevity is unavailable, by contrast, the linear model explains only 37% of variance while the PSEM explains 52% of variance, where this gain occurs from conditioning predictions on phylogenetic similarities. I therefore conclude that PCM and PSEM provide a general and user‐friendly replacement for linear models and can improve performance for fisheries meta‐analyses that are used for fisheries management applications.

Abstract Background and Aims Measures of non-invasive pulse wave (PW) analysis can help to assess the status of the central cardiovascular system and to predict clinical outcomes, including morbidity and mortality. During hemodialysis (HD), fluid is extracted from blood. The resulting reduction in relative blood volume (RBV) and collected ultrafiltration volume (UFV) were hypothesized to substantially influence PW characteristics during HD. Volume overload (VO) is common in HD patients and may affect the chance of improving the cardiovascular status of patients during HD. The present study aimed to explore associations between RBV, UFV, VO and a wide range of PW parameters. Method In a single center in Vienna, Austria, 24 patients on maintenance HD underwent four HD sessions each, with whole-body bioimpedance spectroscopy (BIS) before, and automated, cuff-based PW measurements every 15 minutes, RBV- and UFV-monitoring throughout each session. Associations between RBV or UFV as independent variable and 26 different PW characteristics as dependent variables (52 separate models) were tested using confounder-adjusted generalized estimating equations with sandwich estimator and multilevel nested working covariance structure, reporting standardized effect estimates and drop-in-R² to assess variable importance. Sensitivity models including both RBV and UFV as predictors (26 models) were used to assess effects adjusted for confounding and mediation, respectively. The intra-patient correlation between BIS-derived VO and PW parameters at the start of sessions and PW parameter change by end of sessions was assessed using repeated measures correlation analysis. Results Data from 990 PW measurements were available for analysis from an 88% male cohort with median age of 66 years. In half of the PW parameters analyzed, each percent RBV was significantly associated with in summary about 4.3 to 5.7% (95% confidence intervals [CI] 0.9 to 10.46) of the PW parameter's respective standard deviation (SD), negatively so only in heart rate and R-Peak. UFV was negatively associated with a third of PW parameters (effects ranging from −2.5 to −5.47% SD [95% CIs −0.9 to −10.0]), mostly in classical peripheral and central pressures and peripheral resistance. In models including both predictors, RBV overall exhibited greater effect size and variance capture than UFV, except for peripheral resistance. On within-patient level, VO was positively correlated with initial medians of pressure excess (r=0.34, p=0.034), augmentation-index (0.34, p=0.031) and augmentation-pressure (0.32, p=0.042), increase in heart rate (0.32, p=0.04) and decreases in peripheral resistance (0.31, p=0.05), peripheral (systolic: 0.34, p=0.032; diastolic: 0.45, p=0.004; mean: 0.41, p=0.008) and central (diastolic: 0.46, p=0.003) blood pressures during HD. Conclusion The observed PW characteristics were associated with RBV and UFV during HD and may represent modifiable targets for intervention studies. Pressure excess, S-Peak, R-Peak, cardiac and preload parameters were more closely associated with RBV, while classic (especially diastolic) blood pressure parameters, ejection duration and S/D-Ratio were more associated with UFV, in models using both predictors. On average, blood pressure and peripheral resistance tended to decrease less when a patient began HD in a volume-expanded state, which may affect day-to-day feasibility of more classical pressure targets, but perhaps not of other PW parameters. Multiple PW characteristics have previously been shown to be associated with mortality and morbidity and are potential target parameters for future intervention trials. Utilizing RBV modification as an intervention may offer superior precision compared to UFV goals, requiring further studies. PW technology could also be adopted by HD-machine manufacturers at low cost, enabling more precise and individualized treatment options.

Avec la modélisation géologique et géométallurgique, la modélisation géotechnique est l'une des composantes essentielles de la planification et du développement de projets miniers à ciel ouvert et souterrains. Une caractéristique particulière de nombreuses variables géotechniques est d'être dépendante de la direction, c'est-à-dire que la mesure d'une carotte de sondage dépend non seulement de sa position géographique mais aussi de son orientation. Pour tenir compte de cette caractéristique, il est proposé de régionaliser les variables géotechniques dans un espace à cinq dimensions correspondant au produit sur l'espace géographique à trois dimensions et la sphère à deux dimensions, de sorte que chaque mesure soit indexée par ses coordonnées est, nord, élévation, azimut et pendage. Au lieu de faire des prédictions et des simulations conditionnées à une direction particulière, ce nouveau paradigme permet d'interpoler des variables géotechniques à n'importe quel endroit de l'espace géographique, et pour n'importe quelle direction. La structure de corrélation spatiale peut être inférée et modélisée en utilisant des covariances séparables ou des combinaisons de covariances séparables, sous une hypothèse de stationnarité dans l'espace géographique et d'isotropie sur la sphère. De plus, une simulation conditionnelle peut être effectuée par des méthodes spectrales ou de bandes tournantes, basées sur des produits de champs aléatoires stationnaires dans l'espace géographique et de champs aléatoires isotropes sur la sphère. La méthodologie proposée est illustrée par modélisation de la fréquence de discontinuité linéaire (P10), la désignation de la qualité de la roche (RQD), et le Slope Mass Rating (SMR) dans trois gisements miniers
Together with geological and geometallurgical modeling, geotechnical modeling is one of the essential components for the planning and development of open pit and underground mining projects. A particular characteristic of many geotechnical variables is to be direction-dependent, i.e., the measurement of a core sample not only depends on the in-situ position of this sample but also on its in-situ orientation. To account for this characteristic, it is proposed to regionalize such variables in a five-dimensional space corresponding to the product on the three-dimensional geographical space and the two-dimensional sphere, so that each measurement is indexed by its easting, northing, elevation, azimuth, and dip. Instead of making predictions and simulations conditioned to a particular direction, this new paradigm allows geotechnical variables to be interpolated at any place in the geographic space, for any direction. The spatial correlation structure can be inferred and modeled by using separable covariances or combinations of separable covariances, under an assumption of stationarity in the geographical space and isotropy on the sphere. Also, conditional simulation can be performed by turning bands, based on products of stationary random fields in the geographic space and isotropic random fields on the sphere. The proposed methodology is illustrated with the modeling of the linear discontinuity frequency (P10), the rock quality designation (RQD), and Slope Mass Rating (SMR) in three mineral deposits