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## SELF-SIMILARITY AND LAMPERTI CONVERGENCE FOR FAMILIES OF STOCHASTIC PROCESSES

JORGENSEN, Bent; MARTINEZ, Jose R.; DEMETRIO, Clarice G. B.
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
35.59%
We define a new type of self-similarity for one-parameter families of stochastic processes, which applies to certain important families of processes that are not self-similar in the conventional sense. This includes Hougaard Levy processes such as the Poisson processes, Brownian motions with drift and the inverse Gaussian processes, and some new fractional Hougaard motions defined as moving averages of Hougaard Levy process. Such families have many properties in common with ordinary self-similar processes, including the form of their covariance functions, and the fact that they appear as limits in a Lamperti-type limit theorem for families of stochastic processes.; Danish Natural Science Research Council; FAPESP, Brazil

## Bias-corrected Pearson estimating functions for Taylors power law applied to benthic macrofauna data

JORGENSEN, Bent; DEMETRIO, Clarice G. B.; KRISTENSEN, Erik; BANTA, Gary T.; PETERSEN, Hans Christian; DELEFOSSE, Matthieu
Fonte: ELSEVIER SCIENCE BV Publicador: ELSEVIER SCIENCE BV
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
55.85%
Estimation of Taylors power law for species abundance data may be performed by linear regression of the log empirical variances on the log means, but this method suffers from a problem of bias for sparse data. We show that the bias may be reduced by using a bias-corrected Pearson estimating function. Furthermore, we investigate a more general regression model allowing for site-specific covariates. This method may be efficiently implemented using a Newton scoring algorithm, with standard errors calculated from the inverse Godambe information matrix. The method is applied to a set of biomass data for benthic macrofauna from two Danish estuaries. (C) 2011 Elsevier B.V. All rights reserved.; FAPESP; CNPq (Brazil); Danish Natural Science Research Council

## Optimal Reactive Power Planning Using Risk Analysis

Lopez, Julio C.; Mantovani, J. R. S.; Contreras Sanz, Javier; Munoz, Jose I.; IEEE
Tipo: Conferência ou Objeto de Conferência Formato: 5
ENG
Relevância na Pesquisa
35.84%
In this paper, the optimal reactive power planning problem under risk is presented. The classical mixed-integer nonlinear model for reactive power planning is expanded into two stage stochastic model considering risk. This new model considers uncertainty on the demand load. The risk is quantified by a factor introduced into the objective function and is identified as the variance of the random variables. Finally numerical results illustrate the performance of the proposed model, that is applied to IEEE 30-bus test system to determine optimal amount and location for reactive power expansion.

## Transient Responses to Rapid Changes in Mean and Variance in Spiking Models

Khorsand, Peyman; Chance, Frances
Fonte: Public Library of Science Publicador: Public Library of Science
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
35.74%
The mean input and variance of the total synaptic input to a neuron can vary independently, suggesting two distinct information channels. Here we examine the impact of rapidly varying signals, delivered via these two information conduits, on the temporal dynamics of neuronal firing rate responses. We examine the responses of model neurons to step functions in either the mean or the variance of the input current. Our results show that the temporal dynamics governing response onset depends on the choice of model. Specifically, the existence of a hard threshold introduces an instantaneous component into the response onset of a leaky-integrate-and-fire model that is not present in other models studied here. Other response features, for example a decaying oscillatory approach to a new steady-state firing rate, appear to be more universal among neuronal models. The decay time constant of this approach is a power-law function of noise magnitude over a wide range of input parameters. Understanding how specific model properties underlie these response features is important for understanding how neurons will respond to rapidly varying signals, as the temporal dynamics of the response onset and response decay to new steady-state determine what range of signal frequencies a population of neurons can respond to and faithfully encode.

## Variance estimation in the analysis of microarray data

Wang, Yuedong; Ma, Yanyuan; Carroll, Raymond J.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
35.89%
Microarrays are one of the most widely used high throughput technologies. One of the main problems in the area is that conventional estimates of the variances that are required in the t-statistic and other statistics are unreliable owing to the small number of replications. Various methods have been proposed in the literature to overcome this lack of degrees of freedom problem. In this context, it is commonly observed that the variance increases proportionally with the intensity level, which has led many researchers to assume that the variance is a function of the mean. Here we concentrate on estimation of the variance as a function of an unknown mean in two models: the constant coefficient of variation model and the quadratic variance–mean model. Because the means are unknown and estimated with few degrees of freedom, naive methods that use the sample mean in place of the true mean are generally biased because of the errors-in-variables phenomenon. We propose three methods for overcoming this bias. The first two are variations on the theme of the so-called heteroscedastic simulation–extrapolation estimator, modified to estimate the variance function consistently. The third class of estimators is entirely different, being based on semiparametric information calculations. Simulations show the power of our methods and their lack of bias compared with the naive method that ignores the measurement error. The methodology is illustrated by using microarray data from leukaemia patients.

## Flexible modeling of longitudinal highly-skewed outcomes

Chen, Huichao; Manatunga, Amita K.; Lyles, Robert H.; Peng, Limin; Marcus, Michele
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
35.59%
The analysis of data from epidemiologic and environmental studies present challenges such as skewness of distribution, rounding and multiple measurements over time. To model trends over time based on repeated measurements, we propose a general latent model suitable for highly skewed data. The model assumes that the observed outcome is determined by an unobservable outcome which follows a Weibull distribution. To accommodate correlations among repeated responses over time, we introduce a general random effect from the power variance function (PVF) family of distributions, including the gamma distribution often employed in the literature. The resulting marginal likelihood has a closed form without resorting to numerical or approximation methods. We study estimation and hypothesis testing under these models, with different choices of random effect distributions. Simulation studies are conducted to evaluate their performance. Finally, we apply the proposed method to exposure data collected from the Michigan polybrominated biphenyl (MIPBB) study.

## NONPARAMETRIC ESTIMATION OF GENEWISE VARIANCE FOR MICROARRAY DATA*

Fan, Jianqing; Feng, Yang; Niu, Yue S.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
35.82%
Estimation of genewise variance arises from two important applications in microarray data analysis: selecting significantly differentially expressed genes and validation tests for normalization of microarray data. We approach the problem by introducing a two-way nonparametric model, which is an extension of the famous Neyman-Scott model and is applicable beyond microarray data. The problem itself poses interesting challenges because the number of nuisance parameters is proportional to the sample size and it is not obvious how the variance function can be estimated when measurements are correlated. In such a high-dimensional nonparametric problem, we proposed two novel nonparametric estimators for genewise variance function and semiparametric estimators for measurement correlation, via solving a system of nonlinear equations. Their asymptotic normality is established. The finite sample property is demonstrated by simulation studies. The estimators also improve the power of the tests for detecting statistically differentially expressed genes. The methodology is illustrated by the data from MicroArray Quality Control (MAQC) project.

## A longitudinal Model for repeated interval-observed data with informative dropouts

Chen, Huichao; Manatunga, Amita K.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
35.59%
We consider repeated measures interval-observed data with informative dropouts. We model the repeated outcomes via an unobserved random intercept and it is assumed that the probability of dropout during the study period is linearly related to the random intercept in a complementary log-log scale. Assuming the random effect follows the power variance function (PVF) family suggested by Hougaard (2000), we derive the marginal likelihood in a closed form. We evaluate the performance of the maximum likelihood estimation via simulation studies and apply the proposed method to a real data set.

## Allometric scaling of population variance with mean body size is predicted from Taylor’s law and density-mass allometry

Cohen, Joel E.; Xu, Meng; Schuster, William S. F.
Tipo: Artigo de Revista Científica
EN
Relevância na Pesquisa
35.98%
Two widely tested empirical patterns in ecology are combined here to predict how the variation of population density relates to the average body size of organisms. Taylor’s law (TL) asserts that the variance of the population density of a set of populations is a power-law function of the mean population density. Density–mass allometry (DMA) asserts that the mean population density of a set of populations is a power-law function of the mean individual body mass. Combined, DMA and TL predict that the variance of the population density is a power-law function of mean individual body mass. We call this relationship “variance–mass allometry” (VMA). We confirmed the theoretically predicted power-law form and the theoretically predicted parameters of VMA, using detailed data on individual oak trees (Quercus spp.) of Black Rock Forest, Cornwall, New York. These results connect the variability of population density to the mean body mass of individuals.

## A bivariate survival model with compound Poisson frailty

Wienke, A.; Ripatti, S.; Palmgren, J.; Yashin, A.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
35.59%
A correlated frailty model is suggested for analysis of bivariate time-to-event data. The model is an extension of the correlated power variance function (PVF) frailty model (correlated three-parameter frailty model). It is based on a bivariate extension of the compound Poisson frailty model in univariate survival analysis. It allows for a non-susceptible fraction (of zero frailty) in the population, overcoming the common assumption in survival analysis that all individuals are susceptible to the event under study. The model contains the correlated gamma frailty model and the correlated inverse Gaussian frailty model as special cases. A maximum likelihood estimation procedure for the parameters is presented and its properties are studied in a small simulation study. This model is applied to breast cancer incidence data of Swedish twins. The proportion of women susceptible to breast cancer is estimated to be 15 per cent.

## Phylogenetic Comparative Methods for Evaluating the Evolutionary History of Function-Valued Traits

Goolsby, Eric W.
Fonte: Oxford University Press Publicador: Oxford University Press
Tipo: Artigo de Revista Científica Formato: text/html
EN
Relevância na Pesquisa
35.68%
Phylogenetic comparative methods offer a suite of tools for studying trait evolution. However, most models inherently assume fixed trait values within species. Although some methods can incorporate error around species means, few are capable of accounting for variation driven by environmental or temporal gradients, such as trait responses to abiotic stress or ontogenetic trajectories. Such traits, often referred to as function-valued or infinite-dimensional, are typically expressed as reaction norms, dose–response curves, or time plots and are described by mathematical functions linking independent predictor variables to the trait of interest. Here, I introduce a method for extending ancestral state reconstruction to incorporate function-valued traits in a phylogenetic generalized least squares (PGLS) framework, as well as extensions of this method for testing phylogenetic signal, performing phylogenetic analysis of variance (ANOVA), and testing for correlated trait evolution using recently proposed multivariate PGLS methods. Statistical power of function-valued comparative methods is compared to univariate approaches using data simulations, and the assumptions and challenges of each are discussed in detail.

## Integrative assessment of brain function in PTSD: brain stability and working memory

Veltmeyer, M.; McFarlane, A.; Bryant, R.; Mayo, T.; Gordon, E.; Clark, C.
Fonte: Inperial College Press Publicador: Inperial College Press
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
35.66%
Posttraumatic Stress Disorder (PTSD) is characterized by symptoms of hyperarousal, avoidance and intrusive trauma-related memories and deficits in everyday memory and attention. Separate studies in PTSD have found abnormalities in electroencephalogram EEG, in event-related potential (ERP) and behavioral measures of working memory and attention. The present study seeks to determine whether these abnormalities are related and the extent to which they share this relationship with clinical symptoms. EEG data were collected during an eyes-open paradigm and a one-back working memory task. Behavioral and clinical data (CAPS) were also collected. The PTSD group showed signs of altered cortical arousal as indexed by reduced alpha power and an increased theta/alpha ratio, and clinical and physiological measures of arousal were found to be related. The normal relationship between theta power and ERP indices of working memory was not affected in PTSD, with both sets of measures reduced in the disordered group. Medication appeared to underpin a number of abnormal parameters, including P3 amplitude to targets and the accuracy, though not speed, of target detection. The present study helps to overcome a limitation of earlier studies that assess such parameters independently in different groups of patients that vary in factors such as comorbidity...

## Stochastic multiplicative population growth predicts and interprets Taylor's power law of fluctuation scaling

Cohen, Joel E.; Xu, Meng; Schuster, William S. F.
Fonte: The Royal Society Publicador: The Royal Society
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
35.66%
Taylor's law (TL) asserts that the variance of the density (individuals per area or volume) of a set of comparable populations is a power-law function of the mean density of those populations. Despite the empirical confirmation of TL in hundreds of species, there is little consensus about why TL is so widely observed and how its estimated parameters should be interpreted. Here, we report that the Lewontin–Cohen (henceforth LC) model of stochastic population dynamics, which has been widely discussed and applied, leads to a spatial TL in the limit of large time and provides an explicit, exact interpretation of its parameters. The exponent of TL exceeds 2 if and only if the LC model is supercritical (growing on average), equals 2 if and only if the LC model is deterministic, and is less than 2 if and only if the LC model is subcritical (declining on average). TL and the LC model describe the spatial variability and the temporal dynamics of populations of trees on long-term plots censused over 75 years at the Black Rock Forest, Cornwall, NY, USA.

## Cosmic Microwave Background Anisotropy Window Functions Revisited

Knox, Lloyd
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
25.94%
The primary results of most observations of cosmic microwave background (CMB) anisotropy are estimates of the angular power spectrum averaged through some broad band, called band-powers. These estimates are in turn what are used to produce constraints on cosmological parameters due to all CMB observations. Essential to this estimation of cosmological parameters is the calculation of the expected band-power for a given experiment, given a theoretical power spectrum. Here we derive the "band power" window function which should be used for this calculation, and point out that it is not equivalent to the window function used to calculate the variance. This important distinction has been absent from much of the literature: the variance window function is often used as the band-power window function. We discuss the validity of this assumed equivalence, the role of window functions for experiments that constrain the power in {\it multiple} bands, and summarize a prescription for reporting experimental results. The analysis methods detailed here are applied in a companion paper to three years of data from the Medium Scale Anisotropy Measurement.; Comment: 5 pages, 1 included .eps figure, PRD in press---final published version

## Asymptotic and structural properties of special cases of the Wright function arising in probability theory

Tipo: Artigo de Revista Científica
Relevância na Pesquisa
35.69%
This analysis paper presents previously unknown properties of some special cases of the Wright function whose consideration is necessitated by our work on probability theory and the theory of stochastic processes. Specifically, we establish new asymptotic properties of the particular Wright function ${}_1\Psi_1(\rho,k; \rho,0;x)= \sum_{n=0}^\infty\frac{\Gamma(k+\rho n)}{\Gamma(\rho n)}\,\frac{x^n}{n!}\qquad (|x|<\infty)$ when the parameter $\rho\in (-1,0)\cup (0,\infty)$ and the argument $x$ is real. In the probability theory applications, which are focused on studies of the Poisson-Tweedie mixtures, the parameter $k$ is a non-negative integer. Several representations involving well-known special functions are given for certain particular values of $\rho$. The asymptotics of ${}_1\Psi_1(\rho,k;\rho,0;x)$ are obtained under numerous assumptions on the behavior of the arguments $k$ and $x$ when the parameter $\rho$ is both positive and negative. We also provide some integral representations and structural properties involving the `reduced' Wright function ${}_0\Psi_1(-\!\!\!-; \rho,0;x)$ with $\rho\in (-1,0)\cup (0,\infty)$, which might be useful for the derivation of new properties of members of the power-variance family of distributions. Some of these imply a reflection principle that connects the functions \${}_0\Psi_1(-\!\!\!-; \pm\rho...

## Weak Lensing Reconstruction and Power Spectrum Estimation: Minimum Variance Methods

Seljak, Uros
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
25.94%
Large-scale structure distorts the images of background galaxies, which allows one to measure directly the projected distribution of dark matter in the universe and determine its power spectrum. Here we address the question of how to extract this information from the observations. We derive minimum variance estimators for projected density reconstruction and its power spectrum and apply them to simulated data sets, showing that they give a good agreement with the theoretical minimum variance expectations. The same estimator can also be applied to the cluster reconstruction, where it remains a useful reconstruction technique, although it is no longer optimal for every application. The method can be generalized to include nonlinear cluster reconstruction and photometric information on redshifts of background galaxies in the analysis. We also address the question of how to obtain directly the 3-d power spectrum from the weak lensing data. We derive a minimum variance quadratic estimator, which maximizes the likelihood function for the 3-d power spectrum and can be computed either from the measurements directly or from the 2-d power spectrum. The estimator correctly propagates the errors and provides a full correlation matrix of the estimates. It can be generalized to the case where redshift distribution depends on the galaxy photometric properties...

## Nonparametric estimation of genewise variance for microarray data

Fan, Jianqing; Feng, Yang; Niu, Yue S.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
35.82%
Estimation of genewise variance arises from two important applications in microarray data analysis: selecting significantly differentially expressed genes and validation tests for normalization of microarray data. We approach the problem by introducing a two-way nonparametric model, which is an extension of the famous Neyman--Scott model and is applicable beyond microarray data. The problem itself poses interesting challenges because the number of nuisance parameters is proportional to the sample size and it is not obvious how the variance function can be estimated when measurements are correlated. In such a high-dimensional nonparametric problem, we proposed two novel nonparametric estimators for genewise variance function and semiparametric estimators for measurement correlation, via solving a system of nonlinear equations. Their asymptotic normality is established. The finite sample property is demonstrated by simulation studies. The estimators also improve the power of the tests for detecting statistically differentially expressed genes. The methodology is illustrated by the data from microarray quality control (MAQC) project.; Comment: Published in at http://dx.doi.org/10.1214/10-AOS802 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

## Taylor's power law: before and after 50 years of scientific scrutiny

Xu, Meng
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
35.8%
Taylor's power law (TPL) is one of the few empirical patterns in ecology discovered in the 20th century. It states that the variance of species population density scales as a power-law function of the mean population density. TPL earned its name after Lionel Roy Taylor's work "Aggregation, variance and the mean" published in the March 4, 1961 issue of Nature. During the past half-century, TPL was confirmed for thousands of biological species and even for non-biological quantities. Numerous theories and models have been proposed to explain the mechanisms of TPL. However an understanding of the historical origin of TPL is lacking. This work reviews two research aspects that are fundamental to the discovery of TPL and provides an outlook of the future studies on TPL.; Comment: 23 pages, 1 figure

## Double-power transformations to analyze data

Sato, Erika
Fonte: Rochester Instituto de Tecnologia Publicador: Rochester Instituto de Tecnologia
EN_US
Relevância na Pesquisa
35.7%
Power transformations are commonly used in order to fit simpler and/or more appropriate models to data. These transformations are well-known and well-documented for cases where the predictor variables are not linearly constrained, unlike mixture experiments. In the case of mixture designs, however, for which linear constraints do exist, several linear models proposed in recent literature fall into a power transformation family; this suggests that similar transformations might be useful for mixture experiments, as well. The log-likelihood function for X and y, transformations on the response and predictor variables, was derived for the mixture case where the predictor variables are linearly constrained and was maximized using a specially-written SAS program. To test the effectiveness of this procedure, simulations were done for two different designs and for four different combinations of X, and y. It was found that the 95% confidence region about A and f captured the true values of X and y approximately 90% of the time, regardless of the nature of the design or of the transformation. This procedure appeared to be able to discriminate between the different transformations on the response better than on the predictor variables, particularly when the correct transformation was the log-transformation (i.e....

## Statistical modeling of sugar cane potential bud sprouting within the context of a 3x3x2 factorial experiment

Arce,Osvaldo E. A.; Digonzelli,Patricia A.; Romero,Eduardo R.
Fonte: Revista industrial y agrícola de Tucumán Publicador: Revista industrial y agrícola de Tucumán
Tipo: Artigo de Revista Científica Formato: text/html