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Velocity-Based Movement Modeling for Individual and Population Level Inference  [PDF]
Ephraim M. Hanks, Mevin B. Hooten, Devin S. Johnson, Jeremy T. Sterling
PLOS ONE , 2011, DOI: 10.1371/journal.pone.0022795
Abstract: Understanding animal movement and resource selection provides important information about the ecology of the animal, but an animal's movement and behavior are not typically constant in time. We present a velocity-based approach for modeling animal movement in space and time that allows for temporal heterogeneity in an animal's response to the environment, allows for temporal irregularity in telemetry data, and accounts for the uncertainty in the location information. Population-level inference on movement patterns and resource selection can then be made through cluster analysis of the parameters related to movement and behavior. We illustrate this approach through a study of northern fur seal (Callorhinus ursinus) movement in the Bering Sea, Alaska, USA. Results show sex differentiation, with female northern fur seals exhibiting stronger response to environmental variables.
Bayesian inference for the multivariate skew-normal model: a Population Monte Carlo approach  [PDF]
Brunero Liseo,Antonio Parisi
Statistics , 2013,
Abstract: Frequentist and likelihood methods of inference based on the multivariate skew-normal model encounter several technical difficulties with this model. In spite of the popularity of this class of densities, there are no broadly satisfactory solutions for estimation and testing problems. A general population Monte Carlo algorithm is proposed which: 1) exploits the latent structure stochastic representation of skew-normal random variables to provide a full Bayesian analysis of the model and 2) accounts for the presence of constraints in the parameter space. The proposed approach can be defined as weakly informative, since the prior distribution approximates the actual reference prior for the shape parameter vector. Results are compared with the existing classical solutions and the practical implementation of the algorithm is illustrated via a simulation study and a real data example. A generalization to the matrix variate regression model with skew-normal error is also presented.
Valid population inference for information-based imaging: Information prevalence inference  [PDF]
Carsten Allefeld,Kai G?rgen,John-Dylan Haynes
Statistics , 2015,
Abstract: In multivariate pattern analysis of neuroimaging data, 'second-level' inference is often performed by entering classification accuracies into a t-test vs chance level across subjects. We argue that while the random effects analysis implemented by the t-test does provide population inference if applied to activation differences, it fails to do so in the case of classification accuracy or other 'information-like' measures, because the true value of such measures can never be below chance level. This constraint changes the meaning of the population-level null hypothesis being tested, which becomes equivalent to the global null hypothesis that there is no effect in any subject in the population. Consequently, rejecting it only allows to infer that there are some subjects in which there is an information effect, but not that it generalizes. This statement is supported by theoretical arguments as well as simulations. We review possible alternative approaches to population inference for information-based imaging, converging on the idea that it should not target the mean, but the prevalence of the effect in the population. One method to do so, 'permutation-based information prevalence inference using the minimum statistic', is described in detail and applied to empirical data.
Bayesian Inference for Generalized Linear Mixed Model Based on the Multivariate t Distribution in Population Pharmacokinetic Study  [PDF]
Fang-Rong Yan, Yuan Huang, Jun-Lin Liu, Tao Lu, Jin-Guan Lin
PLOS ONE , 2013, DOI: 10.1371/journal.pone.0058369
Abstract: This article provides a fully Bayesian approach for modeling of single-dose and complete pharmacokinetic data in a population pharmacokinetic (PK) model. To overcome the impact of outliers and the difficulty of computation, a generalized linear model is chosen with the hypothesis that the errors follow a multivariate Student t distribution which is a heavy-tailed distribution. The aim of this study is to investigate and implement the performance of the multivariate t distribution to analyze population pharmacokinetic data. Bayesian predictive inferences and the Metropolis-Hastings algorithm schemes are used to process the intractable posterior integration. The precision and accuracy of the proposed model are illustrated by the simulating data and a real example of theophylline data.
Topological inference for EEG and MEG  [PDF]
James M. Kilner,Karl J. Friston
Statistics , 2010, DOI: 10.1214/10-AOAS337
Abstract: Neuroimaging produces data that are continuous in one or more dimensions. This calls for an inference framework that can handle data that approximate functions of space, for example, anatomical images, time--frequency maps and distributed source reconstructions of electromagnetic recordings over time. Statistical parametric mapping (SPM) is the standard framework for whole-brain inference in neuroimaging: SPM uses random field theory to furnish $p$-values that are adjusted to control family-wise error or false discovery rates, when making topological inferences over large volumes of space. Random field theory regards data as realizations of a continuous process in one or more dimensions. This contrasts with classical approaches like the Bonferroni correction, which consider images as collections of discrete samples with no continuity properties (i.e., the probabilistic behavior at one point in the image does not depend on other points). Here, we illustrate how random field theory can be applied to data that vary as a function of time, space or frequency. We emphasize how topological inference of this sort is invariant to the geometry of the manifolds on which data are sampled. This is particularly useful in electromagnetic studies that often deal with very smooth data on scalp or cortical meshes. This application illustrates the versatility and simplicity of random field theory and the seminal contributions of Keith Worsley (1951--2009), a key architect of topological inference.
GAGA: A New Algorithm for Genomic Inference of Geographic Ancestry Reveals Fine Level Population Substructure in Europeans  [PDF]
Oscar Lao ,Fan Liu,Andreas Wollstein,Manfred Kayser
PLOS Computational Biology , 2014, DOI: doi/10.1371/journal.pcbi.1003480
Abstract: Attempts to detect genetic population substructure in humans are troubled by the fact that the vast majority of the total amount of observed genetic variation is present within populations rather than between populations. Here we introduce a new algorithm for transforming a genetic distance matrix that reduces the within-population variation considerably. Extensive computer simulations revealed that the transformed matrix captured the genetic population differentiation better than the original one which was based on the T1 statistic. In an empirical genomic data set comprising 2,457 individuals from 23 different European subpopulations, the proportion of individuals that were determined as a genetic neighbour to another individual from the same sampling location increased from 25% with the original matrix to 52% with the transformed matrix. Similarly, the percentage of genetic variation explained between populations by means of Analysis of Molecular Variance (AMOVA) increased from 1.62% to 7.98%. Furthermore, the first two dimensions of a classical multidimensional scaling (MDS) using the transformed matrix explained 15% of the variance, compared to 0.7% obtained with the original matrix. Application of MDS with Mclust, SPA with Mclust, and GemTools algorithms to the same dataset also showed that the transformed matrix gave a better association of the genetic clusters with the sampling locations, and particularly so when it was used in the AMOVA framework with a genetic algorithm. Overall, the new matrix transformation introduced here substantially reduces the within population genetic differentiation, and can be broadly applied to methods such as AMOVA to enhance their sensitivity to reveal population substructure. We herewith provide a publically available (http://www.erasmusmc.nl/fmb/resources/GA?GA) model-free method for improved genetic population substructure detection that can be applied to human as well as any other species data in future studies relevant to evolutionary biology, behavioural ecology, medicine, and forensics.
A General HIV Incidence Inference Scheme Based on Likelihood of Individual Level Data and a Population Renewal Equation  [PDF]
Guy Severin Mahiane, Rachid Ouifki, Hilmarie Brand, Wim Delva, Alex Welte
PLOS ONE , 2012, DOI: 10.1371/journal.pone.0044377
Abstract: We derive a new method to estimate the age specific incidence of an infection with a differential mortality, using individual level infection status data from successive surveys. The method consists of a) an SI-type model to express the incidence rate in terms of the prevalence and its derivatives as well as the difference in mortality rate, and b) a maximum likelihood approach to estimate the prevalence and its derivatives. Estimates can in principle be obtained for any chosen age and time, and no particular assumptions are made about the epidemiological or demographic context. This is in contrast with earlier methods for estimating incidence from prevalence data, which work with aggregated data, and the aggregated effect of demographic and epidemiological rates over the time interval between prevalence surveys. Numerical simulation of HIV epidemics, under the presumption of known excess mortality due to infection, shows improved control of bias and variance, compared to previous methods. Our analysis motivates for a) effort to be applied to obtain accurate estimates of excess mortality rates as a function of age and time among HIV infected individuals and b) use of individual level rather than aggregated data in order to estimate HIV incidence rates at times between two prevalence surveys.
David D. Hanagal
Journal of Reliability and Statistical Studies , 2009,
Abstract: Block (1975) extended bivariate exponential distributions (BVEDs) of Freund (1961)and Proschan and Sullo (1974) to multivariate case and called them as Generalized Freund-Weinman's multivariate exponential distributions (MVEDs). In this paper, we obtain MLEs of theparameters and large sample test for testing independence and symmetry of k components in thegeneralized Freund-Weinman's MVEDs.
Inference for Multivariate Normal Mixtures  [PDF]
Jiahua Chen,Xianming Tan
Mathematics , 2008,
Abstract: Multivariate normal mixtures provide a flexible model for high-dimensional data. They are widely used in statistical genetics, statistical finance, and other disciplines. Due to the unboundedness of the likelihood function, classical likelihood-based methods, which may have nice practical properties, are inconsistent. In this paper, we recommend a penalized likelihood method for estimating the mixing distribution. We show that the maximum penalized likelihood estimator is strongly consistent when the number of components has a known upper bound. We also explore a convenient EM-algorithm for computing the maximum penalized likelihood estimator. Extensive simulations are conducted to explore the effectiveness and the practical limitations of both the new method and the ratified maximum likelihood estimators. Guidelines are provided based on the simulation results.
Multivariate Modality Inference Using Gaussian Kernel  [PDF]
Yansong Cheng, Surajit Ray
Open Journal of Statistics (OJS) , 2014, DOI: 10.4236/ojs.2014.45041

The number of modes (also known as modality) of a kernel density estimator (KDE) draws lots of interests and is important in practice. In this paper, we develop an inference framework on the modality of a KDE under multivariate setting using Gaussian kernel. We applied the modal clustering method proposed by [1] for mode hunting. A test statistic and its asymptotic distribution are derived to assess the significance of each mode. The inference procedure is applied on both simulated and real data sets.

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