Search results for "Probability"
showing 10 items of 3417 documents
Role of the noise on the transient dynamics of an ecosystem of interacting species
2002
Abstract We analyze the transient dynamics of an ecosystem described by generalized Lotka–Volterra equations in the presence of a multiplicative noise and a random interaction parameter between the species. We consider specifically three cases: (i) two competing species, (ii) three interacting species (one predator–two preys), (iii) n-interacting species. The interaction parameter in case (i) is a stochastic process which obeys a stochastic differential equation. We find noise delayed extinction of one of two species, which is akin to the noise-enhanced stability phenomenon. Other two noise-induced effects found are temporal oscillations and spatial patterns of the two competing species. In…
Spatio-temporal patterns in population dynamics
2002
Abstract The transient dynamics of interacting biological species extracted from two ecosystems is investigated. We model the environment interaction by a multiplicative noise and the temperature oscillations by a periodic forcing. We find noise-induced effects such as enhanced temporal oscillations, spatial patterns and noise delayed extinction for the model of two competing species. We extend our analysis to an ecosystem of three interacting species, namely one predator and two preys. We find spatial patterns induced by the noise.
Multivariate Nonparametric Tests
2004
Multivariate nonparametric statistical tests of hypotheses are described for the one-sample location problem, the several-sample location problem and the problem of testing independence between pairs of vectors. These methods are based on affine-invariant spatial sign and spatial rank vectors. They provide affine-invariant multivariate generalizations of the univariate sign test, signed-rank test, Wilcoxon rank sum test, Kruskal–Wallis test, and the Kendall and Spearman correlation tests. While the emphasis is on tests of hypotheses, certain references to associated affine-equivariant estimators are included. Pitman asymptotic efficiencies demonstrate the excellent performance of these meth…
Spatial Mark-Recapture Method in the Estimation of Crayfish Population Size
1995
The mark-recapture method is considered for estimation of population size of slowly moving animals like crayfish. The Petersen type estimator for closed population is generalized for situations where recaptures are spatially dependent between the capture sites, and its variance approximation is derived using point processes as models for the population. The method of quadratic forms is suggested to be used as variance estimator. Finally, a trapping design is proposed where onc trap at recapture is replaced by four adjacent traps. A simulation experiment is performed to explain the robusticity of the new trapping design against movements of animals.
Rise and fall of historic tram networks: Logistic approximation and discontinuous events
2019
Abstract A logistic approximation was used to describe, in terms of total length (L) and population (H) variables, the growth and decay of historic transportation systems. Three successive stages, separated for sharp discontinuities were detected for several European tramway and metro systems, corresponding to a fast initial growth followed by an intermediate step of slow growth and a final stage of rapid decay. A common, generalized behaviour was obtained in the L/H vs. H variations relative to critical values of L and H parameters defined from the maximum in the L/H ratio.
Efficient Estimation of Non-Linear Finite Population Parameters by Using Non-Parametrics
2013
Summary Currently, high precision estimation of non-linear parameters such as Gini indices, low income proportions or other measures of inequality is particularly crucial. We propose a general class of estimators for such parameters that take into account univariate auxiliary information assumed to be known for every unit in the population. Through a non-parametric model-assisted approach, we construct a unique system of survey weights that can be used to estimate any non-linear parameter that is associated with any study variable of the survey, using a plug-in principle. Based on a rigorous functional approach and a linearization principle, the asymptotic variance of the estimators propose…
A Random Field Approach to Transect Counts of Wildlife Populations
1991
Line transect counting of a wildlife population is considered a sampling from a planar marked point process, where the marks describe the detectability of the animals. Sampling properties of transect counts and a new density estimator are derived from a counting process, which is a shot-noise field induced by the marked point process. A general formula for the sampling variance of a transect is derived and applied to compare five common types of transects. Some stereological connections of transect sampling and density estimators are shown.
Role of sub- and super-Poisson noise sources in population dynamics
2020
In this paper we present a study on pulse noise sources characterized by sub- and super-Poisson statistics. We make a comparison with their uncorrelated counterpart. i.e. pulse noise with Poisson statistics, while showing that the correlation properties of sub- and super-Poisson noise sources can be efficiently applied to population dynamics. Specifically, we consider a termite population, described by a Langevin equation in the presence of a pulse noise source, and we study its dynamics and stability properties for two models. The first one describes a population of several colonies in a new territory with adverse environmental conditions. The second one considers the development of a sing…
On implementation of the Gibbs sampler for estimating the accuracy of multiple diagnostic tests
2010
Implementation of the Gibbs sampler for estimating the accuracy of multiple binary diagnostic tests in one population has been investigated. This method, proposed by Joseph, Gyorkos and Coupal, makes use of a Bayesian approach and is used in the absence of a gold standard to estimate the prevalence, the sensitivity and specificity of medical diagnostic tests. The expressions that allow this method to be implemented for an arbitrary number of tests are given. By using the convergence diagnostics procedure of Raftery and Lewis, the relation between the number of iterations of Gibbs sampling and the precision of the estimated quantiles of the posterior distributions is derived. An example conc…
Extremal polynomials in stratified groups
2018
We introduce a family of extremal polynomials associated with the prolongation of a stratified nilpotent Lie algebra. These polynomials are related to a new algebraic characterization of abnormal subriemannian geodesics in stratified nilpotent Lie groups. They satisfy a set of remarkable structure relations that are used to integrate the adjoint equations.