1,249 research outputs found
Precise Estimation of Cosmological Parameters Using a More Accurate Likelihood Function
The estimation of cosmological parameters from a given data set requires a
construction of a likelihood function which, in general, has a complicated
functional form. We adopt a Gaussian copula and constructed a copula likelihood
function for the convergence power spectrum from a weak lensing survey. We show
that the parameter estimation based on the Gaussian likelihood erroneously
introduces a systematic shift in the confidence region, in particular for a
parameter of the dark energy equation of state w. Thus, the copula likelihood
should be used in future cosmological observations.Comment: 5 pages, 3 figures. Maches version published by the Physical Review
Letter
An information theoretic approach to statistical dependence: copula information
We discuss the connection between information and copula theories by showing
that a copula can be employed to decompose the information content of a
multivariate distribution into marginal and dependence components, with the
latter quantified by the mutual information. We define the information excess
as a measure of deviation from a maximum entropy distribution. The idea of
marginal invariant dependence measures is also discussed and used to show that
empirical linear correlation underestimates the amplitude of the actual
correlation in the case of non-Gaussian marginals. The mutual information is
shown to provide an upper bound for the asymptotic empirical log-likelihood of
a copula. An analytical expression for the information excess of T-copulas is
provided, allowing for simple model identification within this family. We
illustrate the framework in a financial data set.Comment: to appear in Europhysics Letter
Evolution of the Dependence of Residual Lifetimes
We investigate the dependence properties of a vector of residual lifetimes by means of the copula associated with the conditional distribution function. In particular, the evolution of positive dependence properties (like quadrant dependence and total positivity) are analyzed and expressions for the evolution of measures of association are given
Multivariate Copula Analysis Toolbox (MvCAT): Describing Dependence and Underlying Uncertainty Using a Bayesian Framework
We present a newly developed Multivariate Copula Analysis Toolbox (MvCAT) which includes a wide range of copula families with different levels of complexity. MvCAT employs a Bayesian framework with a residual-based Gaussian likelihood function for inferring copula parameters and estimating the underlying uncertainties. The contribution of this paper is threefold: (a) providing a Bayesian framework to approximate the predictive uncertainties of fitted copulas, (b) introducing a hybrid-evolution Markov Chain Monte Carlo (MCMC) approach designed for numerical estimation of the posterior distribution of copula parameters, and (c) enabling the community to explore a wide range of copulas and evaluate them relative to the fitting uncertainties. We show that the commonly used local optimization methods for copula parameter estimation often get trapped in local minima. The proposed method, however, addresses this limitation and improves describing the dependence structure. MvCAT also enables evaluation of uncertainties relative to the length of record, which is fundamental to a wide range of applications such as multivariate frequency analysis
Risk Assessment and the Effects of Refuge Availability on the Defensive Behaviors of the Southern Unstriped Scorpion (Vaejovis carolinianus)
Selection should favor individuals that acquire, process, and act on relevant environmental signals to avoid predation. Studies have found that scorpions control their use of venom: both when it is released and the total volume expelled. However, this research has not included how a scorpion’s awareness of environmental features influences these decisions. The current study tested 18 Vaejovis carolinianus scorpions (nine females and nine males) by placing them in circular arenas supplied with varying numbers (zero, two, or four) of square refuges and by tracking their movements overnight. The following morning, defensive behaviors were elicited by prodding scorpions on the chelae, prosoma, and metasoma once per second over 90 s. We recorded stings, venom use, chelae pinches, and flee duration. We found strong evidence that, across all behaviors measured, V. carolinianus perceived prods to the prosoma as more threatening than prods to the other locations. We found that stinging was a common behavior and became more dominant as the threat persisted. Though tenuous, we found evidence that scorpions’ defensive behaviors changed based on the number of refuges and that these differences may be sex specific. Our findings suggest that V. carolinianus can assess risk and features of the local environment and, therefore, alter their defensive strategies accordingly
The role of the stress trap in polariton quasiequilibrium condensation in GaAs microcavities
Recent experiments have shown several effects indicative of Bose-Einstein
condensation in polaritons in GaAs-based microcavity structures when a harmonic
potential trap for the two-dimensional polaritons is created by applied stress.
These effects include both real-space and momentum-space narrowing, first-order
coherence, and onset of linear polarization above a particle density threshold.
Similar effects have been seen in systems without traps, raising the question
of how important the role of the trap is in these experiments. In this paper we
present results for both trapped conditions and resonant, non-trapped
conditions in the same sample. We find that the results are qualitatively
different, with two distinct types of transitions. At low density in the trap,
the polaritons remain in the strong-coupling regime while going through the
threshold for onset of coherence; at higher density, there is a different
threshold behavior which occurs with weak coupling and can be identified with
lasing; this transition occurs both with and without a trap
Testing the Gaussian Copula Hypothesis for Financial Assets Dependences
Using one of the key property of copulas that they remain invariant under an
arbitrary monotonous change of variable, we investigate the null hypothesis
that the dependence between financial assets can be modeled by the Gaussian
copula. We find that most pairs of currencies and pairs of major stocks are
compatible with the Gaussian copula hypothesis, while this hypothesis can be
rejected for the dependence between pairs of commodities (metals).
Notwithstanding the apparent qualification of the Gaussian copula hypothesis
for most of the currencies and the stocks, a non-Gaussian copula, such as the
Student's copula, cannot be rejected if it has sufficiently many ``degrees of
freedom''. As a consequence, it may be very dangerous to embrace blindly the
Gaussian copula hypothesis, especially when the correlation coefficient between
the pair of asset is too high as the tail dependence neglected by the Gaussian
copula can be as large as 0.6, i.e., three out five extreme events which occur
in unison are missed.Comment: Latex document of 43 pages including 14 eps figure
Distorted Copulas: Constructions and Tail Dependence
Given a copula C, we examine under which conditions on an order isomorphism ψ of [0, 1] the distortion C ψ: [0, 1]2 → [0, 1], C ψ(x, y) = ψ{C[ψ−1(x), ψ−1(y)]} is again a copula. In particular, when the copula C is totally positive of order 2, we give a sufficient condition on ψ that ensures that any distortion of C by means of ψ is again a copula. The presented results allow us to introduce in a more flexible way families of copulas exhibiting different behavior in the tails
The Bivariate Normal Copula
We collect well known and less known facts about the bivariate normal
distribution and translate them into copula language. In addition, we prove a
very general formula for the bivariate normal copula, we compute Gini's gamma,
and we provide improved bounds and approximations on the diagonal.Comment: 24 page
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