Computational aspects of Bayesian spectral density estimation

Gaussian time-series models are often specified through their spectral density. Such models present several computational challenges, in particular because of the non-sparse nature of the covariance matrix. We derive a fast approximation of the likelihood for such models. We propose to sample from the approximate posterior (that is, the prior times the approximate likelihood), and then to recover the exact posterior through importance sampling. We show that the variance of the importance sampling weights vanishes as the sample size goes to infinity. We explain why the approximate posterior may typically multi-modal, and we derive a Sequential Monte Carlo sampler based on an annealing sequence in order to sample from that target distribution. Performance of the overall approach is evaluated on simulated and real datasets. In addition, for one real world dataset, we provide some numerical evidence that a Bayesian approach to semi-parametric estimation of spectral density may provide more reasonable results than its Frequentist counter-parts

Bayesian nonparametric estimation of the spectral density of a long or intermediate memory Gaussian process

A stationary Gaussian process is said to be long-range dependent (resp., anti-persistent) if its spectral density $f(\lambda)$ can be written as $f(\lambda)=|\lambda|^{-2d}g(|\lambda|)$, where $0<d<1/2$ (resp., $-1/2<d<0$), and $g$ is continuous and positive. We propose a novel Bayesian nonparametric approach for the estimation of the spectral density of such processes. We prove posterior consistency for both $d$ and $g$, under appropriate conditions on the prior distribution. We establish the rate of convergence for a general class of priors and apply our results to the family of fractionally exponential priors. Our approach is based on the true likelihood and does not resort to Whittle's approximation.Comment: Published in at http://dx.doi.org/10.1214/11-AOS955 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Rejoinder: Harold Jeffreys's Theory of Probability Revisited

We are grateful to all discussants of our re-visitation for their strong support in our enterprise and for their overall agreement with our perspective. Further discussions with them and other leading statisticians showed that the legacy of Theory of Probability is alive and lasting. [arXiv:0804.3173]Comment: Published in at http://dx.doi.org/10.1214/09-STS284REJ the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Employee ownership as a signal of management quality

The employees' decision to become shareholder of the company they work for can be a consequence of employers' matching contribution in company stock. From a behavioral perspective, employees would regard these contributions as an implicit investment advice made by their employer. This paper adopts another viewpoint. Since employee ownership can be used as an entrenchment mechanism, we suggest that employer's matching policy can be considered as an imperfect signal of management quality. This paper suggests that employee ownership can be used by managers to compensate their management skills to the market. It recommends that employee ownership policy should not be influenced by the managers.Employee ownership ; corporate governance ; management entrenchment

Dependence of DNA persistence length on ionic strength of solutions with monovalent and divalent salts: a joint theory-experiment study

Using high-throughput Tethered Particle Motion single molecule experiments, the double-stranded DNA persistence length, $L_p$, is measured in solutions with Na$^+$ and Mg$^{2+}$ ions of various ionic strengths, $I$. Several theoretical equations for $L_p(I)$ are fitted to the experimental data, but no decisive theory is found which fits all the $L_p$ values for the two ion valencies. Properly extracted from the particle trajectory using simulations, $L_p$ varies from 30~nm to 55~nm, and is compared to previous experimental results. For the Na$^+$ only case, $L_p$ is an increasing concave function of $I^{-1}$, well fitted by Manning's electrostatic stretching approach, but not by classical Odjik-Skolnick-Fixman theories with or without counter-ion condensation. With added Mg$^{2+}$ ions, $L_p$ shows a marked decrease at low $I$, interpreted as an ion-ion correlation effect, with an almost linear law in $I^{-1}$, fitted by a proposed variational approach

Evaluation des ressources en eau d'une société cévenole traditionnelle (XIXe siècle). Exemple du bassin versant de la Drobie (Ardèche, France).

Les techniques de captage et d'adduction de la ressource hydrique, mises en œuvre par les sociétés traditionnelles du passé récent (XVIIIe – XIXe siècles), ont été décrites et étudiées abondamment et depuis longtemps. Cependant, on connaît encore fort mal les conditions d'accès à l'eau dans ces sociétés ainsi que les volumes hydriques mobilisables. Ce manque de repère est issu d'un ensemble de raisons : le faible intérêt des statisticiens du XIXe siècle pour les sociétés rurales, la rareté des jaugeages des sources ou des captages jusqu'à une date récente, l'intérêt porté à la partie juridique de l'irrigation (droits d'eau) au détriment de l'étude quantitative des ressources en eau d'une société traditionnelle. Pourtant, une meilleure connaissance de la disponibilité en eau de ces sociétés serait utile à bien des égards : l'historien ou le juriste y trouveraient des bases concrètes pour une étude des conflits et des concurrences pour la ressource, comme pour une analyse des droits d'eau et de leur élaboration. Ces données permettraient aussi au géographe d'intéressantes comparaisons avec des sociétés rurales contemporaines encore confrontées au problème de la pénurie hydrique

Employee ownership as a signal of management quality

The employees' decision to become shareholder of the company they work for can be a consequence of employers' matching contribution in company stock. From a behavioral perspective, employees would regard these contributions as an implicit investment advice made by their employer. This paper adopts another viewpoint. Since employee ownership can be used as an entrenchment mechanism, we suggest that employer's matching policy can be considered as an imperfect signal of management quality. This paper suggests that employee ownership can be used by managers to compensate their management skills to the market. It recommends that employee ownership policy should not be influenced by the managers

Measure propagation along C0\mathscr{C}^0-vector field and wave controllability on a rough compact manifold

The celebrated Rauch-Taylor/Bardos-Lebeau-Rauch geometric control condition is central in the study of the observability of the wave equation linking this property to high-frequency propagation along geodesics that are therays of geometric optics. This connection is best understood through the propagation properties of microlocal defect measures that appear as solutions to the wave equation concentrate. For a sufficiently smooth metric this propagation occurs along the bicharacteristic flow. If one considers a merely $\mathscr{C}^1$-metric this bicharacteristic flow may however not exist. The Hamiltonian vector field is only continuous; bicharacteristics do exist (as integral curves of this continuous vector field) but uniqueness is lost. Here, on a compact manifold without boundary, we consider this low regularity setting, revisit the geometric control condition, and address the question of support propagation for a measure solution to an ODE with continuous coefficients. This leads to a sufficient condition for the observability and equivalently the exact controllability of the wave equation. Moreover, we investigate the stabililty of the observability property and the sensitivity of the control process under a perturbation of the metric of regularity as low as Lipschitz