On the occurrence times of componentwise maxima and bias in likelihood inference for multivariate max-stable distributions

Full likelihood-based inference for high-dimensional multivariate extreme value distributions, or max-stable processes, is feasible when incorporating occurrence times of the maxima; without this information, $d$-dimensional likelihood inference is usually precluded due to the large number of terms in the likelihood. However, some studies have noted bias when performing high-dimensional inference that incorporates such event information, particularly when dependence is weak. We elucidate this phenomenon, showing that for unbiased inference in moderate dimensions, dimension $d$ should be of a magnitude smaller than the square root of the number of vectors over which one takes the componentwise maximum. A bias reduction technique is suggested and illustrated on the extreme value logistic model.Comment: 7 page

Accounting for choice of measurement scale in extreme value modeling

We investigate the effect that the choice of measurement scale has upon inference and extrapolation in extreme value analysis. Separate analyses of variables from a single process on scales which are linked by a nonlinear transformation may lead to discrepant conclusions concerning the tail behavior of the process. We propose the use of a Box--Cox power transformation incorporated as part of the inference procedure to account parametrically for the uncertainty surrounding the scale of extrapolation. This has the additional feature of increasing the rate of convergence of the distribution tails to an extreme value form in certain cases and thus reducing bias in the model estimation. Inference without reparameterization is practicably infeasible, so we explore a reparameterization which exploits the asymptotic theory of normalizing constants required for nondegenerate limit distributions. Inference is carried out in a Bayesian setting, an advantage of this being the availability of posterior predictive return levels. The methodology is illustrated on both simulated data and significant wave height data from the North Sea.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS333 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Photonic crystal fibre source of photon pairs for quantum information processing

We demonstrate two key components for optical quantum information processing: a bright source of heralded single photons; and a bright source of entangled photon pairs. A pair of pump photons produces a correlated pair of photons at widely spaced wavelengths (583 nm and 900 nm), via a $\chi^{(3)}$ four-wave mixing process. We demonstrate a non-classical interference between heralded photons from independent sources with a visibility of 95%, and an entangled photon pair source, with a fidelity of 89% with a Bell state.Comment: 4 pages, 3 figure

Photon pair generation using four-wave mixing in a microstructured fibre: theory versus experiment

We develop a theoretical analysis of four-wave mixing used to generate photon pairs useful for quantum information processing. The analysis applies to a single mode microstructured fibre pumped by an ultra-short coherent pulse in the normal dispersion region. Given the values of the optical propagation constant inside the fibre, we can estimate the created number of photon pairs per pulse, their central wavelength and their respective bandwidth. We use the experimental results from a picosecond source of correlated photon pairs using a micro-structured fibre to validate the model. The fibre is pumped in the normal dispersion regime at 708nm and phase matching is satisfied for widely spaced parametric wavelengths of 586nm and 894nm. We measure the number of photons per pulse using a loss-independent coincidence scheme and compare the results with the theoretical expectation. We show a good agreement between the theoretical expectations and the experimental results for various fibre lengths and pump powers.Comment: 23 pages, 9 figure

Study to establish cost projections for production of Redox chemicals

A cost study of four proposed manufacturing processes for redox chemicals for the NASA REDOX Energy Storage System yielded favorable selling prices in the range $0.99 to$1.91/kg of chromic chloride, anhydrous basis, including ferrous chloride. The prices corresponded to specific energy storage costs from under $9 to$17/kWh. A refined and expanded cost analysis of the most favored process yielded a price estimate corresponding to a storage cost of $11/kWh. The findings supported the potential economic viability of the NASA REDOX system

An All Optical Fibre Quantum Controlled-NOT Gate

We report the first experimental demonstration of an optical controlled-NOT gate constructed entirely in fibre. We operate the gate using two heralded optical fibre single photon sources and find an average logical fidelity of 90% and an average process fidelity of 0.83<F<0.91. On the basis of a simple model we are able to conclude that imperfections are primarily due to the photon sources, meaning that the gate itself works with very high fidelity.Comment: 4 pages, 4 figures, comments welcom

Two-photon interference between disparate sources for quantum networking

Quantum networks involve entanglement sharing between multiple users. Ideally, any two users would be able to connect regardless of the type of photon source they employ, provided they fulfill the requirements for two-photon interference. From a theoretical perspective, photons coming from different origins can interfere with a perfect visibility, provided they are made indistinguishable in all degrees of freedom. Previous experimental demonstrations of such a scenario have been limited to photon wavelengths below 900 nm, unsuitable for long distance communication, and suffered from low interference visibility. We report two-photon interference using two disparate heralded single photon sources, which involve different nonlinear effects, operating in the telecom wavelength range. The measured visibility of the two-photon interference is 80+/-4%, which paves the way to hybrid universal quantum networks

On the Estimation of Bivariate Return Curves for Extreme Values

In the multivariate setting, defining extremal risk measures is important in many contexts, such as finance, environmental planning and structural engineering. In this paper, we review the literature on extremal bivariate return curves, a risk measure that is the natural bivariate extension to a return level, and propose new estimation methods based on multivariate extreme value models that can account for both asymptotic dependence and asymptotic independence. We identify gaps in the existing literature and propose novel tools for testing and validating return curves and comparing estimates from a range of multivariate models. These tools are then used to compare a selection of models through simulation and case studies. We conclude with a discussion and list some of the challenges.Comment: 41 pages (without supplementary), 11 figures, 2 table

Improving estimation for asymptotically independent bivariate extremes via global estimators for the angular dependence function

Modelling the extremal dependence of bivariate variables is important in a wide variety of practical applications, including environmental planning, catastrophe modelling and hydrology. The majority of these approaches are based on the framework of bivariate regular variation, and a wide range of literature is available for estimating the dependence structure in this setting. However, this framework is only applicable to variables exhibiting asymptotic dependence, even though asymptotic independence is often observed in practice. In this paper, we consider the so-called `angular dependence function'; this quantity summarises the extremal dependence structure for asymptotically independent variables. Until recently, only pointwise estimators of the angular dependence function have been available. We introduce a range of global estimators and compare them to another recently introduced technique for global estimation through a systematic simulation study, and a case study on river flow data from the north of England, UK

The narrative potential of the British Birth Cohort Studies

This paper draws attention to the narrative potential of longitudinal studies such as the British Birth Cohort Studies (BBCS), and explores the possibility of creating narrative case histories and conducting narrative analysis based on information available from the studies. The BBCS have historically adopted a quantitative research design and used structured interviews and questionnaires to collect data from large samples of individuals born in specific years. However, the longitudinal nature of these studies means that they follow the same sample of individuals from birth through childhood into adult life, and this leads to the creation of data that can be understood as a quantitative auto/biography