348 research outputs found
Stochastic models which separate fractal dimension and Hurst effect
Fractal behavior and long-range dependence have been observed in an
astonishing number of physical systems. Either phenomenon has been modeled by
self-similar random functions, thereby implying a linear relationship between
fractal dimension, a measure of roughness, and Hurst coefficient, a measure of
long-memory dependence. This letter introduces simple stochastic models which
allow for any combination of fractal dimension and Hurst exponent. We
synthesize images from these models, with arbitrary fractal properties and
power-law correlations, and propose a test for self-similarity.Comment: 8 pages, 2 figure
Evaluating epidemic forecasts in an interval format
For practical reasons, many forecasts of case, hospitalization and death
counts in the context of the current COVID-19 pandemic are issued in the form
of central predictive intervals at various levels. This is also the case for
the forecasts collected in the COVID-19 Forecast Hub
(https://covid19forecasthub.org/). Forecast evaluation metrics like the
logarithmic score, which has been applied in several infectious disease
forecasting challenges, are then not available as they require full predictive
distributions. This article provides an overview of how established methods for
the evaluation of quantile and interval forecasts can be applied to epidemic
forecasts in this format. Specifically, we discuss the computation and
interpretation of the weighted interval score, which is a proper score that
approximates the continuous ranked probability score. It can be interpreted as
a generalization of the absolute error to probabilistic forecasts and allows
for a decomposition into a measure of sharpness and penalties for over- and
underprediction
Probabilistic quantitative precipitation field forecasting using a two-stage spatial model
Short-range forecasts of precipitation fields are needed in a wealth of
agricultural, hydrological, ecological and other applications. Forecasts from
numerical weather prediction models are often biased and do not provide
uncertainty information. Here we present a postprocessing technique for such
numerical forecasts that produces correlated probabilistic forecasts of
precipitation accumulation at multiple sites simultaneously. The statistical
model is a spatial version of a two-stage model that represents the
distribution of precipitation by a mixture of a point mass at zero and a Gamma
density for the continuous distribution of precipitation accumulation. Spatial
correlation is captured by assuming that two Gaussian processes drive
precipitation occurrence and precipitation amount, respectively. The first
process is latent and drives precipitation occurrence via a threshold. The
second process explains the spatial correlation in precipitation accumulation.
It is related to precipitation via a site-specific transformation function, so
as to retain the marginal right-skewed distribution of precipitation while
modeling spatial dependence. Both processes take into account the information
contained in the numerical weather forecast and are modeled as stationary
isotropic spatial processes with an exponential correlation function. The
two-stage spatial model was applied to 48-hour-ahead forecasts of daily
precipitation accumulation over the Pacific Northwest in 2004. The predictive
distributions from the two-stage spatial model were calibrated and sharp, and
outperformed reference forecasts for spatially composite and areally averaged
quantities.Comment: Published in at http://dx.doi.org/10.1214/08-AOAS203 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Using conditional kernel density estimation for wind power density forecasting
Of the various renewable energy resources, wind power is widely recognized as one of the most promising. The management of wind farms and electricity systems can benefit greatly from the availability of estimates of the probability distribution of wind power generation. However, most research has focused on point forecasting of wind power. In this paper, we develop an approach to producing density forecasts for the wind power generated at individual wind farms. Our interest is in intraday data and prediction from 1 to 72 hours ahead. We model wind power in terms of wind speed and wind direction. In this framework, there are two key uncertainties. First, there is the inherent uncertainty in wind speed and direction, and we model this using a bivariate VARMA-GARCH (vector autoregressive moving average-generalized autoregressive conditional heteroscedastic) model, with a Student t distribution, in the Cartesian space of wind speed and direction. Second, there is the stochastic nature of the relationship of wind power to wind speed (described by the power curve), and to wind direction. We model this using conditional kernel density (CKD) estimation, which enables a nonparametric modeling of the conditional density of wind power. Using Monte Carlo simulation of the VARMA-GARCH model and CKD estimation, density forecasts of wind speed and direction are converted to wind power density forecasts. Our work is novel in several respects: previous wind power studies have not modeled a stochastic power curve; to accommodate time evolution in the power curve, we incorporate a time decay factor within the CKD method; and the CKD method is conditional on a density, rather than a single value. The new approach is evaluated using datasets from four Greek wind farms
A simple method for finite range decomposition of quadratic forms and Gaussian fields
We present a simple method to decompose the Green forms corresponding to a
large class of interesting symmetric Dirichlet forms into integrals over
symmetric positive semi-definite and finite range (properly supported) forms
that are smoother than the original Green form. This result gives rise to
multiscale decompositions of the associated Gaussian free fields into sums of
independent smoother Gaussian fields with spatially localized correlations. Our
method makes use of the finite propagation speed of the wave equation and
Chebyshev polynomials. It improves several existing results and also gives
simpler proofs.Comment: minor correction for t<
Entangling the free motion of a particle pair: an experimental scenario
The concept of dissociation-time entanglement provides a means of manifesting
non-classical correlations in the motional state of two counter-propagating
atoms. In this article, we discuss in detail the requirements for a specific
experimental implementation, which is based on the Feshbach dissociation of a
molecular Bose-Einstein condensate of fermionic lithium. A sequence of two
magnetic field pulses serves to delocalize both of the dissociation products
into a superposition of consecutive wave packets, which are separated by a
macroscopic distance. This allows to address them separately in a switched
Mach-Zehnder configuration, permitting to conduct a Bell experiment with simple
position measurements. We analyze the expected form of the two-particle wave
function in a concrete experimental setup that uses lasers as atom guides.
Assuming viable experimental parameters the setup is shown to be capable of
violating a Bell inequality.Comment: 9 pages, 3 figures; corresponds to published versio
Gaussian multiplicative Chaos for symmetric isotropic matrices
Motivated by isotropic fully developed turbulence, we define a theory of
symmetric matrix valued isotropic Gaussian multiplicative chaos. Our
construction extends the scalar theory developed by J.P. Kahane in 1985
Non-classical correlations from dissociation time entanglement
We discuss a strongly entangled two-particle state of motion that emerges
naturally from the double-pulse dissociation of a diatomic molecule. This
state, which may be called dissociation-time entangled, permits the unambiguous
demonstration of non-classical correlations by violating a Bell inequality
based on switched single particle interferometry and only position
measurements. We apply time-dependent scattering theory to determine the
detrimental effect of dispersion. The proposed setup brings into reach the
possibility of establishing non-classical correlations with respect to system
properties that are truly macroscopically distinct.Comment: 8 pages, 2 figures; corresponds to published versio
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