87,731 research outputs found
A statistical technique for measuring synchronism between cortical regions in the EEG during rhythmic stimulation
The coherence function has been widely applied in quantifying the degree of synchronism between electroencephalogram (EEG) signals obtained from different brain regions. However, when applied to investigating synchronization resulting from rhythmic stimulation, misleading results can arise from the high correlation of background EEG activity. The authors, thus propose a modified measure, which emphasizes the synchronized stimulus responses and reduces the influence of the spontaneous EEG activity. Critical values for this estimator are derived and tested in Monte Carlo simulations. The effectiveness of the method is illustrated on data recorded from 12 young normal subjects during rhythmic photic stimulation
What is the best risk measure in practice? A comparison of standard measures
Expected Shortfall (ES) has been widely accepted as a risk measure that is
conceptually superior to Value-at-Risk (VaR). At the same time, however, it has
been criticised for issues relating to backtesting. In particular, ES has been
found not to be elicitable which means that backtesting for ES is less
straightforward than, e.g., backtesting for VaR. Expectiles have been suggested
as potentially better alternatives to both ES and VaR. In this paper, we
revisit commonly accepted desirable properties of risk measures like coherence,
comonotonic additivity, robustness and elicitability. We check VaR, ES and
Expectiles with regard to whether or not they enjoy these properties, with
particular emphasis on Expectiles. We also consider their impact on capital
allocation, an important issue in risk management. We find that, despite the
caveats that apply to the estimation and backtesting of ES, it can be
considered a good risk measure. As a consequence, there is no sufficient
evidence to justify an all-inclusive replacement of ES by Expectiles in
applications. For backtesting ES, we propose an empirical approach that
consists in replacing ES by a set of four quantiles, which should allow to make
use of backtesting methods for VaR.
Keywords: Backtesting; capital allocation; coherence; diversification;
elicitability; expected shortfall; expectile; forecasts; probability integral
transform (PIT); risk measure; risk management; robustness; value-at-riskComment: 27 pages, 1 tabl
Coherent frequentism
By representing the range of fair betting odds according to a pair of
confidence set estimators, dual probability measures on parameter space called
frequentist posteriors secure the coherence of subjective inference without any
prior distribution. The closure of the set of expected losses corresponding to
the dual frequentist posteriors constrains decisions without arbitrarily
forcing optimization under all circumstances. This decision theory reduces to
those that maximize expected utility when the pair of frequentist posteriors is
induced by an exact or approximate confidence set estimator or when an
automatic reduction rule is applied to the pair. In such cases, the resulting
frequentist posterior is coherent in the sense that, as a probability
distribution of the parameter of interest, it satisfies the axioms of the
decision-theoretic and logic-theoretic systems typically cited in support of
the Bayesian posterior. Unlike the p-value, the confidence level of an interval
hypothesis derived from such a measure is suitable as an estimator of the
indicator of hypothesis truth since it converges in sample-space probability to
1 if the hypothesis is true or to 0 otherwise under general conditions.Comment: The confidence-measure theory of inference and decision is explicitly
extended to vector parameters of interest. The derivation of upper and lower
confidence levels from valid and nonconservative set estimators is formalize
Evaluation of local orientation for texture classification
The aim of this paper is to present a study where we evaluate the optimal inclusion of the texture orientation
in the classification process. In this paper the orientation for each pixel in the image is extracted using the
partial derivatives of the Gaussian function and the main focus of our work is centred on the evaluation of
the local dominant orientation (which is calculated by combining the magnitude and local orientation) on
the classification results. While the dominant orientation of the texture depends strongly on the observation
scale, in this paper we propose to evaluate the macro-texture by calculating the distribution of the dominant
orientations for all pixels in the image that sample the texture at micro-level. The experimental results were
conducted on standard texture databases and the results indicate that the dominant orientation calculated at
micro-level is an appropriate measure for texture description
Momentum spectroscopy of 1D phase fluctuations in Bose-Einstein condensates
We measure the axial momentum distribution of Bose-Einstein condensates with
an aspect ratio of 152 using Bragg spectroscopy. We observe the Lorentzian
momentum distribution characteristic of one-dimensional phase fluctuations. The
temperature dependence of the width of this distribution provides a
quantitative test of quasi-condensate theory. In addition, we observe a
condensate length consistent with the absence of density fluctuations, even
when phase fluctuations are large.Comment: 4 pages, 3 figures; submitted to Phys. Rev. Let
Feedback control of trapped coherent atomic ensembles
We demonstrate how to use feedback to control the internal states of trapped
coherent ensembles of two-level atoms, and to protect a superposition state
against the decoherence induced by a collective noise. Our feedback scheme is
based on weak optical measurements with negligible back-action and coherent
microwave manipulations. The efficiency of the feedback system is studied for a
simple binary noise model and characterized in terms of the trade-off between
information retrieval and destructivity from the optical probe. We also
demonstrate the correction of more general types of collective noise. This
technique can be used for the operation of atomic interferometers beyond the
standard Ramsey scheme, opening the way towards improved atomic sensors.Comment: 9 pages, 6 figure
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