48,963 research outputs found
Bayesian threshold selection for extremal models using measures of surprise
Statistical extreme value theory is concerned with the use of asymptotically
motivated models to describe the extreme values of a process. A number of
commonly used models are valid for observed data that exceed some high
threshold. However, in practice a suitable threshold is unknown and must be
determined for each analysis. While there are many threshold selection methods
for univariate extremes, there are relatively few that can be applied in the
multivariate setting. In addition, there are only a few Bayesian-based methods,
which are naturally attractive in the modelling of extremes due to data
scarcity. The use of Bayesian measures of surprise to determine suitable
thresholds for extreme value models is proposed. Such measures quantify the
level of support for the proposed extremal model and threshold, without the
need to specify any model alternatives. This approach is easily implemented for
both univariate and multivariate extremes.Comment: To appear in Computational Statistics and Data Analysi
Fresnel operator, squeezed state and Wigner function for Caldirola-Kanai Hamiltonian
Based on the technique of integration within an ordered product (IWOP) of
operators we introduce the Fresnel operator for converting Caldirola-Kanai
Hamiltonian into time-independent harmonic oscillator Hamiltonian. The Fresnel
operator with the parameters A,B,C,D corresponds to classical optical Fresnel
transformation, these parameters are the solution to a set of partial
differential equations set up in the above mentioned converting process. In
this way the exact wavefunction solution of the Schr\"odinger equation governed
by the Caldirola-Kanai Hamiltonian is obtained, which represents a squeezed
number state. The corresponding Wigner function is derived by virtue of the
Weyl ordered form of the Wigner operator and the order-invariance of Weyl
ordered operators under similar transformations. The method used here can be
suitable for solving Schr\"odinger equation of other time-dependent
oscillators.Comment: 6 pages, 2 figure
Adaptive Optimal Scaling of Metropolis-Hastings Algorithms Using the Robbins-Monro Process
We present an adaptive method for the automatic scaling of Random-Walk
Metropolis-Hastings algorithms, which quickly and robustly identifies the
scaling factor that yields a specified overall sampler acceptance probability.
Our method relies on the use of the Robbins-Monro search process, whose
performance is determined by an unknown steplength constant. We give a very
simple estimator of this constant for proposal distributions that are
univariate or multivariate normal, together with a sampling algorithm for
automating the method. The effectiveness of the algorithm is demonstrated with
both simulated and real data examples. This approach could be implemented as a
useful component in more complex adaptive Markov chain Monte Carlo algorithms,
or as part of automated software packages
Inversion formula and Parsval theorem for complex continuous wavelet transforms studied by entangled state representation
In a preceding Letter (Opt. Lett. 32, 554 (2007)) we have proposed complex
continuous wavelet transforms (CCWTs) and found Laguerre--Gaussian mother
wavelets family. In this work we present the inversion formula and Parsval
theorem for CCWT by virtue of the entangled state representation, which makes
the CCWT theory complete. A new orthogonal property of mother wavelet in
parameter space is revealed.Comment: 4 pages no figur
Signal enhancement of the in-plane and out-of-plane Rayleigh wave components
Several groups have reported an enhancement of the ultrasonic Rayleigh wave when scanning close to a surface-breaking defect in a metal sample. This enhancement may be explained as an interference effect where the waves passing directly between source and receiver interfere with those waves reflected back from the defect. We present finite element models of the predicted enhancement when approaching a defect, along with experiments performed using electromagnetic acoustic transducers sensitive to either in-plane or out-of-plane motion. A larger enhancement of the in-plane motion than the out-of-plane motion is observed and can be explained by considering ultrasonic reflections and mode conversion at the defect
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