A Numerical Integration Formula Based on the Bessel Functions

Ogata, Hidenori

doi:10.2977/prims/1145474602

Cited by 48 publications

(37 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Typically, in order to obtain sufficient precision one should include a large number of points into the integral, which is very costly especially at NNLL/NNLO. arTeMiDe evaluates this integral with the Ogata quadratures [68]. The Ogata quadrature is a double exponential quadrature, whose nodes are the zeros of the Bessel function.…”

Section: Artemidementioning

confidence: 99%

Analysis of vector boson production within TMD factorization

2018

View full text Add to dashboard Cite

We present a comprehensive analysis and extraction of the unpolarized transverse momentum dependent (TMD) parton distribution functions, which are fundamental constituents of the TMD factorization theorem. We provide a general review of the theory of TMD distributions, and present a new scheme of scale fixation. This scheme, called the ζ -prescription, allows to minimize the impact of perturbative logarithms in a large range of scales and does not generate undesired power corrections. Within ζ -prescription we consistently include the perturbatively calculable parts up to next-to-next-to-leading order (NNLO), and perform the global fit of the Drell-Yan and Z-boson production, which include the data of E288, Tevatron and LHC experiments. The non-perturbative part of the TMDs are explored checking a variety of models. We support the obtained results by a study of theoretical uncertainties, perturbative convergence, and a dedicated study of the range of applicability of the TMD factorization theorem. The considered non-perturbative models present significant differences in the fitting behavior, which allow us to clearly disfavor most of them. The numerical evaluations are provided by the arTeMiDe code, which is introduced in this work and that can be used for current/future TMD phenomenology.

show abstract

Section: Artemidementioning

confidence: 99%

Analysis of vector boson production within TMD factorization

2018

View full text Add to dashboard Cite

show abstract

“…While reducing the dimension of the integration domain to one appears to be a valuable improvement, the integral of Equation (4), albeit univariate, falls within the category of Hankel-like integrals known to be particularly delicate to compute. This is due to the fact that the integrand has singularities near the real axis (Ogata, 2005). To overcome this limitation, we investigate in the following subsection the use of the noiseless PPCA model to obtain a tractable expression.…”

Section: A General Framework For Globally Sparse Ppcamentioning

confidence: 99%

Bayesian variable selection for globally sparse probabilistic PCA

Bouveyron

Latouche²,

Mattei

2018

Electron. J. Statist.

View full text Add to dashboard Cite

Sparse versions of principal component analysis (PCA) have imposed themselves as simple, yet powerful ways of selecting relevant features of high-dimensional data in an unsupervised manner. However, when several sparse principal components are computed, the interpretation of the selected variables is difficult since each axis has its own sparsity pattern and has to be interpreted separately. To overcome this drawback, we propose a Bayesian procedure called globally sparse probabilistic PCA (GSPPCA) that allows to obtain several sparse components with the same sparsity pattern. This allows the practitioner to identify the original variables which are relevant to describe the data. To this end, using Roweis' probabilistic interpretation of PCA and a Gaussian prior on the loading matrix, we provide the first exact computation of the marginal likelihood of a Bayesian PCA model. To avoid the drawbacks of discrete model selection, a simple relaxation of this framework is presented. It allows to find a path of models using a variational expectation-maximization algorithm. The exact marginal likelihood is then maximized over this path. This approach is illustrated on real and synthetic data sets. In particular, using unlabeled microarray data, GSPPCA infers much more relevant gene subsets than traditional sparse PCA algorithms.

show abstract

“…In order for the integral to converge, we introduce a smoothing term by multiplying the integrand with a damping factor of exp (−k 2 σ 2 ) where σ = 0.5. We tried two other methods in addition to the brute force approach, a quadrature formula to approximate integrals over Bessel functions introduced by Ogata (2005) and applied to the correlation function by Szapudi et al (2005) and FFTlog, an algorithm that performs Fast Fourier or Hankel transforms over logarithmically spaced intervals (Hamilton 2000). As shown in Ogata (2005), integrals involving Bessel functions such as the one that appears in Equation 18 can be approximated as:…”

Section: Nonlinear Biasmentioning

confidence: 99%

Cosmic Emulation: Fast Predictions for the Galaxy Power Spectrum

Kwan

Heitmann

Habib

et al. 2015

ApJ

111

100

View full text Add to dashboard Cite

The halo occupation distribution (HOD) approach has proven to be an effective method for modeling galaxy clustering and bias. In this approach, galaxies of a given type are probabilistically assigned to individual halos in N-body simulations. In this paper, we present a fast emulator for predicting the fully nonlinear galaxy-galaxy auto and galaxy-dark matter cross power spectrum and correlation function over a range of freely specifiable HOD modeling parameters. The emulator is constructed using results from 100 HOD models run on a large ΛCDM Nbody simulation, with Gaussian Process interpolation applied to a PCA-based representation of the galaxy power spectrum. The total error is currently ∼ 1% in the auto correlations and ∼ 2% in the cross correlations from z = 1 to z = 0, over the considered parameter range. We use the emulator to investigate the accuracy of various analytic prescriptions for the galaxy power spectrum, parametric dependencies in the HOD model, and the behavior of galaxy bias as a function of HOD parameters. Additionally, we obtain fully nonlinear predictions for tangential shear correlations induced by galaxy-galaxy lensing from our galaxy-dark matter cross power spectrum emulator.All emulation products are publicly available at

show abstract

A Numerical Integration Formula Based on the Bessel Functions

Cited by 48 publications

References 11 publications

Analysis of vector boson production within TMD factorization

Analysis of vector boson production within TMD factorization

Bayesian variable selection for globally sparse probabilistic PCA

Cosmic Emulation: Fast Predictions for the Galaxy Power Spectrum

Contact Info

Product

Resources

About