VAR Processes with Parameter Constraints

2005 ◽  
pp. 193-231
Keyword(s):  
Parameter Constraints

scholarly journals Towards a self-consistent analysis of the anisotropic galaxy two- and three-point correlation functions on large scales: application to mock galaxy catalogues

2020 ◽  
Author(s):  
Naonori S Sugiyama ◽  
Shun Saito ◽  
Florian Beutler ◽  
Hee-Jong Seo
Keyword(s):  
Correlation Functions ◽  
Hubble Parameter ◽  
Theoretical Models ◽  
Practical Method ◽  
Acoustic Oscillation ◽  
Nonlinear Damping ◽  
Joint Analysis ◽  
Angular Diameter Distance ◽  
Point Correlation ◽  
Parameter Constraints

Abstract We establish a practical method for the joint analysis of anisotropic galaxy two- and three-point correlation functions (2PCF and 3PCF) on the basis of the decomposition formalism of the 3PCF using tri-polar spherical harmonics. We perform such an analysis with MultiDark Patchy mock catalogues to demonstrate and understand the benefit of the anisotropic 3PCF. We focus on scales above 80 h−1 Mpc, and use information from the shape and the baryon acoustic oscillation (BAO) signals of the 2PCF and 3PCF. We also apply density field reconstruction to increase the signal-noise ratio of BAO in the 2PCF measurement, but not in the 3PCF measurement. In particular, we study in detail the constraints on the angular diameter distance and the Hubble parameter. We build a model of the bispectrum or 3PCF that includes the nonlinear damping of the BAO signal in redshift space. We carefully account for various uncertainties in our analysis including theoretical models of the 3PCF, window function corrections, biases in estimated parameters from the fiducial values, the number of mock realizations to estimate the covariance matrix, and bin size. The joint analysis of the 2PCF and 3PCF monopole and quadrupole components shows a $30\%$ and $20\%$ improvement in Hubble parameter constraints before and after reconstruction of the 2PCF measurements, respectively, compared to the 2PCF analysis alone. This study clearly shows that the anisotropic 3PCF increases cosmological information from galaxy surveys and encourages further development of the modeling of the 3PCF on smaller scales than we consider.

scholarly journals Sufficiency of a Gaussian power spectrum likelihood for accurate cosmology from upcoming weak lensing surveys

2021 ◽  
Author(s):  
Robin E Upham ◽  
Michael L Brown ◽  
Lee Whittaker
Keyword(s):  
Power Spectrum ◽  
Random Noise ◽  
Power Spectra ◽  
Stage Iv ◽  
Wishart Distribution ◽  
Weak Lensing ◽  
Dependence Structure ◽  
Gaussian Fields ◽  
Non Gaussian ◽  
Parameter Constraints

Abstract We investigate whether a Gaussian likelihood is sufficient to obtain accurate parameter constraints from a Euclid-like combined tomographic power spectrum analysis of weak lensing, galaxy clustering and their cross-correlation. Testing its performance on the full sky against the Wishart distribution, which is the exact likelihood under the assumption of Gaussian fields, we find that the Gaussian likelihood returns accurate parameter constraints. This accuracy is robust to the choices made in the likelihood analysis, including the choice of fiducial cosmology, the range of scales included, and the random noise level. We extend our results to the cut sky by evaluating the additional non-Gaussianity of the joint cut-sky likelihood in both its marginal distributions and dependence structure. We find that the cut-sky likelihood is more non-Gaussian than the full-sky likelihood, but at a level insufficient to introduce significant inaccuracy into parameter constraints obtained using the Gaussian likelihood. Our results should not be affected by the assumption of Gaussian fields, as this approximation only becomes inaccurate on small scales, which in turn corresponds to the limit in which any non-Gaussianity of the likelihood becomes negligible. We nevertheless compare against N-body weak lensing simulations and find no evidence of significant additional non-Gaussianity in the likelihood. Our results indicate that a Gaussian likelihood will be sufficient for robust parameter constraints with power spectra from Stage IV weak lensing surveys.

scholarly journals KiDS-450: cosmological parameter constraints from tomographic weak gravitational lensing

2016 ◽  
Vol 465 (2) ◽  
pp. 1454-1498 ◽  
Author(s):  
H. Hildebrandt ◽  
M. Viola ◽  
C. Heymans ◽  
S. Joudaki ◽  
K. Kuijken ◽  
...  
Keyword(s):  
Gravitational Lensing ◽  
Cosmological Parameter ◽  
Weak Gravitational Lensing ◽  
Parameter Constraints

scholarly journals refnx: neutron and X-ray reflectometry analysis in Python

2019 ◽  
Vol 52 (1) ◽  
pp. 193-200 ◽  
Author(s):  
Andrew R. J. Nelson ◽  
Stuart W. Prescott
Keyword(s):  
Bayesian Approach ◽  
Volume Fraction ◽  
Scattering Length ◽  
Distribution Functions ◽  
Monte Carlo Algorithm ◽  
Reproducible Research ◽  
Model Parameters ◽  
X Ray ◽  
Multiple Data Sets ◽  
Parameter Constraints

refnx is a model-based neutron and X-ray reflectometry data analysis package written in Python. It is cross platform and has been tested on Linux, macOS and Windows. Its graphical user interface is browser based, through a Jupyter notebook. Model construction is modular, being composed from a series of components that each describe a subset of the interface, parameterized in terms of physically relevant parameters (volume fraction of a polymer, lipid area per molecule etc.). The model and data are used to create an objective, which is used to calculate the residuals, log-likelihood and log-prior probabilities of the system. Objectives are combined to perform co-refinement of multiple data sets and mixed-area models. Prior knowledge of parameter values is encoded as probability distribution functions or bounds on all parameters in the system. Additional prior probability terms can be defined for sets of components, over and above those available from the parameters alone. Algebraic parameter constraints are available. The software offers a choice of fitting approaches, including least-squares (global and gradient-based optimizers) and a Bayesian approach using a Markov-chain Monte Carlo algorithm to investigate the posterior distribution of the model parameters. The Bayesian approach is useful for examining parameter covariances, model selection and variability in the resulting scattering length density profiles. The package is designed to facilitate reproducible research; its use in Jupyter notebooks, and subsequent distribution of those notebooks as supporting information, permits straightforward reproduction of analyses.

scholarly journals The confrontation of the shock-powered synchrotron maser model with the Galactic FRB 200428

2020 ◽  
Vol 500 (2) ◽  
pp. 2704-2710 ◽  
Author(s):  
Yun-Wei Yu ◽  
Yuan-Chuan Zou ◽  
Zi-Gao Dai ◽  
Wen-Fei Yu
Keyword(s):  
Line Of Sight ◽  
Model Parameters ◽  
Observational Constraints ◽  
Synchrotron Emission ◽  
Physical Processes ◽  
X Ray ◽  
Emission Efficiency ◽  
Free Parameters ◽  
Fast Radio Burst ◽  
Parameter Constraints

ABSTRACT The association of FRB 200428 with an X-ray burst (XRB) from the Galactic magnetar SGR 1935+2154 offers important implications for the physical processes responsible for the fast radio burst (FRB) phenomena. By assuming that the XRB emission is produced in the magnetosphere, we investigate the possibility that the FRB emission is produced by shock-powered synchrotron maser (SM), which is phenomenologically described with a number of free parameters. The observational constraints on the model parameters indicate that the model can in principle be consistent with the FRB 200428 observations, if the ejecta lunched by magnetar activities can have appropriate ingredients and structures and the shock processes occur on the line of sight. To be specific, a complete burst ejecta should consist of an ultra-relativistic and extremely highly collimated e± component and a sub-relativistic and wide-spreading baryonic component. The internal shocks producing the FRB emission arise from a collision between the e± ejecta and the remnant of a previous baryonic ejecta at the same direction. The parameter constraints depend on the uncertain spectrum and efficiency of the SM emission. While the spectrum is tentatively described by a spectral index of −2, we estimate the emission efficiency to be around 10−4 by requiring that the synchrotron emission of the shocked material cannot be much brighter than the magnetosphere XRB emission.

scholarly journals A consensus-based global optimization method for high dimensional machine learning problems

2020 ◽  
Author(s):  
Jose Carrillo ◽  
Shi Jin ◽  
Lei Li ◽  
Yuhua Zhu
Keyword(s):  
Optimization Problems ◽  
Computational Cost ◽  
Weighted Average ◽  
Planck Equation ◽  
Optimization Method ◽  
Learning Problems ◽  
High Dimensional ◽  
Nonconvex Functions ◽  
The Individual ◽  
Parameter Constraints

We improve recently introduced consensus-based optimization method, proposed in [R. Pinnau, C. Totzeck, O. Tse and S. Martin, Math. Models Methods Appl. Sci., 27(01):183{204, 2017], which is a gradient-free optimization method for general nonconvex functions. We rst replace the isotropic geometric Brownian motion by the component-wise one, thus removing the dimensionality dependence of the drift rate, making the method more competitive for high dimensional optimization problems. Secondly, we utilize the random mini-batch ideas to reduce the computational cost of calculating the weighted average which the individual particles tend to relax toward. For its mean- eld limit{a nonlinear Fokker-Planck equation{we prove, in both time continuous and semi-discrete settings, that the convergence of the method, which is exponential in time, is guaranteed with parameter constraints independent of the dimensionality. We also conduct numerical tests to high dimensional problems to check the success rate of the method.

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