Convergence of the Wang-Landau Algorithm and Statistical Error

The determination of elemental distributions by electron energy loss spectroscopy necessitates removal of the non-characteristic spectral background from a core-edge at each point in the image. In the scanning transmission electron microscope this is made possible by computer controlled data acquisition. Data may be processed by fitting the pre-edge counts, at two or more channels, to an inverse power law, AE-r, where A and r are parameters and E is energy loss. Processing may be performed in real-time so a single number is saved at each pixel. Detailed analysis, shows that the largest contribution to noise comes from statistical error in the least squares fit to the background. If the background shape remains constant over the entire image, the signal-to-noise ratio can be improved by fitting only one parameter. Such an assumption is generally implicit in subtraction of the “reference image” in energy selected micrographs recorded in the CTEM with a Castaing-Henry spectrometer.

Download Full-text

University of Kiel Radiocarbon Measurements II

Radiocarbon ◽

10.1017/s0033822200000552 ◽

1967 ◽

Vol 9 ◽

pp. 257-260

Author(s):

H. Willkomm ◽

H. Erlenkeuser

Keyword(s):

Proportional Counter ◽

Atmospheric Pressure ◽

Statistical Error ◽

Quartz Tube ◽

Sensitive Volume ◽

Concrete Wall ◽

Lead Shield ◽

Double Ring

Most of the measurements reported here have been obtained with the 4.5-L CO2 counter previously described (Kiel I; Erlenkeuser, 1965). A few samples have been dated with a 3-L proportional counter. The copper counter is surrounded by 28 GM counters in the form of a double ring. The total assembly is shielded by 10 cm of old lead. Neither an inner lead shield between counter and anticoincidence ring nor screening of sensitive volume by a quartz tube-as in the 4.5-L counter-has been used. Background of the small counter is 17.20 cpm or The 0.95 x NBS value is 9.5 cpm at 400 torr. Within statistical error background does not depend on atmospheric pressure. The 3-L counter is placed under a concrete wall, 2.5 m in length and 9.4 m in height.

Download Full-text

Statistical error in calculating the nuclide composition of low-burnup fuel

Atomic Energy ◽

10.1007/s10512-005-0174-x ◽

2005 ◽

Vol 98 (2) ◽

pp. 83-88 ◽

Cited By ~ 1

Author(s):

A. M. Degtyarev ◽

A. A. Myasnikov

Keyword(s):

Statistical Error ◽

Nuclide Composition

Download Full-text

Demonstrating the Tapered Gridded Estimator (TGE) for the Cosmological HI 21-cm Power Spectrum using 150 MHz GMRT observations

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/staa3831 ◽

2020 ◽

Author(s):

Srijita Pal ◽

Somnath Bharadwaj ◽

Abhik Ghosh ◽

Samir Choudhuri

Keyword(s):

Power Spectrum ◽

Unbiased Estimate ◽

Power Spectra ◽

Neutral Hydrogen ◽

Statistical Error ◽

Temperature Fluctuations ◽

Radio Frequency Interference ◽

Rectangular Region ◽

Angular Power Spectrum ◽

The Mean

Abstract We apply the Tapered Gridded Estimator (TGE) for estimating the cosmological 21-cm power spectrum from 150 MHz GMRT observations which corresponds to the neutral hydrogen (HI) at redshift z = 8.28. Here TGE is used to measure the Multi-frequency Angular Power Spectrum (MAPS) Cℓ(Δν) first, from which we estimate the 21-cm power spectrum P(k⊥, k∥). The data here are much too small for a detection, and the aim is to demonstrate the capabilities of the estimator. We find that the estimated power spectrum is consistent with the expected foreground and noise behaviour. This demonstrates that this estimator correctly estimates the noise bias and subtracts this out to yield an unbiased estimate of the power spectrum. More than $47\%$ of the frequency channels had to be discarded from the data owing to radio-frequency interference, however the estimated power spectrum does not show any artifacts due to missing channels. Finally, we show that it is possible to suppress the foreground contribution by tapering the sky response at large angular separations from the phase center. We combine the k modes within a rectangular region in the ‘EoR window’ to obtain the spherically binned averaged dimensionless power spectra Δ2(k) along with the statistical error σ associated with the measured Δ2(k). The lowest k-bin yields Δ2(k) = (61.47)2 K2 at k = 1.59 Mpc−1, with σ = (27.40)2 K2. We obtain a 2 σ upper limit of (72.66)2 K2 on the mean squared HI 21-cm brightness temperature fluctuations at k = 1.59 Mpc−1.

Download Full-text

Calibrating the CreditRisk+ Model at Different Time Scales and in Presence of Temporal Autocorrelation †

Mathematics ◽

10.3390/math9141679 ◽

2021 ◽

Vol 9 (14) ◽

pp. 1679

Author(s):

Jacopo Giacomelli ◽

Luca Passalacqua

Keyword(s):

Time Series ◽

Default Risk ◽

Real Life ◽

Statistical Error ◽

Real Data ◽

Sampling Period ◽

Calibration Procedure ◽

Industry Standards ◽

Default Rate

The CreditRisk+ model is one of the industry standards for the valuation of default risk in credit loans portfolios. The calibration of CreditRisk+ requires, inter alia, the specification of the parameters describing the structure of dependence among default events. This work addresses the calibration of these parameters. In particular, we study the dependence of the calibration procedure on the sampling period of the default rate time series, that might be different from the time horizon onto which the model is used for forecasting, as it is often the case in real life applications. The case of autocorrelated time series and the role of the statistical error as a function of the time series period are also discussed. The findings of the proposed calibration technique are illustrated with the support of an application to real data.

Download Full-text

Prediction of Effective Material Property of Tailor Welded Blanks for Air Bending Process

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.472-475.761 ◽

2012 ◽

Vol 472-475 ◽

pp. 761-766

Author(s):

Yong Chuan Duan ◽

Ying Ping Guan ◽

Xing Dong Ma

Keyword(s):

Finite Element ◽

Tensile Test ◽

Finite Element Model ◽

Material Property ◽

Statistical Error ◽

Element Model ◽

Ann Model ◽

Process Data ◽

Tailor Welded Blanks ◽

Effective Material Property

A method based on artificial neural network (ANN) for predicting the effective material property is put forward in this paper. The finite element model of tensile test specimen is modeled in LS-DYNA code, which has transverse weld at the middle of the specimen and conforms to the ASTM specification. A statistical error analysis model is used to include the random phenomenon in the result of tensile test finite element model and verify the accuracy of finite element model (FEM) simulation. In order to study the effect of the processing parameter with design of experiment is followed, the simulation trail is conducted in all the levels of parameters. It is assumed that Hollomon’s law is followed by tailor welded blanks. The results obtained from fitting the post-process data of FEM by least square method are used to train and develop ANN model, the prediction average error of ANN model is acceptable compared with simulation trail.

Download Full-text

Estimating Differential Latent Variable Graphical Models with Applications to Brain Connectivity

Biometrika ◽

10.1093/biomet/asaa066 ◽

2020 ◽

Author(s):

S Na ◽

M Kolar ◽

O Koyejo

Keyword(s):

Graphical Models ◽

Latent Variable ◽

Graphical Model ◽

Brain Connectivity ◽

Statistical Error ◽

Real Data ◽

Low Rank ◽

Conditional Dependence ◽

Gradient Descent Algorithm ◽

The Difference

Abstract Differential graphical models are designed to represent the difference between the conditional dependence structures of two groups, thus are of particular interest for scientific investigation. Motivated by modern applications, this manuscript considers an extended setting where each group is generated by a latent variable Gaussian graphical model. Due to the existence of latent factors, the differential network is decomposed into sparse and low-rank components, both of which are symmetric indefinite matrices. We estimate these two components simultaneously using a two-stage procedure: (i) an initialization stage, which computes a simple, consistent estimator, and (ii) a convergence stage, implemented using a projected alternating gradient descent algorithm applied to a nonconvex objective, initialized using the output of the first stage. We prove that given the initialization, the estimator converges linearly with a nontrivial, minimax optimal statistical error. Experiments on synthetic and real data illustrate that the proposed nonconvex procedure outperforms existing methods.

Download Full-text