scholarly journals Likelihood-based estimation of substructure content from single-wavelength anomalous diffraction (SAD) intensity data

2021 ◽  
Author(s):  
Kaushik S Hatti ◽  
Airlie J McCoy ◽  
Randy J Read
Keyword(s):  
Measurement Errors ◽  
Target Function ◽  
Protein Composition ◽  
Likelihood Estimation ◽  
Accurate Estimate ◽  
Likelihood Method ◽  
Anomalous Scattering ◽  
Correlated Errors ◽  
Complex Correlation ◽  
Anomalous Signal

AbstractSAD phasing can be challenging when the signal-to-noise ratio is low. In such cases, having an accurate estimate of substructure content can determine whether or not the substructure of anomalous scatterer positions can successfully be determined. We propose a likelihood-based target function to accurately estimate the strength of the anomalous scattering contribution directly from measured intensities, determining a complex correlation parameter relating the Bijvoet mates as a function of resolution. This gives a novel measure of intrinsic anomalous signal. The SAD likelihood target function also accounts for correlated errors in the measurement of intensities from Bijvoet mates, which can arise from the effects of radiation damage. When the anomalous signal is assumed to come primarily from a substructure comprised of one anomalous scatterer with a known value of f” and when the protein composition of the crystal is estimated correctly, the refined complex correlation parameters can be interpreted in terms of the atomic content of the primary anomalous scatterer, before the substructure is known. The maximum likelihood estimation of substructure content was tested on a curated database of 357 SAD cases with useful anomalous signal. The prior estimates of substructure content are highly correlated to the content determined by phasing calculations, with a correlation coefficient (on a log-log basis) of 0.72.SynopsisAn intensity-based likelihood method is provided to estimate scattering from an anomalous substructure considering the effect of measurement errors in Bijvoet pairs and correlations between those errors.

scholarly journals Likelihood-based estimation of substructure content from single-wavelength anomalous diffraction (SAD) intensity data

2021 ◽  
Vol 77 (7) ◽  
Author(s):  
Kaushik S. Hatti ◽  
Airlie J. McCoy ◽  
Randy J. Read
Keyword(s):  
Signal To Noise Ratio ◽  
Target Function ◽  
Protein Composition ◽  
Likelihood Estimation ◽  
Accurate Estimate ◽  
Anomalous Scattering ◽  
Correlated Errors ◽  
Complex Correlation ◽  
Anomalous Signal ◽  
Correlation Parameters

SAD phasing can be challenging when the signal-to-noise ratio is low. In such cases, having an accurate estimate of the substructure content can determine whether or not the substructure of anomalous scatterer positions can successfully be determined. Here, a likelihood-based target function is proposed to accurately estimate the strength of the anomalous scattering contribution directly from the measured intensities, determining a complex correlation parameter relating the Bijvoet mates as a function of resolution. This gives a novel measure of the intrinsic anomalous signal. The SAD likelihood target function also accounts for correlated errors in the measurement of intensities from Bijvoet mates, which can arise from the effects of radiation damage. When the anomalous signal is assumed to come primarily from a substructure comprising one anomalous scatterer with a known value of f′′ and when the protein composition of the crystal is estimated correctly, the refined complex correlation parameters can be interpreted in terms of the atomic content of the primary anomalous scatterer before the substructure is known. The maximum-likelihood estimation of substructure content was tested on a curated database of 357 SAD cases with useful anomalous signal. The prior estimates of substructure content are highly correlated to the content determined by phasing calculations, with a correlation coefficient (on a log–log basis) of 0.72.

Estimating the Cost of Car Warranty in Indonesia using the Gertsbakh-Kordonsky Method

2020 ◽  
Vol 2 (1) ◽  
pp. 33-40
Author(s):  
Anggis Sagitarisman ◽  
Aceng Komarudin Mutaqin
Keyword(s):  
Maximum Likelihood ◽  
Likelihood Estimation ◽  
Type A ◽  
Claim Data ◽  
Likelihood Method ◽  
Selling Price ◽  
One Dimensional ◽  
Warranty Period ◽  
Kolmogorov Smirnov ◽  
Warranty Costs

AbstractCar manufacturers in Indonesia need to determine reasonable warranty costs that do not burden companies or consumers. Several statistical approaches have been developed to analyze warranty costs. One of them is the Gertsbakh-Kordonsky method which reduces the two-dimensional warranty problem to one dimensional. In this research, we apply the Gertsbakh-Kordonsky method to estimate the warranty cost for car type A in XYZ company. The one-dimensional data will be tested using the Kolmogorov-Smirnov to determine its distribution and the parameter of distribution will be estimated using the maximum likelihood method. There are three approaches to estimate the parameter of the distribution. The difference between these three approaches is in the calculation of mileage for units that do not claim within the warranty period. In the application, we use claim data for the car type A. The data exploration indicates the failure of car type A is mostly due to the age of the vehicle. The Kolmogorov-Smirnov shows that the most appropriate distribution for the claim data is the three-parameter Weibull. Meanwhile, the estimated using the Gertsbakh-Kordonsky method shows that the warranty costs for car type A are around 3.54% from the selling price of this car unit without warranty i.e. around Rp. 4,248,000 per unit.Keywords: warranty costs; the Gertsbakh-Kordonsky method; maximum likelihood estimation; Kolmogorov-Smirnov test.                                   AbstrakPerusahaan produsen mobil di Indonesia perlu menentukan biaya garansi yang bersifat wajar tidak memberatkan perusahaan maupun konsumen. Beberapa pendekatan statistik telah dikembangkan untuk menganalisis biaya garansi. Salah satunya adalah metode Gertsbakh-Kordonsky yang mereduksi masalah garansi dua dimensi menjadi satu dimensi. Pada penelitian ini, metode Gertsbakh-Kordonsky akan digunakan untuk mengestimasi biaya garansi untuk mobil tipe A pada perusahaan XYZ. Data satu dimensi hasil reduksi diuji kecocokan distribusinya menggunakan uji kecocokan Kolmogorov-Smirnov dan taksiran parameter distribusinya menggunakan metode penaksir kemungkinan maksimum. Ada tiga pendekatan yang digunakan untuk menaksir parameter distribusi. Perbedaan dari ketiga pendekatan tersebut terletak pada perhitungan jarak tempuh untuk unit yang tidak melakukan klaim dalam periode garansi. Sebagai bahan aplikasi, kami menggunakan data klaim unit mobil tipe A. Hasil eksplorasi data menunjukkan bahwa kegagalan mobil tipe A lebih banyak disebabkan karena faktor usia kendaraan. Hasil uji kecocokan distribusi untuk data hasil reduksi menunjukkan bahwa distribusi yang cocok adalah distribusi Weibull 3-parameter. Sementara itu, hasil perhitungan taksiran biaya garansi menunjukan bahwa taksiran biaya garansi untuk unit mobil tipe A sekitar 3,54% dari harga jual unit mobil tipe A tanpa garansi, atau sekitar Rp. 4.248.000,- per unit.Kata Kunci: biaya garansi; metode Gertsbakh-Kordonsky; penaksiran kemungkinan maksimum; uji Kolmogorov-Smirnov.

Algebraic solutions in determining the coordinates of the radiator by the results of multi-position measurements of field strength

2021 ◽  
Author(s):  
V.A. Ufaev
Keyword(s):  
Maximum Likelihood ◽  
Field Strength ◽  
Reference Point ◽  
Linear Equations ◽  
Type System ◽  
Energy Parameter ◽  
Likelihood Estimation ◽  
Likelihood Method ◽  
Algebraic Solution ◽  
Algebraic Solutions

On the basis of the hypothesis of equality of the measured and true values of the amplitude of the field strength, an algebraic solution for estimating the unknown coordinates and the energy parameter of the radiator is obtained. Initially, by compiling and solving a redefined system of linear equations by pseudo-rotation of matrices, the coordinates of the emitter are determined under the assumption of independence of the distance to the reference point from the coordinates of the emitter. Then make and solve the square equation concerning distance to a reference point with the subsequent estimation of coordinates and an energy parameter. The ambiguity of the algebraic solution is resolved by comparing the maximum likelihood functional and choosing the parameters at which its maximum is reached. According to the simulation of a cellular-type system in multiplicative noise, the results of algebraic solutions by the maximum likelihood method and the calculated ones are close, except for a special zone where anomalous changes occur due to the limitations of the coordinate determination method. Algebraic solutions for maximum likelihood estimation provide an increase in the calculation speed of about 500 times. The proposed principle can be used in solving the ambiguity of algebraic solutions in systems of difference-rangefinder type and in the inverse problem of self-positioning of the receiving point by the amplitude of the electromagnetic field of beacons with a known location. The article contains 4 figures, a list of references from 9 sources.

scholarly journals Application of Iterative Maximum Weighted Likelihood Estimation in 3-D Target Localization

2019 ◽  
Vol 9 (22) ◽  
pp. 4921 ◽  
Author(s):  
Chen ◽  
Wu ◽  
Liu ◽  
Wang
Keyword(s):  
Measurement Errors ◽  
Likelihood Estimation ◽  
Target Localization ◽  
Point Estimate ◽  
Equal Weight ◽  
Target Area ◽  
Water Tank ◽  
Weighted Likelihood ◽  
Weighted Likelihood Estimation ◽  
Weight Factors

Time-of-flight (ToF)-based 3-D target localization is a very challenging topic because of the pseudo-targets introduced by ToF measurement errors in traditional ToF-based methods. Although the influence of errors in ToF measurement can be reduced by the probability-based ToF method, the accuracy of localization is not very high. This paper proposes a new 3-D target localization method, Iterative Maximum Weighted Likelihood Estimation (IMWLE), that takes into account the spatial distribution of pseudo-targets. In our method, each pseudo-target is initially assigned an equal weight. At each iteration, Maximum Weighted Likelihood Estimation (MWLE) is adopted to fit a Gaussian distribution to all pseudo-target positions and assign new weight factors to them. The weight factors of the pseudo-targets, which are far from the target, are reduced to minimize their influence on localization. Therefore, IMWLE can reduce the influence of pseudo-targets that are far from the target and improve the accuracy of localization. The experiments were carried out in a water tank to test the performance of the IMWLE method. Results revealed that the estimated target area can be narrowed down to the target using IMWLE and a point estimate of target location can also be obtained, which shows that IMWLE has a higher degree of accuracy than the probability-based ToF method.

Parameter Estimation of Weibull Distribution Model Based on Ant Colony Algorithm

2014 ◽  
Vol 1070-1072 ◽  
pp. 2073-2078
Author(s):  
Xiu Ji ◽  
Hui Wang ◽  
Chuan Qi Zhao ◽  
Xu Ting Yan
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Ant Colony Algorithm ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Ant Colony ◽  
Likelihood Method ◽  
Distribution Model ◽  
Algorithm Theory

It is difficult to estimate the parameters of Weibull distribution model using maximum likelihood estimation based on particle swarm optimization (PSO) theory for which is easy to fall into premature and needs more variables, ant colony algorithm theory was introduced into maximum likelihood method, and a parameter estimation method based on ant colony algorithm theory was proposed, an example was simulated to verify the feasibility and effectiveness of this method by comparing with ant colony algorithm and PSO.This template explains and demonstrates how to prepare your camera-ready paper for Trans Tech Publications. The best is to read these instructions and follow the outline of this text.

The Poisson Nadarajah–Haghighi Distribution: Properties and Applications to Lifetime Data

2019 ◽  
Vol 27 (01) ◽  
pp. 2050005
Author(s):  
Muhammad Mansoor ◽  
M. H. Tahir ◽  
Aymaan Alzaatreh ◽  
Gauss M. Cordeiro
Keyword(s):  
Maximum Likelihood ◽  
Censored Data ◽  
Survival Data ◽  
Maximum Likelihood Method ◽  
Likelihood Estimation ◽  
Real Data ◽  
Likelihood Method ◽  
Lifetime Data ◽  
Monte Carlo Simulation Study ◽  
Mathematical Properties

A new three-parameter compounded extended-exponential distribution “Poisson Nadarajah–Haghighi” is introduced and studied, which is quite flexible and can be used effectively in modeling survival data. It can have increasing, decreasing, upside-down bathtub and bathtub-shaped failure rate. A comprehensive account of the mathematical properties of the model is presented. We discuss maximum likelihood estimation for complete and censored data. The suitability of the maximum likelihood method to estimate its parameters is assessed by a Monte Carlo simulation study. Four empirical illustrations of the new model are presented to real data and the results are quite satisfactory.

scholarly journals Maximum Likelihood Estimation for Three-Parameter Weibull Distribution Using Evolutionary Strategy

2019 ◽  
Vol 2019 ◽  
pp. 1-8 ◽  
Author(s):  
Fan Yang ◽  
Hu Ren ◽  
Zhili Hu
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Weibull Distribution ◽  
Likelihood Function ◽  
Likelihood Estimation ◽  
Estimation Procedure ◽  
Evolutionary Strategy ◽  
Likelihood Method ◽  
Conventional Algorithm

The maximum likelihood estimation is a widely used approach to the parameter estimation. However, the conventional algorithm makes the estimation procedure of three-parameter Weibull distribution difficult. Therefore, this paper proposes an evolutionary strategy to explore the good solutions based on the maximum likelihood method. The maximizing process of likelihood function is converted to an optimization problem. The evolutionary algorithm is employed to obtain the optimal parameters for the likelihood function. Examples are presented to demonstrate the proposed method. The results show that the proposed method is suitable for the parameter estimation of the three-parameter Weibull distribution.

scholarly journals Eccentricity Parameters Identification for a Motorized Spindle System Based on Improved Maximum Likelihood Method

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Wengui Mao ◽  
Chaoliang Hu ◽  
Jianhua Li ◽  
Zhonghua Huang ◽  
Guiping Liu
Keyword(s):  
Maximum Likelihood ◽  
Measurement Errors ◽  
Maximum Likelihood Method ◽  
Search Algorithm ◽  
A Priori ◽  
Likelihood Method ◽  
Step Size ◽  
Spindle System ◽  
Grinding Machine ◽  
Search Interval

As a kind of rotor system, the electric spindle system is the core component of the precision grinding machine. The vibration caused by the mass imbalance is the main factor that causes the vibration of the grinding machine. Identifying the eccentricity parameters in an electric spindle system is a key issue in eliminating mass imbalances. It is difficult for engineers to understand the approximate range of eccentricity by experience; that is, it is difficult to obtain a priori information about eccentricity. At the same time, due to the geometric characteristics of the electrospindle system, the material factors and the randomness of the measurement response, these uncertain factors, even in a small case, are likely to cause large deviations in the eccentricity recognition results. The search algorithm used in the maximum likelihood method to identify the eccentricity parameters of the electrospindle system is computationally intensive, and the sensitivity in the iterative process brings some numerical problems. This paper introduces an Advance-Retreat Method (ARM) of the search interval to the maximum likelihood method, the unknown parameter increment obtained by the maximum likelihood method is used as the step size in the iteration, and the Advance-Retreat Method of the search interval is used to adjust the next design point so that the objective function value is gradually decreasing. The recognition results under the three kinds of measurement errors show that the improved maximum likelihood method improves the recognition effect of the maximum likelihood method and can reduce the influence of uncertainty factors on the recognition results, and the robustness is satisfactory.

A comparison of satellite-altimetry and ice-thickness measurements of the Ross Ice Shelf, Antarctica

1994 ◽  
Vol 20 ◽  
pp. 357-364 ◽  
Author(s):  
Bamber Jonathan ◽  
Bentley Charles r
Keyword(s):  
Measurement Errors ◽  
Satellite Altimetry ◽  
Altimeter Data ◽  
Ice Thickness ◽  
Correlated Errors ◽  
Ice Shelf ◽  
Height Measurement ◽  
Ross Ice Shelf ◽  
In Situ Data ◽  
Radio Echo Sounding

The launch of ERS-l provides coverage, by satellite altimetry, of a large part of the Ross Ice Shelf ineluding areas of input from Byrd Glacier and Ice Streams D and E. Five 35 d repeats of fast-delivery data, comprising approximately 100000 height estimates, have been used to produce a Digital Elevation Model (DEM) of the Ross Icc Shelf north of 81.5° S. Careful filtering of the altimeter data, which removed about 30% of the measurements, ensured that only valid values were used. The data were grldded to produce a DEM with a cell size of 10km. Repeatability of the data was assessed from an analysis of crossing points of ascending and descending tracks. The rms cross-over difference for the ice shelf was 0.94 m. Using the five repeat tracks gave a random error of 0.30 m for an averaged height measurement. Regionally correlated errors in the orbit and geoid add a systematic long wavelength bias of approximately 2m to the final elevation estimate. Two of the latest geoid models, OSU91-A and JGMI, were compared with the available in situ data and hYdrostatic models based on ice and water densities.The altimetry was compared with ice-thickness data from Ross Icc Shelf Geophysical and Glaciological Survey (RIGGS) stations and Scott Polar Research Institute radio-echo-sounding surveys undertaken in the 1970s. Differences between the DEM and heights calculated from ice thicknesses and a standard density -depth equation lie, in general, within the combined measurement errors. There are, however, several areas where this is not the case. Prominent north-south stripes of different ice thickness shown on a RIGGS map apparently do not exist. Low elevations are associated with high-density ice draining from East Antarctic outlet glaciers. The grounding line of Icc Streams D and E and an ice plain behind it are clearly demarcated by the break in surface slope. Grounded ice north of Steershead is also observed

scholarly journals Penalized likelihood estimation of a trivariate additive probit model

Biostatistics ◽  
2017 ◽  
Vol 18 (3) ◽  
pp. 569-585 ◽  
Author(s):  
Panagiota Filippou ◽  
Giampiero Marra ◽  
Rosalba Radice
Keyword(s):  
Penalized Likelihood ◽  
Trust Region ◽  
Correlation Coefficients ◽  
Likelihood Estimation ◽  
Probit Model ◽  
R Package ◽  
Likelihood Method ◽  
Spatial Effects ◽  
Trust Region Algorithm ◽  
Smoothing Parameter Selection

SUMMARY This article proposes a penalized likelihood method to estimate a trivariate probit model, which accounts for several types of covariate effects (such as linear, nonlinear, random, and spatial effects), as well as error correlations. The proposed approach also addresses the difficulty in estimating accurately the correlation coefficients, which characterize the dependence of binary responses conditional on covariates. The parameters of the model are estimated within a penalized likelihood framework based on a carefully structured trust region algorithm with integrated automatic multiple smoothing parameter selection. The relevant numerical computation can be easily carried out using the SemiParTRIV() function in a freely available R package. The proposed method is illustrated through a case study whose aim is to model jointly adverse birth binary outcomes in North Carolina.

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