scholarly journals Bayesian Estimation Applied to Stochastic Localization with Constraints due to Interfaces and Boundaries

2013 ◽  
Vol 2013 ◽  
pp. 1-17 ◽  
Author(s):  
Wolfgang Hoegele ◽  
Rainer Loeschel ◽  
Barbara Dobler ◽  
Oliver Koelbl ◽  
Piotr Zygmanski
Keyword(s):  
Bayesian Estimation ◽  
Minimum Mean Square Error ◽  
Computational Effort ◽  
Estimation Accuracy ◽  
Knowledge Map ◽  
Beam Model ◽  
Mean Square ◽  
Simulation Studies ◽  
Hard Constraints ◽  
Mean Square Errors

Purpose. We present a systematic Bayesian formulation of the stochastic localization/triangulation problem close to constraining interfaces.Methods. For this purpose, the terminology of Bayesian estimation is summarized suitably for applied researchers including the presentation of Maximum Likelihood (ML), Maximum A Posteriori (MAP), and Minimum Mean Square Error (MMSE) estimation. Explicit estimators for triangulation are presented for the linear 2D parallel beam and the nonlinear 3D cone beam model. The priors in MAP and MMSE optionally incorporate (A) the hard constraints about the interface and (B) knowledge about the probability of the object with respect to the interface. All presented estimators are compared in several simulation studies for live acquisition scenarios with 10,000 samples each.Results. First, the presented application shows that MAP and MMSE perform considerably better, leading to lower Root Mean Square Errors (RMSEs) in the simulation studies compared to the ML approach by typically introducing a bias. Second, utilizing priors including (A) and (B) is very beneficial compared to just including (A). Third, typically MMSE leads to better results than MAP, by the cost of significantly higher computational effort.Conclusion. Depending on the specific application and prior knowledge, MAP and MMSE estimators strongly increase the estimation accuracy for localization close to interfaces.

scholarly journals On Smoothed MWSD Estimation of Mixing Proportion

2021 ◽  
pp. 971-982
Author(s):  
Satish Konda ◽  
Mehra, K.L. ◽  
Ramakrishnaiah Y.S.
Keyword(s):  
Monte Carlo ◽  
Asymptotic Normality ◽  
Minimum Mean Square Error ◽  
Monte Carlo Study ◽  
Mean Square ◽  
Random Samples ◽  
Two Component ◽  
Mixing Proportion ◽  
Mean Square Error Criterion ◽  
Mean Square Errors

The problem considered in the present paper is estimation of mixing proportions of mixtures of two (known) distributions by using the minimum weighted square distance (MWSD) method. The two classes of smoothed and unsmoothed parametric estimators of mixing proportion proposed in a sense of MWSD due to Wolfowitz(1953) in a mixture model F(x)=p (x)+(1-p) (x) based on three independent and identically distributed random samples of sizes n and , =1,2 from the mixture and two component populations. Comparisons are made based on their derived mean square errors (MSE). The superiority of smoothed estimator over unsmoothed one is established theoretically and also conducting Monte-Carlo study in sense of minimum mean square error criterion. Large sample properties such as rates of a.s. convergence and asymptotic normality of these estimators are also established. The results thus established here are completely new in the literature.

Optimal Wavelength Selection for Quantitative Analysis

1986 ◽  
Vol 40 (2) ◽  
pp. 185-190 ◽  
Author(s):  
K. Sasaki ◽  
S. Kawata ◽  
S. Minami
Keyword(s):  
Quantitative Analysis ◽  
Minimum Mean Square Error ◽  
Mathematical Formulation ◽  
Computation Time ◽  
Mean Square ◽  
Wavelength Selection ◽  
Selection For ◽  
Mixture Samples ◽  
Mean Square Errors ◽  
Optimal Set

A new computer algorithm has been developed for selecting the optimal set of wavelengths for spectroscopic quantitative analysis of mixture samples. The method is based on the criterion of the minimum mean square error between concentrations of the mixture components and their estimates. The branch and bound algorithm finds the optimal set from all possible combinations of wavelengths. This algorithm saves computation time significantly, compared with the enumerative method. The mathematical formulation of the lower bound of the mean square errors for the combinations in a given subset is derived as a recurrence inequality. Experimental results of wavelength selection for infrared absorption spectra of xylene-isomer mixtures are shown to demonstrate the effectiveness of the algorithm in terms of computation complexity and accuracy in quantitative analysis for the fixed measurement time.

On Estimating Ratio and Product of Population Parameters

1982 ◽  
Vol 31 (1-2) ◽  
pp. 69-76 ◽  
Author(s):  
R. Karan Singh
Keyword(s):  
Mean Square Error ◽  
Minimum Mean Square Error ◽  
Mean Square ◽  
Population Parameters ◽  
Class Of Estimators ◽  
Mean Square Errors

A generalized estimator representing a class of estimators for the estimation of ratio and product of population parameters has been proposed. A sub­class of optimum estimators from the proposed class has been investigated and it has been shown that every member of the sub­class has the same minimum mean square error. Further the optimum value (depending upon population parameters) when replaced from sample values gives the estimators having the minimum mean square errors of the optimum estimators.

Robust Kalman-Type Filter for Non-Gaussian Noise: Performance Analysis With Unknown Noise Covariances

2019 ◽  
Vol 141 (9) ◽  
Author(s):  
Seyed Fakoorian ◽  
Alireza Mohammadi ◽  
Vahid Azimi ◽  
Dan Simon
Keyword(s):  
Kalman Filter ◽  
Gaussian Noise ◽  
Optimality Criterion ◽  
Minimum Mean Square Error ◽  
Mean Square ◽  
Process Noise ◽  
Noise Covariance ◽  
Maximum Correntropy Criterion ◽  
Non Gaussian ◽  
Mean Square Errors

The Kalman filter (KF) is optimal with respect to minimum mean square error (MMSE) if the process noise and measurement noise are Gaussian. However, the KF is suboptimal in the presence of non-Gaussian noise. The maximum correntropy criterion Kalman filter (MCC-KF) is a Kalman-type filter that uses the correntropy measure as its optimality criterion instead of MMSE. In this paper, we modify the correntropy gain in the MCC-KF to obtain a new filter that we call the measurement-specific correntropy filter (MSCF). The MSCF uses a matrix gain rather than a scalar gain to provide better selectivity in the way that it handles the innovation vector. We analytically compare the performance of the KF with that of the MSCF when either the measurement or process noise covariance is unknown. For each of these situations, we analyze two mean square errors (MSEs): the filter-calculated MSE (FMSE) and the true MSE (TMSE). We show that the FMSE of the KF is less than that of the MSCF. However, the TMSE of the KF is greater than that of the MSCF under certain conditions. Illustrative examples are provided to verify the analytical results.

Cancelable Biometric System for face Based on linear minimum mean square error Model.

2019 ◽  
Vol 28 (1) ◽  
pp. 145-152
Author(s):  
Abd El-aziz Ebrahim Hsaneen ◽  
EL-Sayed M. El-Rabaei ◽  
Moawad I. Dessouky ◽  
Ghada El-bamby ◽  
Fathi E. Abd El-Samie ◽  
...  
Keyword(s):  
Mean Square Error ◽  
Minimum Mean Square Error ◽  
Error Model ◽  
Mean Square ◽  
Biometric System

Segmenting Star Images with Complex Backgrounds Based on Correlation between Objects and 1D Gaussian Morphology

2021 ◽  
Vol 11 (9) ◽  
pp. 3763
Author(s):  
Yunlong Zou ◽  
Jinyu Zhao ◽  
Yuanhao Wu ◽  
Bin Wang
Keyword(s):  
Mean Square Error ◽  
Selection Process ◽  
Minimum Mean Square Error ◽  
Correlation Coefficients ◽  
False Alarms ◽  
Mean Square ◽  
Segmentation Method ◽  
Space Objects ◽  
High Earth Orbits ◽  
Star Images

Space object recognition in high Earth orbits (between 2000 km and 36,000 km) is affected by moonlight and clouds, resulting in some bright or saturated image areas and uneven image backgrounds. It is difficult to separate dim objects from complex backgrounds with gray thresholding methods alone. In this paper, we present a segmentation method of star images with complex backgrounds based on correlation between space objects and one-dimensional (1D) Gaussian morphology, and the focus is shifted from gray thresholding to correlation thresholding. We build 1D Gaussian functions with five consecutive column data of an image as a group based on minimum mean square error rules, and the correlation coefficients between the column data and functions are used to extract objects and stars. Then, lateral correlation is repeated around the identified objects and stars to ensure their complete outlines, and false alarms are removed by setting two values, the standard deviation and the ratio of mean square error and variance. We analyze the selection process of each thresholding, and experimental results demonstrate that our proposed correlation segmentation method has obvious advantages in complex backgrounds, which is attractive for object detection and tracking on a cloudy and bright moonlit night.

scholarly journals An Estimator for Weather Radar Doppler Power Spectrum via Minimum Mean Square Error

2021 ◽  
pp. 1-16
Author(s):  
Eiichi Yoshikawa ◽  
Naoya Takizawa ◽  
Hiroshi Kikuchi ◽  
Tomoaki Mega ◽  
Tomoo Ushio
Keyword(s):  
Power Spectrum ◽  
Mean Square Error ◽  
Minimum Mean Square Error ◽  
Weather Radar ◽  
Mean Square ◽  
Doppler Power

scholarly journals Histamine Control in Raw and Processed Tuna: A Rapid Tool Based on NIR Spectroscopy

Foods ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 885
Author(s):  
Sergio Ghidini ◽  
Luca Maria Chiesa ◽  
Sara Panseri ◽  
Maria Olga Varrà ◽  
Adriana Ianieri ◽  
...  
Keyword(s):  
Root Mean Square ◽  
Near Infrared ◽  
Nir Spectroscopy ◽  
Partial Least Square ◽  
Least Square ◽  
Partial Least Square Regression ◽  
Coefficient Of Determination ◽  
Mean Square ◽  
Tuna Fish ◽  
Mean Square Errors

The present study was designed to investigate whether near infrared (NIR) spectroscopy with minimal sample processing could be a suitable technique to rapidly measure histamine levels in raw and processed tuna fish. Calibration models based on orthogonal partial least square regression (OPLSR) were built to predict histamine in the range 10–1000 mg kg−1 using the 1000–2500 nm NIR spectra of artificially-contaminated fish. The two models were then validated using a new set of naturally contaminated samples in which histamine content was determined by conventional high-performance liquid chromatography (HPLC) analysis. As for calibration results, coefficient of determination (r2) > 0.98, root mean square of estimation (RMSEE) ≤ 5 mg kg−1 and root mean square of cross-validation (RMSECV) ≤ 6 mg kg−1 were achieved. Both models were optimal also in the validation stage, showing r2 values > 0.97, root mean square errors of prediction (RMSEP) ≤ 10 mg kg−1 and relative range error (RER) ≥ 25, with better results showed by the model for processed fish. The promising results achieved suggest NIR spectroscopy as an implemental analytical solution in fish industries and markets to effectively determine histamine amounts.

scholarly journals Automatic modelling of human musculoskeletal ligaments – Framework overview and model quality evaluation

2021 ◽  
pp. 1-14
Author(s):  
Noura Hamze ◽  
Lukas Nocker ◽  
Nikolaus Rauch ◽  
Markus Walzthöni ◽  
Matthias Harders ◽  
...  
Keyword(s):  
Statistical Model ◽  
Soft Tissues ◽  
Automatic Generation ◽  
Cadaveric Study ◽  
Patient Specific ◽  
Mean Square ◽  
Shape Modelling ◽  
Morphological Studies ◽  
Insertion Sites ◽  
Mean Square Errors

BACKGROUND: Accurate segmentation of connective soft tissues in medical images is very challenging, hampering the generation of geometric models for bio-mechanical computations. Alternatively, one could predict ligament insertion sites and then approximate the shapes, based on anatomical knowledge and morphological studies. OBJECTIVE: In this work, we describe an integrated framework for automatic modelling of human musculoskeletal ligaments. METHOD: We combine statistical shape modelling with geometric algorithms to automatically identify insertion sites, based on which geometric surface/volume meshes are created. As clinical use case, the framework has been applied to generate models of the forearm interosseous membrane. Ligament insertion sites in the statistical model were defined according to anatomical predictions following a published approach. RESULTS: For evaluation we compared the generated sites, as well as the ligament shapes, to data obtained from a cadaveric study, involving five forearms with 15 ligaments. Our framework permitted the creation of models approximating ligaments’ shapes with good fidelity. However, we found that the statistical model trained with the state-of-the-art prediction of the insertion sites was not always reliable. Average mean square errors as well as Hausdorff distances of the meshes could increase by an order of magnitude, as compared to employing known insertion locations of the cadaveric study. Using those, an average mean square error of 0.59 mm and an average Hausdorff distance of less than 7 mm resulted, for all ligaments. CONCLUSIONS: The presented approach for automatic generation of ligament shapes from insertion points appears to be feasible but the detection of the insertion sites with a SSM is too inaccurate, thus making a patient-specific approach necessary.

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