Accuracy Of Maximum Likelihood Estimator Research Articles

Bayesian Error-in-Variables Models for the Identification of Distribution Grids

The increasing integration of renewable energy requires a good model of the existing power distribution infrastructure, represented by its admittance matrix. However, a reliable estimate may either be missing or quickly become obsolete, as distribution grids are continuously modified. In this work, we propose a method for estimating the admittance matrix from voltage and current measurements. By focusing on <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu $ </tex-math></inline-formula> PMU measurements and partially observed networks, we show that voltage collinearity and noisy samples of all electric variables are the main challenges for accurate identification. Moreover, the accuracy of maximum likelihood estimation is often insufficient in real-world scenarios. To overcome this problem, we develop a flexible Bayesian framework that allows one to exploit different forms of prior knowledge about individual line parameters, as well as network-wide characteristics such as the sparsity of the interconnections. Most importantly, we show how to use maximum likelihood estimates for tuning relevant hyperparameters, hence making the identification procedure self-contained. We also discuss numerical aspects of the maximum a posteriori estimate computation. Realistic simulations conducted on benchmark electrical systems demonstrate that, compared to other algorithms, our method can achieve significantly greater accuracy than previously developed methods.

Meiosis at three loci in autotetraploids: Probabilities of gamete modes and genotypes without and with preferential cross-over formation.

A long-standing goal in the field of polyploid biology has been the derivation of mathematical models of gamete mode formation. These models form the basis of statistical inference and evolutionary theory. Here, we present 3-locus models of gamete mode formation in autotetraploids without and with preferential cross-over formation. The three loci are assumed to occur on one arm of the same chromosome. For preferential cross-over formation, one of the three loci affects the tendency for sets of sister chromatids to pair and therefore affects rates of recombination. The models are derived such that the process of double reduction is a function of rates of synaptic partner switches and recombination, as opposed to being independent of these processes. We assume potentially one synaptic partner switch per meiosis. We also assume the coefficient of coincidence is one, such that cross-over events are independent, given a set of cross-over rates. Illustrative cases are examined demonstrating differences in the gamete mode probabilities without and with preferential cross-over formation. Lastly, we explore the accuracy of maximum likelihood estimates of the probability of synaptic partner switches and preferential cross-over formation when the locus controlling preference is at a proximal, middle, or distal location on the chromosome arm. All Supplementary Information is available at https://github.com/ckgriswold/3-locus-autotetraploid-meiosis .

Optimization of Aeolus' aerosol optical properties by maximum-likelihood estimation

Abstract. The European Space Agency (ESA) Earth Explorer Mission Aeolus was launched in August 2018, carrying the first Doppler wind lidar in space. Its primary payload, the Atmospheric LAser Doppler INstrument (ALADIN), is an ultraviolet (UV) high-spectral-resolution lidar (HSRL) measuring atmospheric backscatter from air molecules and particles in two separate channels. The primary mission product is globally distributed line-of-sight wind profile observations in the troposphere and lower stratosphere. Atmospheric optical properties are provided as a spin-off product. Being an HSRL, Aeolus is able to independently measure the particle extinction coefficients, co-polarized particle backscatter coefficients and the co-polarized lidar ratio (the cross-polarized return signal is not measured). This way, the retrieval is independent of a priori lidar ratio information. The optical properties are retrieved using the standard correct algorithm (SCA), which is an algebraic inversion scheme and therefore sensitive to measurement noise. In this work, we reformulate the SCA into a physically constrained maximum-likelihood estimation (MLE) problem and demonstrate a predominantly positive impact and considerable noise suppression capabilities. These improvements originate from the use of all available information by the MLE in conjunction with the expected physical bounds concerning positivity and the expected range of the lidar ratio. To consolidate and to illustrate the improvements, the new MLE algorithm is evaluated against the SCA on end-to-end simulations of two homogeneous scenes and for real Aeolus data collocated with measurements by a ground-based lidar and the Cloud–Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) satellite. The largest improvements were seen in the retrieval precision of the extinction coefficients and lidar ratio ranging up to 1 order of magnitude or more in some cases due to effective noise dampening. In real data cases, the increased precision of MLE with respect to the SCA is demonstrated by increased horizontal homogeneity and better agreement with the ground truth, though proper uncertainty estimation of MLE results is challenged by the constraints, and the accuracy of MLE and SCA retrievals can depend on calibration errors, which have not been considered.

Methods of Estimation and Bias Corrected Maximum Likelihood Estimators of Unit Burr III Distribution

In this article, various classical estimation methods are employed to estimate the parameters of unit Burr III distribution. Further, the associated second-order bias corrections of the MLEs of its parameters are obtained by using a modified bias-corrected approach. In addition, another parametric bootstrap bias correction method is also considered for model parameters. Extensive Monte-Carlo simulation studies are performed to evaluate different estimation methods in terms of their average biases and mean squared error, and the performance of these estimators are compared as well. Our results reveal that the bias corrections improve the accuracy of maximum likelihood estimates. Finally, one real data example is discussed to illustrate the applicability of the unit Burr III distribution.

Application of differential evolution for wind speed distribution parameters estimation

Weibull distribution is an extensively used statistical distribution for analyzing wind speed and determining energy potential studies. Estimation of the wind speed distribution parameter is essential as it significantly affects the success of Weibull distribution application to wind energy. Various estimation methods viz. graphical method, moment method (MM), maximum likelihood method (ML), modified maximum likelihood method, and energy pattern factor method or power density method have been presented in various reported research studies for accurate estimation of distribution parameters. ML is the most preferred approach to study the parameter estimation. ML works on the principle of forming a likelihood function and maximizing the function for parameter estimation. ML generally uses the numerical based iterative method, such as Newton–Raphson. However, the iterative methods proposed in the literature are generally computationally intensive. In this paper, an efficient technique utilizing differential evolution (DE) algorithm to enhance the estimation accuracy of maximum likelihood estimation has been presented. The [Formula: see text] of GA-Weibull, SA-Weibull, and DE-Weibull is 0.958, 0.953, and 0.973 respectively, and value of RMSE of DE-Weibull 0.0083, GA-Weibull (0.0104), and SA-Weibull (0.0110), for the yearly wind speed data are obtained. The lowest root mean square error and larger regression value for both monthly and yearly wind speed data indicate that the DE-Weibull distribution has the best goodness of fit and advocate the DE algorithm for the parameter estimation.

Improving Equipment Reliability and System Maintenance and Repair Efficiency

Mean time to failure of modern machinery and equipment, their individual parts and components can be calculated over the years. Methods for determining the optimal frequency of maintenance and repair, based on the collection and processing of information about the reliability of industrial facilities, during their testing in laboratories and at special sites, as well as through long, operational tests require considerable time and become expensive. The purpose of this work is to develop methods for processing information about the reliability of equipment in automated systems for maintenance and repair, which will reduce the time to collect information on equipment failures and improve the cost-effectiveness of maintenance and repair. Small, multiple-censored right-side samples of equipment operating time for failure are formed as a result of failure data collection in an automated system for equipment maintenance and repair. Calculation of reliability indicators for such samples is performed using the maximum likelihood estimation method. The article presents experimental studies of the accuracy of the maximum likelihood estimates of the parameter of the exponential distribution law for small, multiple right-censored samples. The studies were carried out by computer modeling of censored samples, similar to samples that are formed when monitoring equipment during operation. Methods of simulation modeling of random processes on a computer and methods of regression analysis were used. Analysis show that most of the maximum likelihood estimates obtained from small, multiple-censored right-side samples have significant deviations from the true values. A technique for improving the accuracy of maximum likelihood estimates is proposed. The scientific novelty is regression models are constructed that establish the relationship between the deviation of the maximum likelihood estimate from the true value and the parameters characterizing the sample structure. These models calculate and introduce corrections to maximum likelihood estimates. The use of the developed regression models will reduce the time to collect information about the reliability of the equipment, while maintaining the reliability of the results.

Logarithmic inverse Lindley distribution: Model, properties and applications

In this paper, we proposed a new extension of inverse Lindley distribution called Logarithmic inverse Lindley (LIL).To this end, an extension of the Marshall-Olkin generalization approach, by Marshall and Olkin (1997), has been used. This generalization method was introduced by Pappas et al. (2012). It is shown that the distribution belongs to the family of upside-down bathtub shaped distribution. The properties of the LIL distribution are discussed and the maximum likelihood estimation is used to evaluate the parameters involved. The moments of the new model are derived. We use the Lambert function to derive explicit expressions for the quantiles and its special case (the median). A Monte Carlo simulation study is presented to exhibit the performance and accuracy of maximum likelihood estimates of the LIL model parameters. Finally, the usefulness of the new model for modeling reliability data is illustrated using a real data set to show the performance of the new distribution.

Amplitude estimation of rectangular narrow-band radio pulse with unknown duration and initial phase

This study investigates algorithms for the estimation of amplitude of the radio signal with rectangular envelope and unknown duration and initial phase. The synthesis and analysis of quasi-likelihood and quasi-coherent estimation algorithm have been performed. This algorithm implies that the unknown duration and initial phase are replaced with certain expected values of these parameters. The loss in accuracy of amplitude estimation owing to the a priori lack of knowledge of the duration and the initial phase is analyzed. The quasi-likelihood noncoherent algorithm for amplitude estimation with the initial phase adaptation is synthesized and its statistical characteristics such as the estimate bias and variance are determined. The relationships of the loss in estimation accuracy owing to the a priori lack of knowledge of signal duration are derived. The maximum likelihood algorithm for amplitude estimation was synthesized and analyzed. This algorithm implies that the unknown duration and the initial phase are replaced with their maximum likelihood estimates. The gain in accuracy of the maximum likelihood estimate as compared to the quasi-likelihood ones was investigated. It is shown that a priori lack of knowledge of the signal duration does not affect asymptotically the accuracy of maximum likelihood estimate of amplitude at large values of signal-to-noise ratio.

IoT Localization for Bistatic Passive UHF RFID Systems With 3-D Radiation Pattern

Passive radio-frequency identification (RFID) systems carry critical importance for Internet of Things (IoT) applications due to their energy harvesting capabilities. RFIDbased position estimation, in particular, is expected to facilitate a wide array of location-based services for IoT applications with low-power requirements. In this paper, considering monostatic and bistatic configurations and 3-D antenna radiation pattern, we investigate the accuracy of received signal strength-based wireless localization using passive ultra high frequency RFID systems. The Cramer-Rao lower bound (CRLB) for the localization accuracy is derived, and is compared with the accuracy of maximum likelihood estimators for various RFID antenna configurations. Numerical results show that due to RFID tag/antenna sensitivity, and the directional antenna pattern, the localization accuracy can degrade at blind locations that remain outside of the RFID reader antennas' main beam patterns. In such cases optimizing elevation angle of antennas are shown to improve localization coverage, while using bistatic configuration improves localization accuracy significantly.

Estimation of 2- and 3-parameter BURR type XII distribution using EM algorithm

The Burr Type XII distribution is one of the systems of continuous distributions and is widely known because the distribution includes the characteristics of various well known distributions such as Weibull and gamma distributions. Maximum likelihood estimation (MLE) has been a common method in estimating model parameters. In this paper, we present an alternative method that is expectation-maximization (EM) algorithm to estimate the two- and three- parameter Burr Type XII distributions in the presence of complete and censored data. Furthermore, simulation study is conducted to compare the efficiency and accuracy of MLE and EM algorithm. We discover that EM estimation is more efficient and accurate than those estimates obtained via MLE approach.________________________________________GRAPHICAL ABSTRACT

On the Accuracy of Maximum Likelihood Estimation for Primary User Behavior in Cognitive Radio Networks

The primary user (PU)'s busy/idle behavior in a cognitive radio network is conventionally modeled using a two-state Markov chain. Maximum likelihood (ML) estimation is widely applied to estimate the state transition probabilities. This letter derives a precise expression of the probability mass function (PMF) for the ML estimator, which has not been reported in the literature. By leveraging the exact PMF expression, the essential relation among the number of samples, transition probabilities, and estimation accuracy is revealed.

Quazi-likelihood estimation of motion parameters during the target probing with a sequence of optical pulses

Characteristics of quasi-likelihood estimates of the target range, velocity, and acceleration have been obtained during the probing with a sequence of optical pulses. The losses in accuracy of quasi-likelihood estimates as compared with the accuracy of maximum likelihood estimates were also found.

A New Two-Parameter Lifetime Distribution with Increasing Failure Rate

A new two-parameter lifetime distribution with increasing failure rate is introduced. Various properties of the proposed distribution are discussed. The distribution parameters are estimated by the EM algorithm and the asymptotic variances and covariances of these estimators are obtained. The accuracy of maximum likelihood estimation of variances and covariances are studies by simulation. Some experimental results based on real data sets illustrate the results.

Inverting Random Functions III: Discrete MLE Revisited

This paper continues our earlier investigations into the inversion of random functions in a general (abstract) setting. In Section 2, we investigate a concept of invertibility and the invertibility of the composition of random functions defined on finite sets. In Section 3, we resolve some questions concerning the number of samples required to ensure the accuracy of maximum likelihood estimation (MLE) in the presence of ‘nuisance’ parameters. A direct application to phylogeny reconstruction is given.

Estimation of pulse repetition period with the use of a recirculator

A new structure of a quasiprobable measurer of repetition period of pulses against the white noise background is suggested. The loss in accuracy of quasiprobable estimation, in compared with the accuracy of maximum likelihood estimation, is determined for regular and discontinuous pulses.

Evaluation of maximum-likelihood threshold estimation with tone-in-noise masking

There has been much recent interest in the use of adaptive psychophysical procedures based on maximum-likelihood estimation (MLE) in order to minimize testing time. The speed and accuracy of MLE was compared to a standard transformed up-down algorithm in a two-interval forced-choice task. Thresholds for detecting a 2 kHz tone in either a broadband or a notched-noise were estimated in three normal-hearing listeners. The transformed up-down algorithm tracked 79% correct with either two, four, six or eight final turnarounds, whereas the MLE procedure tracked 70%, 80% or 90% correct. MLE was always quickest, but with a penalty in increased variability. Use of the MLE procedure to track 70% or 80% correct also resulted in a tendency to overestimate listeners' sensitivity. Reducing the number of turnarounds in the up-down procedure from eight to two reduced the number of trials required by nearly half and resulted in thresholds with similar magnitude and variability to those obtained using MLE to track 90% correct.

CFAR detection and estimation for STAP radar

The algorithm presented here provides both a constant false-alarm rate (CFAR) detection and a maximum likelihood (ML) Doppler-bearing estimator of a target in a background of unknown Gaussian noise. A target is detected, and its parameters estimated within each range gate by evaluating a statistical test for each Doppler-angle cell and by selecting the cell with maximum output and finally comparing it with a threshold. Its CFAR performance is analyzed by the use of the sample matrix inversion (SMI) method and is evaluated in the cases of a fully adaptive space-time adaptive processing (STAP) and two partially adaptive STAPs. The performances of these criteria show that the probability of detection is a function only of the sample size K used to estimate the covariance matrix and a generalized signal-to-noise ratio. The choice of the number K is a tradeoff between performance and computational complexity. The performance curves demonstrate that the finer the resolution is, the poorer the detection capability. That means that one can trade off the accuracy of ML estimation with the performance of the CFAR detection criterion.

Estimating target location from scattered field data

Accuracy of maximum likelihood estimation of the location of a known target from noisy forward or back scattering data is established by computing the Cramer-Rao bounds for the variance of the estimation error. It is demonstrated through examples that inclusion of evanescent wave scattering data leads to a significant improvement in these bounds when the wavelength is long compared to the distance of the target from the receiving antennas. This result is particularly useful in ground penetrating radar (GPR) applications where ground losses mandate operating wavelength that is long relative to target dimensions and depth.

Precision and accuracy of regional radioactivity quantitation using the maximum likelihood EM reconstruction algorithm

The imaging characteristics of maximum likelihood (ML) reconstruction using the EM algorithm for emission tomography have been extensively evaluated. There has been less study of the precision and accuracy of ML estimates of regional radioactivity concentration. The authors developed a realistic brain slice simulation by segmenting a normal subject's MRI scan into gray matter, white matter, and CSF and produced PET sinogram data with a model that included detector resolution and efficiencies, attenuation, scatter, and randoms. Noisy realizations at different count levels were created, and ML and filtered backprojection (FBP) reconstructions were performed. The bias and variability of ROI values were determined. In addition, the effects of ML pixel size, image smoothing and region size reduction were assessed. Hit estimates at 3,000 iterations (0.6 sec per iteration on a parallel computer) for 1-cm(2) gray matter ROIs showed negative biases of 6%+/-2% which can be reduced to 0%+/-3% by removing the outer 1-mm rim of each ROI. FBP applied to the full-size ROIs had 15%+/-4% negative bias with 50% less noise than hit. Shrinking the FBP regions provided partial bias compensation with noise increases to levels similar to ML. Smoothing of ML images produced biases comparable to FBP with slightly less noise. Because of its heavy computational requirements, the ML algorithm will be most useful for applications in which achieving minimum bias is important.