Traditional Maximum Likelihood Method Research Articles

Comparison of accuracy and reliability of random forest, support vector machine, artificial neural network and maximum likelihood method in land use/cover classification of urban setting

Accurate land use and land cover (LULC) is crucial for sustainable urban planning and for many scientific researches. However, the demand for accurate LULC maps is increasing; it is required to compare the classification algorithms to choose the best one. Though, machine and deep learning algorithms are widely used across the world their application is limited in Bangladesh. Accurate urban LULC mapping is challenging because urban heterogeneity affects image classification models in specific feature extraction. In this research, the accuracy of machine learning algorithms (MLA) of RF (Random Forest), SVM (Support Vector Machine), deep learning algorithm (DLA) of ANN (Artificial Neural Network) and traditional Maximum Likelihood (MaxL) method was compared in LULC classification of Dhaka city. Model accuracy of MLA and DLA was tested by statistical indices of sensitivity, specificity, precision, recall F1 etc. There is a high correlation between SVM and ANN models were found. The overall accuracy of the maps was 0.93, 0.94, 0.91 and 0.95 and kappa was 0.89, 0.91, 0.86 and 0.93 for the MaxL, RF, SVM and ANN models respectively. The user accuracy and producer accuracy largely varied according to LULC classes in the applied models. The lowest accuracy of the models was found for bare land classification followed by built-up and vegetation. The high mixture of LULC classes affects the accuracy of built up and bare land classification which produces the lowest accuracy in the MaxL model. The findings indicate that the most accurate and reliable model for urban LULC classification was the ANN model.

On Fitting Probability Distribution to Univariate Grouped Actuarial Data with Both Group Mean and Relative Frequencies

Many publicly available datasets relevant to actuarial work contain data grouped in various ways. For example, operational loss data are often reported in a grouped format that includes group boundaries, loss frequency, and average or total amount of loss for each group. The process of fitting a parametric distribution to grouped data becomes more complex but potentially more accurate when additional information, such as group means, is incorporated in the estimation process. This article compares the relative performance of three methods of inference using distributions suitable for actuarial applications, particularly those that are right-skewed, heavy-tailed, and left-truncated. We compare the traditional maximum likelihood method, which only considers the group limits and frequency of observations in each group, to two research innovations: a modified maximum likelihood method and a modified generalized method of moments approach, both of which incorporate additional group mean information in the estimation process. We perform a simulation study where the proposed methods outperform the traditional maximum likelihood method and the maximum entropy when the true underlying distribution is both known and unknown. Further, we apply the methods to three actuarial datasets: operational loss data, pension fund data, and car insurance claims data. Here we compare the performance of the three methods along with the maximum entropy distribution (under the traditional maximum likelihood and the modified maximum likelihood methods) and find that for all three datasets the proposed methods outperform the traditional maximum likelihood method. We conclude that there is merit in considering the proposed methods while fitting a parametric distribution to grouped data.

A comparative study of multiband mamdani fuzzy classification methods for west of Iraq satellite image

In our paper, performance of four fuzzy membership function generation methods was studied. These methods were studied in the context of implementing Mamdani fuzzy classification on a set of satellite images for western Iraqi territory. The first method generate triangulate membership functions using mean, minimum (min) and maximum (max) of histogram attribute values (AV), while peak and standard deviation (STD) of these AV were used in the second. On the other hand, in the third and fourth methods, Gaussian membership functions are generated using same mentioned values in the first and second method respectively. The goal was to generate a Mamdani type fuzzy inference system the membership function (MF) of each fuzzy set and implementing the AV of western Iraqi territory training data sets. A pixel-by-pixel comparison of each method with traditional maximum likelihood method (ML) was made on data sets comprising six bands of satellite imagery of the western Iraqi region taken by the Landsat-5 satellite. Simulation results of these performance comparisons singled out that the method using Gaussian MFs together with peak and STD of the AV as the best achiever with a similarity of 83.16 percent for band (3) of the studied area.

Spatial Modulation: An Attractive Secure Solution to Future Wireless Networks

As a green and secure wireless transmission method, secure spatial modulation is becoming a hot research area. Its basic idea is to exploit both the index of activated transmit antenna and amplitude phase modulation signal to carry messages, improve security, and save energy. In this article, we review its crucial challenges: transmit antenna selection, artificial noise projection, power allocation (PA), and joint detection at the desired receiver. We proposed a low-complexity maximum likelihood (ML) detector, which efficiently reduces the complexity of detection. Meanwhile, for the sake of improving further secrecy rate (SR) performance, a PA strategy is designed on the basis of a deep neural-network (DNN). Simulation results show that the proposed low-complexity ML detector achieves lower complexity but the same bit error rate performance, compared to the traditional ML method, while the proposed DNN method strikes a good balance between complexity and SR performance.

Different inference approaches for the estimators of the sushila distribution

In this paper, we order to evaluate via Monte Carlo simulations the performance of sample properties of the estimates of the estimates for Sushila distribution, introduced by Shanker et al. (2013). We consider estimates obtained by six estimation methods, the known approaches of maximum likelihood, moments and Bayesian method, and other less traditional methods: L-moments, ordinary least-squares and weighted least-squares. As a comparison criterion, the biases and the roots of mean-squared errors were used through nine scenarios with samples ranging from 30 to 300 (every 30rd). In addition, we also considered a simulation and a real data application to illustrate the applicability of the proposed estimators as well as the computation time to get the estimates. In this case, the Bayesian method was also considered. The aim of the study was to find an estimation method to be considered as a better alternative or at least interchangeable with the traditional maximum likelihood method considering small or large sample sizes and with low computational cost.

On log-bimodal alpha-power distributions with application to nickel contents and erosion data

Abstract In this paper, we present a new parametric class of distributions based on the log-alpha-power distribution, which contains the well-known log-normal distribution as a special case. This new family is useful to deal with unimodal as well as bimodal data with asymmetry and kurtosis coefficients ranging far from that expected based on the log-normal distribution. The usual approach is considered to perform inferences, and the traditional maximum likelihood method is employed to estimate the unknown parameters. Monte Carlo simulation results indicate that the maximum likelihood approach is quite effective to estimate the model parameters. We also derive the observed and expected Fisher information matrices. As a byproduct of such study, it is shown that the Fisher information matrix is nonsingular throughout the sample space. Empirical applications of the proposed family of distributions to real data are provided for illustrative purposes.

Beta ridge regression estimators: simulation and application

The beta regression model is commonly used when analyzing data that come in the form of rates or percentages. However, a problem that may encounter when analyzing these kinds of data that has not been investigated for this model is the multicollinearity problem. It is well known that the maximum likelihood (ML) method is very sensitive to high inter-correlation among the explanatory variables. Therefore, this paper proposes some ridge estimators for the beta regression model to remedy the problem of instability of the traditional ML method and increase the efficiency of estimation. The performance of ridge estimators is compared to the ML estimator through the mean squared error (MSE) and the mean absolute error (MAE) criteria by conducting a Monte-Carlo simulation study and through an empirical application. According to the simulation and application results, the proposed estimators outperform the ML estimator in terms of MSE and MAE.

Accurate genetic and environmental covariance estimation with composite likelihood in genome-wide association studies.

Genetic and environmental covariances between pairs of complex traits are important quantitative measurements that characterize their shared genetic and environmental architectures. Accurate estimation of genetic and environmental covariances in genome-wide association studies (GWASs) can help us identify common genetic and environmental factors associated with both traits and facilitate the investigation of their causal relationship. Genetic and environmental covariances are often modeled through multivariate linear mixed models. Existing algorithms for covariance estimation include the traditional restricted maximum likelihood (REML) method and the recent method of moments (MoM). Compared to REML, MoM approaches are computationally efficient and require only GWAS summary statistics. However, MoM approaches can be statistically inefficient, often yielding inaccurate covariance estimates. In addition, existing MoM approaches have so far focused on estimating genetic covariance and have largely ignored environmental covariance estimation. Here we introduce a new computational method, GECKO, for estimating both genetic and environmental covariances, that improves the estimation accuracy of MoM while keeping computation in check. GECKO is based on composite likelihood, relies on only summary statistics for scalable computation, provides accurate genetic and environmental covariance estimates across a range of scenarios, and can accommodate SNP annotation stratified covariance estimation. We illustrate the benefits of GECKO through simulations and applications on analyzing 22 traits from five large-scale GWASs. In the real data applications, GECKO identified 50 significant genetic covariances among analyzed trait pairs, resulting in a twofold power gain compared to the previous MoM method LDSC. In addition, GECKO identified 20 significant environmental covariances. The ability of GECKO to estimate environmental covariance in addition to genetic covariance helps us reveal strong positive correlation between the genetic and environmental covariance estimates across trait pairs, suggesting that common pathways may underlie the shared genetic and environmental architectures between traits.

A broad class of zero‐or‐one inflated regression models for rates and proportions

AbstractWe introduce a family of distributions with bounded support for continuous rates or proportions when the data contain zeros or ones. On the basis of this class of distributions, we propose a novel class of regression models which is useful for modelling fractional data observed on [0, 1) or (0, 1]. The response variable of the new class of regression models has a mixed continuous‐discrete distribution with probability mass at zero or one, and the parameters of the mixture distribution are modelled through regression structures involving covariates and unknown parameters. An advantage of this class of regression models is the ability to deal with atypical observations. We consider a frequentist approach to performing inferences, and the traditional maximum likelihood method is employed to estimate the regression parameters. We also propose a residual analysis for the novel class of regression models to assess departures from model assumptions. Additionally, global and local influence methods are discussed. An empirical application that employs real data is considered to illustrate the usefulness of the new class of regression models in practice.

Locally optimum watermark decoder in NSST domain using RSS-based Cauchy distribution

It is important to consider the tradeoff between imperceptibility and robustness requirements in developing an image-watermarking technique, some statistical model-based image watermarking schemes have been designed in the past decade. The effectiveness of a statistical watermark decoder depends highly on the modeling of the transform-domain coefficients and the use of hypothesis testing. In this study, a multiplicative image watermarking scheme is proposed in the nonsubsampled Shearlet transform (NSST) domain, where NSST coefficients are modeled by ranked set sample (RSS) based Cauchy statistical distribution and locally most powerful (LMP) test criterion is applied. Digital image watermarking technique consists of two parts, namely, embedding and extracting. In the embedding process, to achieve relatively good imperceptibility and robustness, watermark data is inserted into the significant NSST directional subband that has the highest energy value, by modifying nonlinearly the significant NSST coefficients. In the extracting phase, a scheme is proposed for designing a blind NSST domain watermark decoder incorporating the RSS based Cauchy statistical distribution and LMP test criterion. Here, the RSS method is used to estimate the location parameter and shape parameter of Cauchy statistical distribution instead of traditional maximum-likelihood (ML) method, which can provide the Cauchy model with higher precision parameters. Experimental results on a set of standard test images show significant improvements in imperceptibility and robustness using the proposed method compared with the best known state-of-the-art approaches.

Changes in spatiotemporal drought characteristics over northeast China from 1960 to 2018 based on the modified nested Copula model

Drought forecasting is helpful for understanding the inherent mechanism of hydrological extremes and taking corresponding measures to mitigate drought impacts. Northeast China, which is an important, major grain-producing area in China, has been challenged by substantial losses due to frequent drought. In this study, to predict the spatiotemporal variation in drought events over Northeast China, a model-based simulation framework is proposed based on precipitation data at 70 meteorological stations from 1960 to 2018. The core of the model framework is run theory, modified Copula model- based Bayesian-MCMC, Gibbs sampling, and a new definition of drought intensity center and drought intensity accumulation area. The results showed that a total of 6408 drought events occurred at the 70 meteorological stations in Northeast China over the past 59 years. The empirical distribution functions of longitude, latitude, and time can be used to fit the edge distribution of the original variable. In comparison to the traditional maximum likelihood method, the Bayesian-MCMC method is more accurate for parameter estimation of the Copula model. The Frank Copula is the optimum joint function of longitude and latitude, while the Gaussian Copula is the optimum joint function of location and time. Gibbs sampling can provide a relatively larger sample size for predicting future drought conditions. The spatiotemporal variation in drought in Northeast China changes similarly throughout the year. Drought is mainly concentrated in southwestern Liaoning from February to April. The drought intensity center moves to the northeast from May to September. Western Heilongjiang is the main drought-stricken area from October to November. The drought intensity center moves southwest from December to January of the following year. This study provides a method for effectively predicting drought events and is of great significance to the protection, development, and utilization of water resources.

Simplified ML-Based Carrier Frequency Offset and Phase Noise Estimation for CO-OFDM Systems

The coherent optical orthogonal frequency division multiplexing (CO-OFDM) has become prominent among emerging telecommunication techniques and applications. However, carrier frequency offset (CFO) and laser phase noise adversely impact and degrade the performance of the CO-OFDM systems. In this paper, a simplified maximum-likelihood (ML) approach, which eliminates the need for the exhaustive search associated with traditional ML methods, is derived and utilized for the estimation of CFO and laser phase noise in CO-OFDM systems. Furthermore, to obtain an improved performance, the proposed simplified low-complexity ML estimator is uniquely combined with an efficient data-dependent pilot-aided (DD-PA) technique, for the acquisition of both the CFO and the laser phase noise. The performance of the simplified ML-based estimators is compared with existing methods and verified in a 16-ary quadrature amplitude modulation (16-QAM) CO-OFDM system with polarization mode dispersion (PMD), chromatic dispersion (CD) and other polarization dependent losses (PDLs) along the fiber link.

Land cover dynamic change in the Napahai Basin using the optimized random forest model

Based on the optimized random forest (ORF) model proposed in our research, data of the Landsat-OLI, Landsat-TM images, and digital elevation model were used by us to obtain the land cover maps during several periods in the Napahai Basin. Model performance testing results show that producer accuracy and kappa coefficient of the ORF approach are 0.916 and 0.903, which are higher than the traditional maximum likelihood method. Furthermore, we analyzed the characteristic of land cover dynamic change and seasonal variation of wetlands landscape in 2002 and 2017, and revealed their driving mechanisms and ecological response process. The conclusions are as follows: (1) Lake area expanded in the past 15 years because of increased glacial runoff generated from global warming. Construction land and farmland replaced wetland areas in the middle and downstream regions. Moreover, due to the limitation of hydrothermal conditions in the canyon, few forests in the northeastern basin transferred to shrubs. (2) Dam, which was constructed in northern Napahai lake, controls water storage and made the lake area stable after 2013, so, area change percentage in 2017 from wet to dry season is lower than 2002. The wetland region in the central and downstream basin was synthetically affected by climate change and drainage projects, so its environment condition becomes dryer, and vegetation communities’ succession shows a reversed process. (3) Ecological problems in the Napahai Basin were mainly reflected at aspects of agricultural nonpoint source pollution, overgrazing, and urbanization. These factors affected lake, soil, and groundwater in the Napahai Basin and destroyed the ecological health of wetland landscapes. Therefore, in order to realize sustainable development environmental resources, local government should propose the effective policies to restore the degraded ecosystem and protect natural wetland.

Crop Type Identification and Mapping Using Machine Learning Algorithms and Sentinel-2 Time Series Data

In this paper, the random forests method and the support vector machine in machine learning are explored and compared to the traditional statistical-based maximum likelihood method with 126 features from Sentinel-2A images. The spectral reflectance of 12 bands, 96 texture parameters, 7 vegetation indices, and 11 phenological parameters are successfully extracted from Sentinel-2A images in 2017. The classification result shows that the optimal combination of 13 features yields overall accuracies of traditional classification and machine learning classification of 88.96% and 98%, respectively. Short-wave infrared information shows a significant effect on distinguishing rice, corn, and soybean. The water vapor band plays a significant role in distinguishing between corn and rice. In the multiclassification problem, the machine learning methods have robustness with the identification accuracy of greater than 95% for each crop type, whereas the traditional classification result shows imbalanced accuracies for different crops.

Overcoming the challenge of small effective sample sizes in home‐range estimation

AbstractTechnological advances have steadily increased the detail of animal tracking datasets, yet fundamental data limitations exist for many species that cause substantial biases in home‐range estimation. Specifically, the effective sample size of a range estimate is proportional to the number of observed range crossings, not the number of sampled locations. Currently, the most accurate home‐range estimators condition on an autocorrelation model, for which the standard estimation frame‐works are based on likelihood functions, even though these methods are known to underestimate variance—and therefore ranging area—when effective sample sizes are small.Residual maximum likelihood (REML) is a widely used method for reducing bias in maximum‐likelihood (ML) variance estimation at small sample sizes. Unfortunately, we find that REML is too unstable for practical application to continuous‐time movement models. When the effective sample sizeNis decreased toN ≤ (10), which is common in tracking applications, REML undergoes a sudden divergence in variance estimation. To avoid this issue, while retaining REML’s first‐order bias correction, we derive a family of estimators that leverage REML to make a perturbative correction to ML. We also derive AIC values for REML and our estimators, including cases where model structures differ, which is not generally understood to be possible.Using both simulated data and GPS data from lowland tapir (Tapirus terrestris), we show how our perturbative estimators are more accurate than traditional ML and REML methods. Specifically, when(5) home‐range crossings are observed, REML is unreliable by orders of magnitude, ML home ranges are ~30% underestimated, and our perturbative estimators yield home ranges that are only ~10% underestimated. A parametric bootstrap can then reduce the ML and perturbative home‐range underestimation to ~10% and ~3%, respectively.Home‐range estimation is one of the primary reasons for collecting animal tracking data, and small effective sample sizes are a more common problem than is currently realized. The methods introduced here allow for more accurate movement‐model and home‐range estimation at small effective sample sizes, and thus fill an important role for animal movement analysis. Given REML’s widespread use, our methods may also be useful in other contexts where effective sample sizes are small.

Fast High-Fidelity Readout of a Single Trapped-Ion Qubit via Machine-Learning Methods

In this work, we introduce machine learning methods to implement readout of a single qubit on $^{171}\mathrm{Yb^{+}}$ trapped-ion system. Different machine learning methods including convolutional neural networks and fully-connected neural networks are compared with traditional methods in the tests. The results show that machine learning methods have higher fidelity, more robust readout results in relatively short time. To obtain a 99% readout fidelity, neural networks only take half of the detection time needed by traditional threshold or maximum likelihood methods. Furthermore, we implement the machine learning algorithms on hardware-based field-programmable gate arrays and an ARM processor. An average readout fidelity of 99.5% (with $10^5$ magnitude trials) within 171 $\mu$s is demonstrated on the embedded hardware system for $^{171}\mathrm{Yb^{+}}$ ion trap.

An I/Q-Channel Modeling Maximum Likelihood Super-Resolution Imaging Method for Forward-Looking Scanning Radar

Deconvolution techniques provide efficient implementations for super-resolution imaging for forward-looking scanning radar. However, deconvolution is normally an ill-posed problem, and the solution is extremely sensitive to noise. From a statistical perspective, maximum likelihood (ML) methods are able to condition the ill-posed problem into a well-posed one. Nevertheless, traditional ML methods only consider the amplitude of the echo and by ignoring the phase that do not adequately model the radar imaging system. In this letter, an I/Q-channel modeling ML method is proposed for forward-looking scanning radar. First, the probability model of the echo is deduced by jointly considering noise in the I and Q channels. Then, a probability density function of the received data is deduced and used to formulate the likelihood function. Finally, the targets can be precisely estimated by maximizing this likelihood function. The results of simulations and experiments are provided to illustrate the effectiveness of the proposed method.

Designing repetitive screening procedures with imperfect inspections: An empirical Bayes approach

A batch of expensive items, such as IC chips, is often inspected multiple times in a sequential manner to further discover more conforming items. After several rounds of screening, we need to estimate the number of conforming items that still remain in the batch. We propose in this paper an empirical Bayes estimation method and compare its performance with that of the traditional maximum likelihood method. In the repetitive screening procedure, another important decision problem is when to stop the screening process and salvage the remaining items. We propose various types of stopping rules and illustrate their procedures with a simulated inspection data. Finally, we explore various extensions to our empirical Bayes estimation method in multiple inspection plans.

An Effective Method to Identify Heritable Components from Multivariate Phenotypes.

Multivariate phenotypes may be characterized collectively by a variety of low level traits, such as in the diagnosis of a disease that relies on multiple disease indicators. Such multivariate phenotypes are often used in genetic association studies. If highly heritable components of a multivariate phenotype can be identified, it can maximize the likelihood of finding genetic associations. Existing methods for phenotype refinement perform unsupervised cluster analysis on low-level traits and hence do not assess heritability. Existing heritable component analytics either cannot utilize general pedigrees or have to estimate the entire covariance matrix of low-level traits from limited samples, which leads to inaccurate estimates and is often computationally prohibitive. It is also difficult for these methods to exclude fixed effects from other covariates such as age, sex and race, in order to identify truly heritable components. We propose to search for a combination of low-level traits and directly maximize the heritability of this combined trait. A quadratic optimization problem is thus derived where the objective function is formulated by decomposing the traditional maximum likelihood method for estimating the heritability of a quantitative trait. The proposed approach can generate linearly-combined traits of high heritability that has been corrected for the fixed effects of covariates. The effectiveness of the proposed approach is demonstrated in simulations and by a case study of cocaine dependence. Our approach was computationally efficient and derived traits of higher heritability than those by other methods. Additional association analysis with the derived cocaine-use trait identified genetic markers that were replicated in an independent sample, further confirming the utility and advantage of the proposed approach.

High-Cycle Fatigue P-S-N Curve Estimating Method Based on Maximum Likelihood Method for Turbine Coupling Bolt Materials

The tensile fatigue tests and S-N curve fitting results of the coupling bolt material 25CrMo were given in this paper. It has been proved that the high-cycle fatigue properties of the bolt material can be accurately described by the three-parameter exponential S-N curve model by comparing the fitting results based on different S-N curve models. The fatigue limit of the high-cycle P-S-N curve calculated by the traditional maximum likelihood method was proved to have a high probability of being higher than the accurate fatigue limit. Therefore, a modified method based on maximum likelihood method was proposed so as to calculate the high-cycle P-S-N curve more accurately. The P-S-N of 25CrMo calculated using the modified method was given in this paper.