Maximum Likelihood and Minimum-Steps Methods for Estimating Evolutionary Trees from Data on Discrete Characters

Relative Efficiencies of the Maximum Likelihood, Maximum Parsimony, and Neighbor-Joining Methods for Estimating Protein Phylogeny

Many clinical or prevention studies involve missing or censored outcomes. Maximum likelihood (ML) methods provide a conceptually straightforward approach to estimation when the outcome is partially missing. Methods of implementing ML methods range from the simple to the complex, depending on the type of data and the missing-data mechanism. Simple ML methods for ignorable missing-data mechanisms (when data are missing at random) include complete-case analysis, complete-case analysis with covariate adjustment, survival analysis with covariate adjustment, and analysis via propensity-to-be-missing scores. More complex ML methods for ignorable missing-data mechanisms include the analysis of longitudinal dropouts via a marginal model for continuous data or a conditional model for categorical data. A moderately complex ML method for categorical data with a saturated model and either ignorable or nonignorable missing-data mechanisms is a perfect fit analysis, an algebraic method involving closed-form estimates and variances. A complex and flexible ML method with categorical data and either ignorable or nonignorable missing-data mechanisms is the method of composite linear models, a matrix method requiring specialized software. Except for the method of composite linear models, which can involve challenging matrix specifications, the implementation of these ML methods ranges in difficulty from easy to moderate.

Calculation of the uncertainty in complication probability for various dose–response models, applied to the parotid gland

A Poisson ridge regression estimator

Three-parameter Weibull probability distribution function is used to represent the time-to-failure data. For parameter estimation, the errors-in-variables, maximum likelihood, and least squares methods are compared. The results obtained from five data sets show that maximum likelihood method gives the most reliable parameter estimates which are close to those obtained by errors-in-variables approach. The least squares method gave the poorest results in most cases. For parameter estimation, the Luus-Jaakola direct search optimization procedure yielded the optimal parameter values in negligible computation time, taking less than a second of computation time on a Pentium4/2.66MHz personal computer for 50 data points.

An eigenvector (EV) method for the determination of directional spectra from heave, pitch and roll buoy data is presented. Both a direct and an iterative form (based on an algorithm by Pawka) of this data-adaptive procedure are developed. The direct form outperforms the Longuet-Higgins et al. method, the cosine spread model and the maximum likelihood (ML) method for both simulated and real data. In the iterative form, the iterative EV method is superior to the other methods tested, including the iterative ML method for unimodal peaks when the noise-to-signal ratio is greater than 0.2 and for bimodal peaks at all noise levels. With real data, the direct EV method produced errors within an 80% confidence zone of the data cross-spectral matrix within the stopping criteria of Lawson and Long. Errors of the iterative EV and iterative ML methods were lower than for both the direct EV and ML results and were about the same magnitude when compared to each other. The iterative EV method, however, produced...

The objective of this paper was to predict a model for describing stand structure of tree heights (h) and diameters at breast height (dbh). The research material consisted of data collected from 64 stands of Norway spruce (Picea abies Karst.) and 91 stands of Scots pine (Pinus sylvestris L.) located in southern Finland. Both stand types contained birch (Betula pendula Roth and B. pubescent Ehrh.) admixtures. The traditional univariate approach (Model I) of using the dbh distribution (Johnson’s SB) together with a height curve (Näslund’s function) was compared against the bivariate approaches, Johnson’s SBB distribution (Model II) and Model Ie. In Model Ie within-dbh-class h-variation was included by transforming a normally distributed homogenous error of linearized Näslund’s function to concern real heights. Basal-area-weighted distributions were estimated using the maximum likelihood (ML) method. Species-specific prediction models were derived using linear regression analysis. The models were compared with Kolmogorov-Smirnov tests for marginal distributions, accuracy of stand variables and the dbh-h relationship of individual trees. The differences in the stand characteristics between the models were marginal. Model I gave a slightly better fit for spruce, but Model II was better for pine stands. The univariate Model I resulted in clearly too narrow marginal h-distribution for pine. It is recommended applying of a constrained ML method for reasonable dbh-h relationship instead of using a pure ML method when fitting the SBB model.

Recent work has developed maximum likelihood (ML) methods for track-to-track data association and fusion in a multisensor, i.e., more than two sensor, environment. In order to conserve bandwidth, only the state estimates and corresponding covariance matrices are shared amongst the nodes. The fusion engine uses this track information to determine which tracks associate to the same target and then computes a fused track to improve the accuracy of the state estimates. The simplest class of ML methods assumes that the track errors from different sensors are uncorrelated. The more computationally demanding ML methods incorporate the cross-correlations that are due to the common process noise in the kinematic model of the target. In order to account for track correlations in practice, the cross-covariance matrices must be approximated from the single sensor covariance matrices. This paper introduces new methods to approximate the cross-covariance matrices, and these approximations lead to a third class of association and estimation methods. The paper then uses simulations to assess the performance of the different association and estimation techniques. The simulations include results when the sensor tracks are produced by either a Kalman filter or an interacting multiple model (IMM) filter.

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.

Accurate determination of the effective reproduction number (Rt) is a very important strategy in the epidemiology of contagious diseases, including coronavirus disease 2019 (COVID-19). This study compares different methods of estimating the Rt of susceptible population to identify the most accurate method for estimating Rt. A secondary study. The value of Rt was estimated using attack rate (AR), exponential growth (EG), maximum likelihood (ML), time-dependent (TD), and sequential Bayesian (SB) methods, for Iran, the United States, the United Kingdom, India, and Brazil from June to October 2021. In order to accurately compare these methods, a simulation study was designed using forty scenarios. The lowest mean square error (MSE) was observed for TD and ML methods, with 15 and 12 cases, respectively. Therefore, considering the estimated values of Rt based on the TD method, it was found that Rt values in the United Kingdom (1.33; 95% CI: 1.14-1.52) and the United States (1.25; 95% CI: 1.12-1.38) substantially have been more than those in other countries, such as Iran (1.07; 95% CI: 0.95-1.19), India (0.99; 95% CI: 0.89-1.08), and Brazil (0.98; 95% CI: 0.84-1.14) from June to October 2021. The important result of this study is that TD and ML methods lead to a more accurate estimation of Rt of population than other methods. Therefore, in order to monitor and determine the epidemic situation and have a more accurate prediction of the incidence rate, as well as control COVID-19 and similar diseases, the use of these two methods is suggested to more accurately estimate Rt.

Brassicaceae, one of the most diverse and economically valuable plant families, is distributed all over the world. Previous studies have suggested that Brassicaceae originated and diversified in the Old World. In this study, the phylogenetic relationships of 17 tribes of Brassicaceae from the Qinghai–Tibet Plateau (QTP) and adjacent areas were investigated using nuclear ribosomal internal transcribed spacer (nrITS) and chloroplast DNA sequence data (rbcL and petB‐petD) with maximum likelihood, maximum parsimony, and Bayesian methods. As suggested by both the nrITS and chloroplast DNA trees, Cardaria pubescens (C.A.Mey.) Jarm. (Lepidieae) and Draba lanceolata Royle (Arabideae) should be classified in the Eutremeae and Cardamineae, respectively. Based on over 700 newly sequenced and published nrITS sequences of Brassicaceae, an up‐to‐date comprehensive phylogeny of the family was reconstructed using the maximum likelihood method. In the phylogenetic tree, 10 monophyletic tribes were detected. They were used to clarify the lineage diversification and dispersal patterns of the 10 tribes. The results showed that most of the monophyletic tribes may have originated in different regions of the world, and then dispersed into other regions surrounding the QTP. Rapid lineage diversification rate shifts were detected in several tribes, such as Anastaticeae, which experienced a rapid shift event ∼1.38 Mya, corresponding to the rapid uplift of the QTP, indicating that the recent uplift of the QTP could have promoted diversification in Brassicaceae across and adjacent to the QTP.

Analysis of snow load probabilistic models and calculation of reference snow pressure using maximum likelihood method for multiple cities in Liaoning Province, China

Aim of study: The aim of this work was to model diameter distributions of Quercus suber stands. The ultimate goal was to construct models enabling the development of more affordable forest inventory methods. This is the first study of this type on cork oak forests in the area.Area of study: The area of study is “Los Alcornocales” Natural Park (Cádiz-Málaga, Spain).Material and methods: The diameter distributions of 100 permanent plots were modelled with the two-parameter Weibull function. Distribution parameters were fitted with the non-linear regression, maximum likelihood, moment and percentile-based methods. Goodness of fit with the different methods was compared in terms of number of plots rejected by the Kolmogorov-Smirnov test, bias, mean square error and mean absolute error. The scale and shape parameters in the Weibull function were related to the stand variables by using the parameter prediction model.Main results: The best fitting was obtained with the non-linear regression approach, using as initial values those obtained by maximum likelihood method, the percentage of rejections by the Kolmogorov-Smirnov test was 2% of the total number of cases. The scale parameter (b) was successfully modelled in terms of the quadratic mean diameter under cork (R2 adj = 0.99). The shape parameter (c) was modelled by using maximum diameter, minimum diameter and plot elevation (R2 adj = 0.40).Research highlights: The proposed model diameter distribution can be a highly useful tool for the inventorying and management of cork oak forests.Key words: maximum likelihood method; moment method; non linear regression approach; parameter prediction model; percentile method; scale parameter; shape parameter.

We propose a super-resolution resolution algorithm on the basis of maximum likelihood (ML) method and edge-orient diffusion. By using Hammerseley-Clifford theorem, an image field assumed to be a Markov random field is Gibbs distributed. An edge-orient diffusion function is introduced and employed in the Gibbs prior. According to Bayesian theorem, the solution to the maximum likelihood function is equal to that to maximum a posterior function. Therefore we incorporate ML with a prior distributed function. Experimental results illustrate that our method has a powerful super-resolution restoration performance. Compared with traditional ML method, our approach can not only obtain super-resolution images, but also eliminate noise artifacts effectively without smoothing edges.

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.