An approximate maximum likelihood approach, applied to phylogenetic trees.

A novel type of approximation scheme to the maximum likelihood (ML) approach is presented and discussed in the context of phylogenetic tree reconstruction from aligned DNA sequences. It is based on a parameterized approximation to the conditional distribution of hidden variables (related, e.g., to the sequences of unobserved branch point ancestors) given the observed data. A modified likelihood, based on the extended data, is then maximized with respect to the parameters of the model as well as to those involved in the approximation. With a suitable form of the approximation, the proposed method allows for simpler updating of the parameters, at the cost of an increased parameter count and a slight decrease in performance. The method is tested on phylogenetic tree reconstruction from artificially generated sequences, and its performance is compared to that of ML, showing that the approach is competitive for reasonably similar sequences. The method is also applied to real DNA sequences from primates, yielding a result consistent with those obtained by other standard algorithms.     

Point and interval estimation of baseline risk and treatment effect based on logistic model for observational studies

In observational studies with dichotomous outcome of a population, researchers usually report treatment effect alone, although both baseline risk and treatment effect are needed to evaluate the significance of the treatment effect to the population. In this article, we study point and interval estimates including confidence region of baseline risk and treatment effect based on logistic model, where baseline risk is the risk of outcome of the population under control treatment while treatment effect is measured by the risk difference between outcomes of the population under active versus control treatments. Using approximate normal distribution of the maximum‐likelihood (ML) estimate of the model parameters, we obtain an approximate joint distribution of the ML estimate of the baseline risk and the treatment effect. Using the approximate joint distribution, we obtain point estimate and confidence region of the baseline risk and the treatment effect as well as point estimate and confidence interval of the treatment effect when the ML estimate of the baseline risk falls into specified range. These interval estimates reflect nonnormality of the joint distribution of the ML estimate of the baseline risk and the treatment effect. The method can be easily implemented by using any software that generates normal distribution. The method can also be used to obtain point and interval estimates of baseline risk and any other measure of treatment effect such as risk ratio and the number needed to treat. The method can also be extended from logistic model to other models such as log‐linear model.     

A restricted maximum likelihood estimator for truncated height samples

A restricted maximum likelihood (ML) estimator is presented and evaluated for use with truncated height samples. In the common situation of a small sample truncated at a point not far below the mean, the ordinary ML estimator suffers from high sampling variability. The restricted estimator imposes an a priori value on the standard deviation and freely estimates the mean, exploiting the known empirical stability of the former to obtain less variable estimates of the latter. Simulation results validate the conjecture that restricted ML behaves like restricted ordinary least squares (OLS), whose properties are well established on theoretical grounds. Both estimators display smaller sampling variability when constrained, whether the restrictions are correct or not. The bias induced by incorrect restrictions sets up a decision problem involving a bias-precision tradeoff, which can be evaluated using the mean squared error (MSE) criterion. Simulated MSEs suggest that restricted ML estimation offers important advantages when samples are small and truncation points are high, so long as the true standard deviation is within roughly 0.5 cm of the chosen value.     

分子系统进化关系分析的一种新方法--贝叶斯法在硬蜱属中的应用

距离矩阵邻接法、最大简约法和最大似然法是重建生物系统关系的3种主要方法。普遍认为最大似然法在原理上优于前二种方法，但其计算复杂费时。由于现行计算机的能力尚达不到其要求而实用性差，特别是在处理大数据集样本(即大于25个分类单元)时，用此方法几乎不可能。新近提出的贝叶斯法(Bayesianmethod)既保留了最大似然法的基本原理，又引进了马尔科夫链的蒙特卡洛方法，并使计算时间大大缩短。本文用贝叶斯法对硬蜱属(Ixodes)19个种的线粒体16S rDNA片段进行了系统进化分析。从总体上看，分析结果与现有的基于形态学的分类体系基本吻合。但与现存的假说相反，莱姆病的主要宿主蓖籽硬蜱复合种组并非单系。通过比较贝叶斯法与其它三种方法的结果，我们认为贝叶斯法是一种系统进化分析的好方法，它既能根据分子进化的现有理论和各种模型用概率重建系统进化关系，又克服了最大似然法计算速度慢、不适用于大数据集样本的缺陷。贝叶斯法根据后验概率直观地表示系统进化关系的分析结果，不需要用自引导法进行检验。可以预料，贝叶斯法将会被广泛地应用到系统进化分析上[动物学报49(3)：380—388，2003]。     

Property and efficiency of the maximum likelihood method for molecular phylogeny

Summary The maximum likelihood (ML) method for constructing phylogenetic trees (both rooted and unrooted trees) from DNA sequence data was studied. Although there is some theoretical problem in the comparison of ML values conditional for each topology, it is possible to make a heuristic argument to justify the method. Based on this argument, a new algorithm for estimating the ML tree is presented. It is shown that under the assumption of a constant rate of evolution, the ML method and UPGMA always give the same rooted tree for the case of three operational taxonomic units (OTUs). This also seems to hold approximately for the case with four OTUs. When we consider unrooted trees with the assumption of a varying rate of nucleotide substitution, the efficiency of the ML method in obtaining the correct tree is similar to those of the maximum parsimony method and distance methods. The ML method was applied to Brown et al.'s data, and the tree topology obtained was the same as that found by the maximum parsimony method, but it was different from those obtained by distance methods.     

Application of Artificial Bee Colony Algorithm to Maximum Likelihood DOA Estimation

Maximum Likelihood (ML) method has an excellent performance for Direction-Of-Arrival (DOA) estimation, but a multidimensional nonlinear solution search is required which complicates the computation and prevents the method from practical use. To reduce the high computational burden of ML method and make it more suitable to engineering applications, we apply the Artificial Bee Colony (ABC) algorithm to maximize the likelihood function for DOA estimation. As a recently proposed bio-inspired computing algorithm, ABC algorithm is originally used to optimize multivariable functions by imitating the behavior of bee colony finding excellent nectar sources in the nature environment. It offers an excellent alternative to the conventional methods in ML-DOA estimation. The performance of ABC-based ML and other popular meta-heuristic-based ML methods for DOA estimation are compared for various scenarios of convergence, Signal-to-Noise Ratio (SNR), and number of iterations. The computation loads of ABC-based ML and the conventional ML methods for DOA estimation are also investigated. Simulation results demonstrate that the proposed ABC based method is more efficient in computation and statistical performance than other ML-based DOA estimation methods.     

A heuristic approach of maximum likelihood method for inferring phylogenetic tree and an application to the mammalian SOX-3 origin of the testis-determining gene SRY

Applying the tree bisection and reconnection (TBR) algorithm, we have developed a heuristic method (maximum likelihood (ML)-TBR) for inferring the ML tree based on tree topology search. For initial trees from which iterative processes start in ML-TBR, two cases were considered: one is 100 neighbor-joining (NJ) trees based on the bootstrap resampling and the other is 100 randomly generated trees. The same ML tree was obtained in both cases. All different iterative processes started from 100 independent initial trees ultimately converged on one optimum tree with the largest log-likelihood value, suggesting that a limited number of initial trees will be quite enough in ML-TBR. This also suggests that the optimum tree corresponds to the global optimum in tree topology space and thus probably coincides with the ML tree inferred by intact ML analysis. This method has been applied to the inference of phylogenetic tree of the SOX family members. The mammalian testis-determining gene SRY is believed to have evolved from SOX-3, a member of the SOX family, based on several lines of evidence, including their sequence similarity, the location of SOX-3 on the X chromosome and some aspects of their expression. This model should be supported directly from the phylogenetic tree of the SOX family, but no evidence has been provided to date. A recently published NJ tree shows implausibly remote origin of SRY, suggesting that a more sophisticated method is required for understanding this problem. The ML tree inferred by the present method showed that the SRYs of marsupial and placental mammals form a monophyletic cluster which had diverged from the mammalian SOX-3 in the early evolution of mammals.     

MAXIMUM-LIKELIHOOD APPROACHES APPLIED TO QUANTITATIVE GENETICS OF NATURAL POPULATIONS

Growing interest in adaptive evolution in natural populations has spurred efforts to infer genetic components of variance and covariance of quantitative characters. Here, I review difficulties inherent in the usual least-squares methods of estimation. A useful alternative approach is that of maximum likelihood (ML). Its particular advantage over least squares is that estimation and testing procedures are well defined, regardless of the design of the data. A modified version of ML, REML, eliminates the bias of ML estimates of variance components. Expressions for the expected bias and variance of estimates obtained from balanced, fully hierarchical designs are presented for ML and REML. Analyses of data simulated from balanced, hierarchical designs reveal differences in the properties of ML, REML, and F-ratio tests of significance. A second simulation study compares properties of REML estimates obtained from a balanced, fully hierarchical design (within-generation analysis) with those from a sampling design including phenotypic data on parents and multiple progeny. It also illustrates the effects of imposing nonnegativity constraints on the estimates. Finally, it reveals that predictions of the behavior of significance tests based on asymptotic theory are not accurate when sample size is small and that constraining the estimates seriously affects properties of the tests. Because of their great flexibility, likelihood methods can serve as a useful tool for estimation of quantitative-genetic parameters in natural populations. Difficulties involved in hypothesis testing remain to be solved.     

Methods for Fitting the Right-Truncated Weibull Distribution to Life-Test and Survival Data

This paper develops mathematical and computational methods for fitting, by the method of maximum likelihood (ML), the two-parameter, right-truncated Weibull distribution (RTWD) to life-test or survival data. Some important statistical properties of the RTWD are derived and ML estimating equations for the scale and shape parameters of the RTWD are developed. The ML equations are used to express the scale parameter as an analytic function of the shape parameter and to establish a computationally useful lower bound on the ML estimate of the shape parameter. This bound is a function only of the sample observations and the (known) truncation point T. The ML equations are reducible to a single nonlinear, transcendental equation in the shape parameter, and a computationally efficient algorithm is described for solving this equation. The practical use of the methods is illustrated in two numerical examples.     

REML estimation of variance parameters in nonlinear mixed effects models using the SAEM algorithm

Nonlinear mixed effects models are now widely used in biometrical studies, especially in pharmacokinetic research or for the analysis of growth traits for agricultural and laboratory species. Most of these studies, however, are often based on ML estimation procedures, which are known to be biased downwards. A few REML extensions have been proposed, but only for approximated methods. The aim of this paper is to present a REML implementation for nonlinear mixed effects models within an exact estimation scheme, based on an integration of the fixed effects and a stochastic estimation procedure. This method was implemented via a stochastic EM, namely the SAEM algorithm. The simulation study showed that the proposed REML estimation procedure considerably reduced the bias observed with the ML estimation, as well as the residual mean squared error of the variance parameter estimations, especially in the unbalanced cases. ML and REML based estimators of fixed effects were also compared via simulation. Although the two kinds of estimates were very close in terms of bias and mean square error, predictions of individual profiles were clearly improved when using REML vs. ML. An application of this estimation procedure is presented for the modelling of growth in lines of chicken.     

AI applications to medical images: From machine learning to deep learning

PurposeArtificial intelligence (AI) models are playing an increasing role in biomedical research and healthcare services. This review focuses on challenges points to be clarified about how to develop AI applications as clinical decision support systems in the real-world context.MethodsA narrative review has been performed including a critical assessment of articles published between 1989 and 2021 that guided challenging sections.ResultsWe first illustrate the architectural characteristics of machine learning (ML)/radiomics and deep learning (DL) approaches. For ML/radiomics, the phases of feature selection and of training, validation, and testing are described. DL models are presented as multi-layered artificial/convolutional neural networks, allowing us to directly process images. The data curation section includes technical steps such as image labelling, image annotation (with segmentation as a crucial step in radiomics), data harmonization (enabling compensation for differences in imaging protocols that typically generate noise in non-AI imaging studies) and federated learning. Thereafter, we dedicate specific sections to: sample size calculation, considering multiple testing in AI approaches; procedures for data augmentation to work with limited and unbalanced datasets; and the interpretability of AI models (the so-called black box issue). Pros and cons for choosing ML versus DL to implement AI applications to medical imaging are finally presented in a synoptic way.ConclusionsBiomedicine and healthcare systems are one of the most important fields for AI applications and medical imaging is probably the most suitable and promising domain. Clarification of specific challenging points facilitates the development of such systems and their translation to clinical practice.     

A note on estimating crude odds ratios in case-control studies with differentially misclassified exposure

Morrissey and Spiegelman (1999, Biometrics 55, 338 344) provided a comparative study of adjustment methods for exposure misclassification in case-control studies equipped with an internal validation sample. In addition to the maximum likelihood (ML) approach, they considered two intuitive procedures based on proposals in the literature. Despite appealing ease of computation associated with the latter two methods, efficiency calculations suggested that ML was often to be recommended for the analyst with access to a numerical routine to facilitate it. Here, a reparameterization of the likelihood reveals that one of the intuitive approaches, the inverse matrix method, is in fact ML under differential misclassification. This correction is intended to alert readers to the existence of a simple closed-form ML estimator for the odds ratio in this setting so that they may avoid assuming that a commercially inaccessible optimization routine must be sought to implement ML.     

On the differences between maximum likelihood and regression interval mapping in the analysis of quantitative trait loci

The differences between maximum-likelihood (ML) and regression (REG) interval mapping in the analysis of quantitative trait loci (QTL) are investigated analytically and numerically by simulation. The analytical investigation is based on the comparison of the solution sets of the ML and REG methods in the estimation of QTL parameters. Their differences are found to relate to the similarity between the conditional posterior and conditional probabilities of QTL genotypes and depend on several factors, such as the proportion of variance explained by QTL, relative QTL position in an interval, interval size, difference between the sizes of QTL, epistasis, and linkage between QTL. The differences in mean squared error (MSE) of the estimates, likelihood-ratio test (LRT) statistics in testing parameters, and power of QTL detection between the two methods become larger as (1) the proportion of variance explained by QTL becomes higher, (2) the QTL locations are positioned toward the middle of intervals, (3) the QTL are located in wider marker intervals, (4) epistasis between QTL is stronger, (5) the difference between QTL effects becomes larger, and (6) the positions of QTL get closer in QTL mapping. The REG method is biased in the estimation of the proportion of variance explained by QTL, and it may have a serious problem in detecting closely linked QTL when compared to the ML method. In general, the differences between the two methods may be minor, but can be significant when QTL interact or are closely linked. The ML method tends to be more powerful and to give estimates with smaller MSEs and larger LRT statistics. This implies that ML interval mapping can be more accurate, precise, and powerful than REG interval mapping. The REG method is faster in computation, especially when the number of QTL considered in the model is large. Recognizing the factors affecting the differences between REG and ML interval mapping can help an efficient strategy, using both methods in QTL mapping to be outlined.     

Robustness of maximum likelihood tree estimation against different patterns of base substitutions

Summary In the maximum likelihood (ML) method for estimating a molecular phylogenetic tree, the pattern of nucleotide substitutions for computing likelihood values is assumed to be simpler than that of the actual evolutionary process, simply because the process, considered to be quite devious, is unknown. The problem, however, is that there has been no guarantee to endorse the simplification.To study this problem, we first evaluated the robustness of the ML method in the estimation of molecular trees against different nucleotide substitution patterns, including Jukes and Cantor's, the simplest ever proposed. Namely, we conducted computer simulations in which we could set up various evolutionary models of a hypothetical gene, and define a true tree to which an estimated tree by the ML method was to be compared. The results show that topology estimation by the ML method is considerably robust against different ratios of transitions to transversions and different GC contents, but branch length estimation is not so. The ML tree estimation based on Jukes and Cantor's model is also revealed to be resistant to GC content, but rather sensitive to the ratio of transitions to transversions.We then applied the ML method with different substitution patterns to nucleotide sequence data ontax gene from T-cell leukemia viruses whose evolutionary process must have been more complicated than that of the hypothetical gene. The results are in accordance with those from the simulation study, showing that Jukes and Cantor's model is as useful as a more complicated one for making inferences about molecular phylogeny of the viruses.     

Parsimony, likelihood, and the role of models in molecular phylogenetics

Methods such as maximum parsimony (MP) are frequently criticized as being statistically unsound and not being based on any "model." On the other hand, advocates of MP claim that maximum likelihood (ML) has some fundamental problems. Here, we explore the connection between the different versions of MP and ML methods, particularly in light of recent theoretical results. We describe links between the two methods--for example, we describe how MP can be regarded as an ML method when there is no common mechanism between sites (such as might occur with morphological data and certain forms of molecular data). In the process, we clarify certain historical points of disagreement between proponents of the two methodologies, including a discussion of several forms of the ML optimality criterion. We also describe some additional results that shed light on how much needs to be assumed about underlying models of sequence evolution in order to successfully reconstruct evolutionary trees.     

Machine learning approach for automatic recognition of tomato-pollinating bees based on their buzzing-sounds

Bee-mediated pollination greatly increases the size and weight of tomato fruits. Therefore, distinguishing between the local set of bees–those that are efficient pollinators–is essential to improve the economic returns for farmers. To achieve this, it is important to know the identity of the visiting bees. Nevertheless, the traditional taxonomic identification of bees is not an easy task, requiring the participation of experts and the use of specialized equipment. Due to these limitations, the development and implementation of new technologies for the automatic recognition of bees become relevant. Hence, we aim to verify the capacity of Machine Learning (ML) algorithms in recognizing the taxonomic identity of visiting bees to tomato flowers based on the characteristics of their buzzing sounds. We compared the performance of the ML algorithms combined with the Mel Frequency Cepstral Coefficients (MFCC) and with classifications based solely on the fundamental frequency, leading to a direct comparison between the two approaches. In fact, some classifiers powered by the MFCC–especially the SVM–achieved better performance compared to the randomized and sound frequency-based trials. Moreover, the buzzing sounds produced during sonication were more relevant for the taxonomic recognition of bee species than analysis based on flight sounds alone. On the other hand, the ML classifiers performed better in recognizing bees genera based on flight sounds. Despite that, the maximum accuracy obtained here (73.39% by SVM) is still low compared to ML standards. Further studies analyzing larger recording samples, and applying unsupervised learning systems may yield better classification performance. Therefore, ML techniques could be used to automate the taxonomic recognition of flower-visiting bees of the cultivated tomato and other buzz-pollinated crops. This would be an interesting option for farmers and other professionals who have no experience in bee taxonomy but are interested in improving crop yields by increasing pollination.     

Stochastic search strategy for estimation of maximum likelihood phylogenetic trees

The maximum likelihood (ML) method of phylogenetic tree construction is not as widely used as other tree construction methods (e.g., parsimony, neighbor-joining) because of the prohibitive amount of time required to find the ML tree when the number of sequences under consideration is large. To overcome this difficulty, we propose a stochastic search strategy for estimation of the ML tree that is based on a simulated annealing algorithm. The algorithm works by moving through tree space by way of a "local rearrangement" strategy so that topologies that improve the likelihood are always accepted, whereas those that decrease the likelihood are accepted with a probability that is related to the proportionate decrease in likelihood. Besides greatly reducing the time required to estimate the ML tree, the stochastic search strategy is less likely to become trapped in local optima than are existing algorithms for ML tree estimation. We demonstrate the success of the modified simulated annealing algorithm by comparing it with two existing algorithms (Swofford's PAUP* and Felsenstein's DNAMLK) for several theoretical and real data examples.     

A Note on Estimating Crude Odds Ratios in Case–Control Studies with Differentially Misclassified Exposure

Summary. Morrissey and Spiegelman (1999, Biometrics 55 , 338–344) provided a comparative study of adjustment methods for exposure misclassification in case‐control studies equipped with an internal validation sample. In addition to the maximum likelihood (ML) approach, they considered two intuitive procedures based on proposals in the literature. Despite appealing ease of computation associated with the latter two methods, efficiency calculations suggested that ML was often to be recommended for the analyst with access to a numerical routine to facilitate it. Here, a reparameterization of the likelihood reveals that one of the intuitive approaches, the inverse matrix method, is in fact ML under differential misclassification. This correction is intended to alert readers to the existence of a simple closed‐form ML estimator for the odds ratio in this setting so that they may avoid assuming that a commercially inaccessible optimization routine must be sought to implement ML.     

Assessment of fish communities using environmental DNA: Effect of spatial sampling design in lentic systems of different sizes

Freshwater fish biodiversity is quickly decreasing and requires effective monitoring and conservation. Environmental DNA (eDNA)‐based methods have been shown to be highly sensitive and cost‐efficient for aquatic biodiversity surveys, but few studies have systematically investigated how spatial sampling design affects eDNA‐detected fish communities across lentic systems of different sizes. We compared the spatial patterns of fish diversity determined using eDNA in three lakes of small (SL; 3 ha), medium (ML; 122 ha) and large (LL; 4,343 ha) size using a spatially explicit grid sampling method. A total of 100 water samples (including nine, 17 and 18 shoreline samples and six, 14 and 36 interior samples from SL, ML and LL, respectively) were collected, and fish communities were analysed using eDNA metabarcoding of the mitochondrial 12S region. Together, 30, 35 and 41 fish taxa were detected in samples from SL, ML, and LL, respectively. We observed that eDNA from shoreline samples effectively captured the majority of the fish diversity of entire waterbodies, and pooled samples recovered fewer species than individually processed samples. Significant spatial autocorrelations between fish communities within 250 m and 2 km of each other were detected in ML and LL, respectively. Additionally, the relative sequence abundances of many fish species exhibited spatial distribution patterns that correlated with their typical habitat occupation. Overall, our results support the validity of a shoreline sampling strategy for eDNA‐based fish community surveys in lentic systems but also suggest that a spatially comprehensive sampling design can reveal finer distribution patterns of individual species.