H广义线性模型中的参数估计的比较

本文研究H广义线性模型中未知参数的两种估计方法,一种是边际似然函数法,另一种是Lee和Nelder提出来的L-N法．对于一类具有两个随机效应的典型的Poisson-Gamma类模型,在一些正则性条件之下,我们已经证明了其中固定效应卢的L-N估计的强相合性及渐近正态性,并得到了其收敛于真值的速度．针对这类模型,本文进一步给出了其边际似然函数的解析表达式,并且通过Monte Carlo模拟,对模型中固定效应β的边际似然估计和L—N估计进行了比较,模拟表明L—N估计比边际似然估计在拟Poisson-Gamma模型中有着更加优良的表现,具有更高的精度。     

刀切法估计动物种群扩散型指数

一、引言研究动物种群空间格局,无论在生态学理论还是应用上都具有重要意义。用扩散型指数研究种群空间格局不受格局类型的限制,能反映空间格局的连续统(Continuum).长期以来,对扩散型指数的数值估计,大多采用矩法或最大似然法,由于扩散型指数的统计分布一般都比较复杂,而非正态,因而用建立在正态分布基础上的矩估计或最大似然估     

赤拟谷盗模拟种公畜选择──常规与改进方法的比较

本实验用实验昆虫赤拟谷盗两个世代各３０个家系的８５９和７２６只蛹的２３日龄蛹长和蛹宽作为选择性状模拟种公畜选择,对常规方法和改进方法进行比较。以Ｈｅｎｄｅｒｓｏｎ方法Ⅲ和综合指数作为常规方法,用约束最大似然法（ＲＥＭＬ）和ＢＬＵＰ估计方差组分和育种值为改进方法。结果表明,常规法估计遗传参数在两世代中不稳定,而改进方法弥补此缺点。对两世代个体和家系育种值排队,结果表明两种方法在前几名无差别,说明在选择强度大（留种率低）时,两种方法效果基本一致。     

最大似然法及其应用

最大似然法是参数估计的一种重要方法。 在遗传学研究中,广泛地应用于计数资料的总 体成数估计。由于估计值以满足在观察结果中 的出现概率最大为条件,故又称最大似然估计。     

利用最大似然法进行水稻产量性状基因的分子作图

本研究根据对估计标记－数量性状基因座位（ＱＴＬ）之间重组率的两种分析方法（矩量法和最大似然法）、两种方差模型（ＱＴＬ基因型之间的方差同质和异质模型）的分析,揭示了ＬＯＤ值在标记－ＱＴＬ连锁检测上所得结果的相关性高于重组率估计值的相关性。采用最大似然法和异质方差模型,估计了水稻产量构成有关的ＱＴＬ与分布于１１对染色体上的５１个限制性片段长度多态性（ＲＦＬＰ）标记之间的重组率,并对似然比（以ＬＯＤ值表示）进行Ｘ￣２检验,发现７个存在显著连锁关系的标记－性状组合,其平均重组率为１０．０％。这些标记分布于第１、５、６、８和１１等５对染色体上,涉及７个ＲＦＬＰ标记和３个产量构成性状,即每穗颖花数（ＲＧ５７３、ＲＺ６１７、ＲＧ１０３）、单株穗数（ＲＧ６４Ｂ）和每穗实粒数（ＲＧ１０１、ＲＧ２４４、ＲＧ６５３）。     

三点自交法和两点最大似然法构建水稻F2群体分子标记连锁图谱的比较

根据连锁遗传的原理,列出了三点自交法和两点自交最大似然(ML)法估算显性标记遗传距离的具体步骤和算法,将水稻F2群体含香味基因Aro及其连锁的RFLP数据转变为显性标记数据后,用上述两种方法构建的连锁图谱与用MAPMAKER软件计算共显性数据得到的图谱排序相同、标记间距离相近．但是标记数据存在较大程度偏分离时,由三点自交法构建的图谱中标记间图距有增大趋势．作者为提高作图精确性,简化计算过程,讨论了三点自交法对估算重组值的影响及其在分子标记作图中的应用价值,并建议将共显性标记转变为显性标记时进行两次自交ML法估算。     

与偏分离位点连锁的QTL作图的统计方法

提出了一种统计方法,可以估计与偏分离位点连锁的QTL的位置和效应。该方法利用回交群体中呈现偏分离的分子标记,首先用最大似然法对偏分离位点与标记位点之间的重组率和配子存活率进行估计,然后用区间作图法估计加性-显性模型下QTL的位置和效应参数。该方法可用于对常规作图研究中表现偏分离的标记进行分析,以帮助我们发现新的偏分离基因（或不育基因）和数量性状位点。     

一个适于最大似然法估计物种分化年代的进化速率平滑近似方法

众所周知 ,物种分化年代的估计对分子钟 (进化速率恒定 )假定很敏感。另一方面 ,在远缘物种 (例如哺乳纲不同目的动物 )的比较中 ,分子钟几乎总是不成立的。这样在估计分化时间时考虑不同进化区系的速率差异至为重要。最大似然法可以很自然地考虑这种速率差异 ,并且可以同时分析多个基因位点的资料以及同时利用多重化石校正数据。以前提出的似然法需要研究者将进化树的树枝按速率分组 ,本文提出一个近似方法以使这个过程自动化。本方法综合了以前的似然法、贝斯法及近似速率平滑法的一些特征。此外 ,还对算法加以改进 ,以适应综合数据分析时某些基因在某些物种中缺乏资料的情形。应用新提出的方法来分析马达加斯加的倭狐猴的分化年代 ,并与以前的似然法及贝斯法的分析进行了比较     

以雾灵山夜蛾科为材料评估进化模型对DNA条码分类的影响

为了探究进化模型对DNA条形码分类的影响, 本研究以雾灵山夜蛾科44个种的标本为材料, 获得COI基因序列。使用邻接法（neighbor-joining）、 最大简约法（maximum parsimony）、 最大似然法（maximum likelihood）以及贝叶斯法（Bayesian inference）构建系统发育树, 并且对邻接法的12种模型、 最大似然法的7种模型、 贝叶斯法的2种模型进行模型成功率的评估。结果表明, 邻接法的12种模型成功率相差不大, 较稳定; 最大似然法及贝叶斯法的不同模型成功率存在明显差异, 不稳定; 最大简约法不基于模型, 成功率比较稳定。邻接法及最大似然法共有6种相同的模型, 这6种模型在不同的方法中成功率存在差异。此外, 分子数据中存在单个物种仅有一条序列的情况, 显著降低了模型成功率, 表明在DNA条形码研究中, 每个物种需要有多个样本。     

赤拟合盗模拟种公畜选择—常规与改进方法的比较

本实验用实验昆虫赤拟谷盗两个世代各３０个家系的８５９和７２６只桶的２３日龄蛹长和肾宽作为选择性状模拟种公畜选择,对常规方法和改进方法进行比较。以Ｈｅｎｄｅｒｓｏｎ方法ＩＩＩ和综合指数作为常规方法,用约束最大似然法和ＢＬＵＰ估计方差组分和育种值为改进方法。结果表明,常规法估计遗传参数在两世代中不稳定,而改进方法弥补此缺点,对两世代个体和家系育种值排队,结果表明两种方法在前几名无差别,说明在选择强度大     

Joint modeling of survival and longitudinal data: likelihood approach revisited

The maximum likelihood approach to jointly model the survival time and its longitudinal covariates has been successful to model both processes in longitudinal studies. Random effects in the longitudinal process are often used to model the survival times through a proportional hazards model, and this invokes an EM algorithm to search for the maximum likelihood estimates (MLEs). Several intriguing issues are examined here, including the robustness of the MLEs against departure from the normal random effects assumption, and difficulties with the profile likelihood approach to provide reliable estimates for the standard error of the MLEs. We provide insights into the robustness property and suggest to overcome the difficulty of reliable estimates for the standard errors by using bootstrap procedures. Numerical studies and data analysis illustrate our points.     

Comparing analysis methods for mutation-accumulation data: a simulation study

We simulated single-generation data for a fitness trait in mutation-accumulation (MA) experiments, and we compared three methods of analysis. Bateman-Mukai (BM) and maximum likelihood (ML) need information on both the MA lines and control lines, while minimum distance (MD) can be applied with or without the control. Both MD and ML assume gamma-distributed mutational effects. ML estimates of the rate of deleterious mutation had larger mean square error (MSE) than MD or BM had due to large outliers. MD estimates obtained by ignoring the mean decline observed from comparison to a control are often better than those obtained using that information. When effects are simulated using the gamma distribution, reducing the precision with which the trait is assayed increases the probability of obtaining no ML or MD estimates but causes no appreciable increase of the MSE. When the residual errors for the means of the simulated lines are sampled from the empirical distribution in a MA experiment, instead of from a normal one, the MSEs of BM, ML, and MD are practically unaffected. When the simulated gamma distribution accounts for a high rate of mild deleterious mutation, BM detects only approximately 30% of the true deleterious mutation rate, while MD or ML detects substantially larger fractions. To test the robustness of the methods, we also added a high rate of common contaminant mutations with constant mild deleterious effect to a low rate of mutations with gamma-distributed deleterious effects and moderate average. In that case, BM detects roughly the same fraction as before, regardless of the precision of the assay, while ML fails to provide estimates. However, MD estimates are obtained by ignoring the control information, detecting approximately 70% of the total mutation rate when the mean of the lines is assayed with good precision, but only 15% for low-precision assays. Contaminant mutations with only tiny deleterious effects could not be detected with acceptable accuracy by any of the above methods.     

Numerical non-identifiability regions of the minimal model of glucose kinetics: superiority of Bayesian estimation

The so-called minimal model (MM) of glucose kinetics is widely employed to estimate insulin sensitivity (S(I)) both in clinical and epidemiological studies. Usually, MM is numerically identified by resorting to Fisherian parameter estimation techniques, such as maximum likelihood (ML). However, unsatisfactory parameter estimates are sometimes obtained, e.g. S(I) estimates virtually zero or unrealistically high and affected by very large uncertainty, making the practical use of MM difficult. The first result of this paper concerns the mathematical demonstration that these estimation difficulties are inherent to MM structure which can expose S(I) estimation to the risk of numerical non-identifiability. The second result is based on simulation studies and shows that Bayesian parameter estimation techniques are less sensitive, in terms of both accuracy and precision, than the Fisherian ones with respect to these difficulties. In conclusion, Bayesian parameter estimation can successfully deal with difficulties of MM identification inherently due to its structure.     

Bayesian Modeling of Age-Specific Survival in Nesting Studies Under Dirichlet Priors

There has been much work done in nest survival analysis using the maximum likelihood (ML) method. The ML method suffers from the instability of numerical calculations when models having a large number of unknown parameters are used. A Bayesian approach of model fitting is developed to estimate age-specific survival rates for nesting studies using a large class of prior distributions. The computation is done by Gibbs sampling. Some latent variables are introduced to simplify the full conditional distributions. The method is illustrated using both a real and a simulated data set. Results indicate that Bayesian analysis provides stable and accurate estimates of nest survival rates.     

Comparison of Bayesian and maximum-likelihood inference of population genetic parameters

Comparison of the performance and accuracy of different inference methods, such as maximum likelihood (ML) and Bayesian inference, is difficult because the inference methods are implemented in different programs, often written by different authors. Both methods were implemented in the program MIGRATE, that estimates population genetic parameters, such as population sizes and migration rates, using coalescence theory. Both inference methods use the same Markov chain Monte Carlo algorithm and differ from each other in only two aspects: parameter proposal distribution and maximization of the likelihood function. Using simulated datasets, the Bayesian method generally fares better than the ML approach in accuracy and coverage, although for some values the two approaches are equal in performance. MOTIVATION: The Markov chain Monte Carlo-based ML framework can fail on sparse data and can deliver non-conservative support intervals. A Bayesian framework with appropriate prior distribution is able to remedy some of these problems. RESULTS: The program MIGRATE was extended to allow not only for ML(-) maximum likelihood estimation of population genetics parameters but also for using a Bayesian framework. Comparisons between the Bayesian approach and the ML approach are facilitated because both modes estimate the same parameters under the same population model and assumptions.     

Multigeneration maximum-likelihood analysis applied to mutation-accumulation experiments in Caenorhabditis elegans

We develop a maximum-likelihood (ML) approach to estimate genomic mutation rates (U) and average homozygous mutation effects (s) from mutation-accumulation (MA) experiments in which phenotypic assays are carried out in several generations. We use simulations to compare the procedure's performance with the method of moments traditionally used to analyze MA data. Similar precision is obtained if mutation effects are small relative to the environmental standard deviation, but ML can give estimates of mutation parameters that have lower sampling variances than those obtained by the method of moments if mutations with large effects have accumulated. The inclusion of data from intermediate generations may improve the precision. We analyze life-history trait data from two Caenorhabditis elegans MA experiments. Under a model with equal mutation effects, the two experiments provide similar estimates for U of approximately 0.005 per haploid, averaged over traits. Estimates of s are more divergent and average at -0.51 and -0.13 in the two studies. Detailed analysis shows that changes of mean and variance of genetic values of MA lines in both C. elegans experiments are dominated by mutations with large effects, but the analysis does not rule out the presence of a large class of deleterious mutations with very small effects.     

A bias in ML estimates of branch lengths in the presence of multiple signals

Sequence data often have competing signals that are detected by network programs or Lento plots. Such data can be formed by generating sequences on more than one tree, and combining the results, a mixture model. We report that with such mixture models, the estimates of edge (branch) lengths from maximum likelihood (ML) methods that assume a single tree are biased. Based on the observed number of competing signals in real data, such a bias of ML is expected to occur frequently. Because network methods can recover competing signals more accurately, there is a need for ML methods allowing a network. A fundamental problem is that mixture models can have more parameters than can be recovered from the data, so that some mixtures are not, in principle, identifiable. We recommend that network programs be incorporated into best practice analysis, along with ML and Bayesian trees.     

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.     

Estimation of evolutionary parameters with phylogenetic trees

An important issue in the phylogenetic analysis of nucleotide sequence data using the maximum likelihood (ML) method is the underlying evolutionary model employed. We consider the problem of simultaneously estimating the tree topology and the parameters in the underlying substitution model and of obtaining estimates of the standard errors of these parameter estimates. Given a fixed tree topology and corresponding set of branch lengths, the ML estimates of standard evolutionary model parameters are asymptotically efficient, in the sense that their joint distribution is asymptotically normal with the variance–covariance matrix given by the inverse of the Fisher information matrix. We propose a new estimate of this conditional variance based on estimation of the expected information using a Monte Carlo sampling (MCS) method. Simulations are used to compare this conditional variance estimate to the standard technique of using the observed information under a variety of experimental conditions. In the case in which one wishes to estimate simultaneously the tree and parameters, we provide a bootstrapping approach that can be used in conjunction with the MCS method to estimate the unconditional standard error. The methods developed are applied to a real data set consisting of 30 papillomavirus sequences. This overall method is easily incorporated into standard bootstrapping procedures to allow for proper variance estimation.     

GCHap: fast MLEs for haplotype frequencies by gene counting

GCHap quickly finds maximum likelihood estimates (MLEs) of frequencies of haplotypes given genotype information on a random sample of individuals. It uses the gene counting method but by excluding haplotypes with zero MLE at an early stage, this implementation uses many orders of magnitude less space and time than naive implementations. A second program, ApproxGCHap, is provided to give alternate estimates for data sets with large numbers of loci or large amounts of missing genotypes. AVAILABILITY: The Java classes and Javadocs pages for GCHap can be obtained from bioinformatics.med.utah.edu/~alun