Maximum Likelihood Estimation of Exponential Polynomial Rate for Poisson Data

The heterogeneous Poisson process with discretized exponential quadratic rate function is considered. Maximum likelihood estimates of the parameters of the rate function are derived for the case when the data consists of numbers of occurrences in consecutive equal time periods. A likelihood ratio test of the null hypothesis of exponential quadratic rate is presented. Its power against exponential linear rate functions is estimated using Monte Carlo simulation. The maximum likelihood method is compared with a log-linear least squares techniques. An application of the technique to the analysis of mortality rates due to congenital malformations is presented.     

Sparse Sampling and Maximum Likelihood Estimation for Boolean Models

A condition for practical independence of contact distribution functions in Boolean models is obtained. This result allows the authors to use maximum likelihcod methods, via sparse sampling, for estimating unknown parameters of an isotropic Boolean model. The second part of this paper is devoted to a simulation study of the proposed method. AMS classification: 60D05     

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.     

A Note on Maximum Likelihood Ratio Test of No Outliers in Regression Models

A derivation of the maximum likelihood ratio test for testing no outliers in regression models is given using the method of WETHERILL (1981, pp. 106–107) for estimating the regression parameters. This method is essentially similar to the one outlined in BARNETT and LEWIS (1978, p. 263), although by our detailed derivation it is easier to see that the maximum likelihood estimate of θ of model (3) under the hypothesis that the i^th observation in an outlier is the same as that obtained from model (1) when the i^th observation is removed.     

Boolean Models: Maximum Likelihood Estimation from Circular Clumps

This paper deals with the problem of making inferences on the maximum radius and the intensity of the Poisson point process associated to a Boolean Model of circular primary grains with uniformly distributed random radii. The only sample information used is observed radii of circular clumps (DUPAC, 1980). The behaviour of maximum likelihood estimation has been evaluated by means of Monte Carlo methods.     

The Planning of Sample Sizes for Maximum Likelihood Estimation of the Parameters of the Weibull Distribution

Based on maximum likelihood estimators the problem of setting confidence limits for the scale and shape parameters of the Weibull distribution with two parameters is considered. Approximation formulae for the determination of sample sizes for the parameter estimation are given for complete and type II censored samples.     

Fitting Regression Models to Ordinal Data

This paper deals with the analysis of ordinal data by means of a threshold model. Maximum likelihood estimation is discussed and two examples are used to illustrate the methods.     

Maximum Likelihood Estimation of Simultaneous Pairwise Linear Structural Relationships

The problem of assessing the relative calibrations and relative accuracies of a set of p instruments, each designed to measure the same characteristic on a common group of individuals is considered by using the EM algorithm. As shown, the EM algorithm provides a general solution for this problem. Its implementation is simple and in its most general form requires no extra iterative procedures within the M step. One important feature of the algorithm in this set up is that the error variance estimates are always positive. Thus, it can be seen as a kind of restricted maximization procedure. The expected information matrix for the maximum likelihood estimators is derived, upon which the large sample estimated covariance matrix for the maximum likelihood estimators can be computed. The problem of testing hypothesis about the calibration lines can be approached by using the Wald statistics. The approach is illustrated by re-analysing two data sets in the literature.     

非线性再生散度随机效应模型的极大似然估计及随机逼近算法

非线性再生散度随机效应模型包括了非线性随机效应模型和指数族非线性随机效应模型等．通过视模型中的随机效应为假想的缺失数据和应用Metropolis-Hastings(简称MH) 算法,提出了模型参数极大似然估计的随机逼近算法．模拟研究和实例分析表明了该算法的可行性．     

A Comment on Maximum Likelihood Estimation for Finite Mixtures of Distributions

Iterative numerical methods are necessary to find the maximum likelihood estimates for finite mixture distributions. This paper shows that it will often be possible to analytically reduce the number of equations that must ultimately be solved numerically. Such a reduction in dimensionality has not generally been used, or sought after, for mixture distributions. Yet such results are easily derived when each mixture component is assumed to be from the same parametric model within the exponential family.     

A Life Table Regression Analysis for Complex Survey Data

A methodology for obtaining maximum likelihood estimates of life table regression coefficients from complex survey data is presented. Certain of the issues of writing a likelihood for survey data are presented and discussed. The proposed methodology includes consideration of the sampling design in any inference by using design based variance estimates for the parameters. An example is given using data from the 1973 United States National Survey of Family Growth.     

A Rapid and Efficient Estimation Procedure for the Negative Binomial Distribution

This paper presents a new noniterative procedure for estimating the parameters of a negative binomial distribution. The procedure uses the first moment equation and an equation based on the weighted sample mean, with weights ω_x∝ α^z. The selection of a value for α is examined. A simulation study has been carried out and also the method has been applied to the 35 data sets analysed by Martin and Katti (1965, Biometrics) in order to compare it with the method of moments and with the method of maximum likelihood (ML). We conclude that the new procedure has greater relative efficiency than the method of moments; it gives estimates which are consistently close to ML and are easy to calculate.     

非线性再生散度随机效应模型的极大似然估计及EM算法

非线性再生散度随机效应模型是指数族非线性随机效应模型和非线性再生散度模型的推广和发展．通过视模型中的随机效应为假想的缺失数据和应用Metropolis-Hastings（MH）算法,提出了模型参数极大似然估计的Monte-Carlo EM（MCEM）算法,并用模拟研究和实例分析说明了该算法的可行性．     

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.     

Phylogenetic Reconstruction of a Known HIV-1 CRF04_cpx Transmission Network Using Maximum Likelihood and Bayesian Methods

The CRF04_cpx strains of HIV-1 accounts for approximately 2–10% of the infected population in Greece, across different transmission risk groups. CRF04_cpx was the lineage documented in an HIV-1 transmission network in Thessalonica, northern Greece. Most of the transmissions occurred through unprotected heterosexual contacts between 1989 and 1993. Blood samples were available for six patients, obtained 6–10 years later, except for one patient sampled in 1991. Our objective was to examine whether the transmission history is compatible with the evolutionary tree of the virus, in partial gag, partial env, and partial gag+env. The inferred phylogenetic tree obtained using maximum likelihood and Bayesian methods in partial gag+env was much closer to the transmission tree than that using either env or gag separately. Our findings suggest that the epidemiological relationships among patients who have been infected by a common source correspond almost exactly to the evolutionary trees of the virus, given that enough phylogenetic signal is present in the alignment. Moreover, we found evidence that recombination is not the most parsimonious explanation for the phylogenetic incongruence between gag and env. For patients with known infection dates, the estimated dates of the coalescent events obtained using molecular clock calculations based on a newly developed Bayesian method in gag + env were in agreement with the actual infection dates.This article contains online supplementary material.Reviewing Editor: Dr. Lauren Ancel-MeyersIsolated sequences from patients belonging to the CRF04_cpx transmission network always correspond to partially characterized gag, env, and gag+env genomic regions.