Maximum Likelihood Estimation of Genetic Parameters in Cell Populations

In this paper we consider a cell population such as bacteria consisting of two types of cells, mutant and nonmutant. Under the mutation and homogeneous pure birth processes, this paper derives a maximum likelihood estimation procedure for estimating mutation rate and birth rate. The method is applied to Newcombe's data; further some Monte Carlo studies are generated. The numerical results indicate that the method is quite efficient for estimating genetic parameters in cell populations.     

Maximum Likelihood Estimation of Genetic Parameters for Quantitative traits from Autotetraploid Self-Fertilized Populations

Assuming equality of genotypic effects over different loci, this paper provides an ML procedure for estimating genetic parameters for quantitative traits from autotetraploid self-fertilized populations. The results are illustrated by computer generated data involving P₁, P₂, F₂, B₁ and B₂ populations.     

Maximum Likelihood Estimation of the Mortality Rate Function

Maximum likelihood estimator is obtained for the mortality rate function of a specific type appearing in survival data analysis. Strict consistency of this estimator is proved.     

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.     

Maximum Likelihood Analysis of Population Differences in Allelic Frequencies

Statistical techniques are presented for the analysis of geographic variation in allelic frequencies. Likelihood ratio test criteria are derived from a multinominal sampling distribution, and are used to answer three questions. (1) Are there geographic differences in allelic frequencies? (2) Are population differences in allelic frequencies associated with environmental differences? (3) Is there any residual "lack of fit" variation among populations, after accounting for that variation associated with environmental differences? The two- and three-allele cases are explicitly treated, and the extension to more alleles is indicated.     

Employing a Monte Carlo Algorithm in Newton-Type Methods for Restricted Maximum Likelihood Estimation of Genetic Parameters

Estimation of variance components by Monte Carlo (MC) expectation maximization (EM) restricted maximum likelihood (REML) is computationally efficient for large data sets and complex linear mixed effects models. However, efficiency may be lost due to the need for a large number of iterations of the EM algorithm. To decrease the computing time we explored the use of faster converging Newton-type algorithms within MC REML implementations. The implemented algorithms were: MC Newton-Raphson (NR), where the information matrix was generated via sampling; MC average information(AI), where the information was computed as an average of observed and expected information; and MC Broyden''s method, where the zero of the gradient was searched using a quasi-Newton-type algorithm. Performance of these algorithms was evaluated using simulated data. The final estimates were in good agreement with corresponding analytical ones. MC NR REML and MC AI REML enhanced convergence compared to MC EM REML and gave standard errors for the estimates as a by-product. MC NR REML required a larger number of MC samples, while each MC AI REML iteration demanded extra solving of mixed model equations by the number of parameters to be estimated. MC Broyden''s method required the largest number of MC samples with our small data and did not give standard errors for the parameters directly. We studied the performance of three different convergence criteria for the MC AI REML algorithm. Our results indicate the importance of defining a suitable convergence criterion and critical value in order to obtain an efficient Newton-type method utilizing a MC algorithm. Overall, use of a MC algorithm with Newton-type methods proved feasible and the results encourage testing of these methods with different kinds of large-scale problem settings.     

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.     

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     

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.     

Methodology and Accuracy of Estimation of Quantitative Trait Loci Parameters in a Half-Sib Design Using Maximum Likelihood

Maximum likelihood methods were developed for estimation of the six parameters relating to a marker-linked quantitative trait locus (QTL) segregating in a half-sib design, namely the QTL additive effect, the QTL dominance effect, the population mean, recombination between the marker and the QTL, the population frequency of the QTL alleles, and the within-family residual variance. The method was tested on simulated stochastic data with various family structures under two genetic models. A method for predicting the expected value of the likelihood was also derived and used to predict the lower bound sampling errors of the parameter estimates and the correlations between them. It was found that standard errors and confidence intervals were smallest for the population mean and variance, intermediate for QTL effects and allele frequency, and highest for recombination rate. Correlations among standard errors of the parameter estimates were generally low except for a strong negative correlation (r = -0.9) between the QTL's dominance effect and the population mean, and medium positive and negative correlations between the QTL's additive effect and, respectively, recombination rate (r = 0.5) and residual variance (r = -0.6). The implications for experimental design and method of analysis on power and accuracy of marker-QTL linkage experiments were discussed.     

Conditional Maximum Likelihood Estimation Following a Group Sequential Test

We consider estimation after a group sequential test. An estimator that is unbiased or has small bias may have substantial conditional bias (Troendle and Yu, 1999, Coburger and Wassmer, 2001). In this paper we derive the conditional maximum likelihood estimators of both the primary parameter and a secondary parameter, and investigate their properties within a conditional inference framework. The method applies to both the usual and adaptive group sequential test designs. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

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 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.     

2-D Impulse Noise Suppression by Recursive Gaussian Maximum Likelihood Estimation

An effective approach termed Recursive Gaussian Maximum Likelihood Estimation (RGMLE) is developed in this paper to suppress 2-D impulse noise. And two algorithms termed RGMLE-C and RGMLE-CS are derived by using spatially-adaptive variances, which are respectively estimated based on certainty and joint certainty & similarity information. To give reliable implementation of RGMLE-C and RGMLE-CS algorithms, a novel recursion stopping strategy is proposed by evaluating the estimation error of uncorrupted pixels. Numerical experiments on different noise densities show that the proposed two algorithms can lead to significantly better results than some typical median type filters. Efficient implementation is also realized via GPU (Graphic Processing Unit)-based parallelization techniques.     

A Maximum Likelihood Estimator for Shape Parameters of S‐Distributions

The S‐distribution is a four‐parameter distribution that is defined in terms of a differential equation, in which the cumulative is represented as the dependent variable: The article proposes a maximum likelihood estimator for the shape parameters of this distribution.