A nonparametrie maximum likelihood estimator for incomplete renewal data

The problem of estimating the lifetime distribution based ondata from independently and identically distributed stationaryrenewal processes is addressed. The data are incomplete. A nonparametricmaximum likelihood estimate of the Lifetime distribution isderived using the em algorithm. The missing information principleis used to estimate the standard error of the estimated distribution.The methodology is applied to a problem in the nursing professionwhere nurses withdraw from active service for a period of timebefore returning to take up post at a later date. It is importantthat nurse manpower planners accurately predict this patternof return. The data analysed are from the Northern Ireland nursingprofession.     

Alternative implementations of Monte Carlo EM algorithms for likelihood inferences

Two methods of computing Monte Carlo estimators of variance components using restricted maximum likelihood via the expectation-maximisation algorithm are reviewed. A third approach is suggested and the performance of the methods is compared using simulated data.     

Estimating time to pregnancy from current durations in a cross-sectional sample

A new design for estimating the distribution of time to pregnancy is proposed and investigated. The design is based on recording current durations in a cross-sectional sample of women, leading to statistical problems similar to estimating renewal time distributions from backward recurrence times. Non-parametric estimation is studied in some detail and a parametric approach is indicated. The results are illustrated on Monte Carlo simulations and on data from a recent European collaborative study. The role and applicability of this approach is discussed.     

Mixture model for inferring susceptibility to mastitis in dairy cattle: a procedure for likelihood-based inference

A Gaussian mixture model with a finite number of components and correlated random effects is described. The ultimate objective is to model somatic cell count information in dairy cattle and to develop criteria for genetic selection against mastitis, an important udder disease. Parameter estimation is by maximum likelihood or by an extension of restricted maximum likelihood. A Monte Carlo expectation-maximization algorithm is used for this purpose. The expectation step is carried out using Gibbs sampling, whereas the maximization step is deterministic. Ranking rules based on the conditional probability of membership in a putative group of uninfected animals, given the somatic cell information, are discussed. Several extensions of the model are suggested.     

The gamma-frailty Poisson model for the nonparametric estimation of panel count data

In this article, we study nonparametric estimation of the mean function of a counting process with panel observations. We introduce the gamma frailty variable to account for the intracorrelation between the panel counts of the counting process and construct a maximum pseudo-likelihood estimate with the frailty variable. Three simulated examples are given to show that this estimation procedure, while preserving the robustness and simplicity of the computation, improves the efficiency of the nonparametric maximum pseudo-likelihood estimate studied in Wellner and Zhang (2000, Annals of Statistics 28, 779-814). A real example from a bladder tumor study is used to illustrate the method.     

Estimation of unbiased recombination values in the presence of misclassification of a trait using RFLP maps

The effect of misclassification of phenotypes of a trait on the estimation of recombination value was investigated. The effect was larger for closer linkage. If a locus is dominant and linked with the misclassfied trait locus in the repulsion phase, then the effect on the recombination value between the two loci is largest. A method for estimating the unbiased recombination value and the misclassification rate using maximum likelihood associated with an EM algorithm is also presented. This method was applied to a numerical example from rice genome data. It was concluded that the present method combined with the metric multi-dimensional scaling method is useful for the detection of misclassified markers and for the estimation of unbiased recombination values.     

Maximum likelihood and Bayesian methods for estimating the distribution of selective effects among classes of mutations using DNA polymorphism data

Maximum likelihood and Bayesian approaches are presented for analyzing hierarchical statistical models of natural selection operating on DNA polymorphism within a panmictic population. For analyzing Bayesian models, we present Markov chain Monte-Carlo (MCMC) methods for sampling from the joint posterior distribution of parameters. For frequentist analysis, an Expectation-Maximization (EM) algorithm is presented for finding the maximum likelihood estimate of the genome wide mean and variance in selection intensity among classes of mutations. The framework presented here provides an ideal setting for modeling mutations dispersed through the genome and, in particular, for the analysis of how natural selection operates on different classes of single nucleotide polymorphisms (SNPs).     

A continuous time version and a generalization of a Markov-recapture model for trapping experiments

Wileyto et al. [E.P. Wileyto, W.J. Ewens, M.A. Mullen, Markov-recapture population estimates: a tool for improving interpretation of trapping experiments, Ecology 75 (1994) 1109] propose a four-state discrete time Markov process, which describes the structure of a marking-capture experiment as a method of population estimation. They propose this method primarily for estimation of closed insect populations. Their method provides a mark-recapture estimate from a single trap observation by allowing subjects to mark themselves. The estimate of the unknown population size is based on the assumption of a closed population and a simple Markov model in which the rates of marking, capture, and recapture are assumed to be equal. Using the one step transition probability matrix of their model, we illustrate how to go from an embedded discrete time Markov process to a continuous time Markov process assuming exponentially distributed holding times. We also compute the transition probabilities after time t for the continuous time case and compare the limiting behavior of the continuous and discrete time processes. Finally, we generalize their model by relaxing the assumption of equal per capita rates for marking, capture, and recapture. Other questions about how their results change when using a continuous time Markov process are examined.     

Estimation of components of genetic variance and heritability for flowering time and yield in gerbera using Derivative-Free Restricted Maximum Likelihood (DFRML)

Summary Additive genetic components of variance and narrow-sense heritabilities were estimated for flowering time (FT) and cut-flower yield (Y) for six generations of the Davis Population of gerbera using Derivative-Free Restricted Maximum Likelihood (DFRML). Additive genetic variance accounted for 54% of the total variability for FT and 30% of the total variability for Y. The heritability of FT (0.54) agreed with previous ANOVA-based estimates. However, the heritability of Y (0.30) was substantially lower than estimates using ANOVA. The advantages of DFRML and its applications in the estimation of components of genetic variance and heritabilities of plant populations are discussed.     

Pike and salmon as sister taxa: Detailed intraclade resolution and divergence time estimation of Esociformes + Salmoniformes based on whole mitochondrial genome sequences

The increasing number of taxa and loci in molecular phylogenetic studies of basal euteleosts has brought stability in a controversial area. A key emerging aspect to these studies is a sister Esociformes (pike) and Salmoniformes (salmon) relationship. We evaluate mitochondrial genome support for a sister Esociformes and Salmoniformes hypothesis by surveying many potential outgroups for these taxa, employing multiple phylogenetic approaches, and utilizing a thorough sampling scheme. Secondly, we conduct a simultaneous divergence time estimation and phylogenetic inference in a Bayesian framework with fossil calibrations focusing on relationships within Esociformes + Salmoniformes. Our dataset supports a sister relationship between Esociformes and Salmoniformes; however the nearest relatives of Esociformes + Salmoniformes are inconsistent among analyses. Within the order Esociformes, we advocate for a single family, Esocidae. Subfamily relationships within Salmonidae are poorly supported as Salmoninae sister to Thymallinae + Coregoninae.