scholarly journals On the use of the moments method of estimation to obtain approximate maximum likelihood estimates of linkage between a genetic marker and a quantitative locus

Heredity ◽  
1992 ◽  
Vol 68 (1) ◽  
pp. 43-46 ◽  
Author(s):  
A Darvasi ◽  
J I Weller
Keyword(s):  
Maximum Likelihood ◽  
Genetic Marker ◽  
Maximum Likelihood Estimates ◽  
Approximate Maximum Likelihood ◽  
Moments Method

Retention or Attrition Models

1989 ◽  
Vol 14 (1) ◽  
pp. 1-20 ◽  
Author(s):  
Irwin Guttman ◽  
Ingram Olkin
Keyword(s):  
Maximum Likelihood ◽  
Bayesian Analysis ◽  
Maximum Likelihood Estimates ◽  
Attrition Rates ◽  
Approximate Maximum Likelihood ◽  
Alternative Models

A model for retention and its counterpart, attrition, is presented. In a prototype example, students enter a program in each of k terms; some of the students complete the program, and the remainder leave. A key feature in the models proposed is that there is a dampening effect from term to term because the probability of leaving the program diminishes as the terms progress. The focus of this paper is the study of alternative models for the dampening in attrition rates. A number of alternative dampening effects are proposed that provide for different rates of attrition. Approximate maximum likelihood estimates for the underlying parameters in each model and a Bayesian analysis are provided.

scholarly journals Estimating Linkage Disequilibrium Between a Polymorphic Marker Locus and a Trait Locus in Natural Populations

Genetics ◽  
1999 ◽  
Vol 151 (1) ◽  
pp. 359-371 ◽  
Author(s):  
Z W Luo ◽  
S Suhai
Keyword(s):  
Linkage Disequilibrium ◽  
Maximum Likelihood ◽  
Genetic Marker ◽  
Positional Cloning ◽  
Genetic Parameters ◽  
Marker Locus ◽  
Maximum Likelihood Estimates ◽  
Accurate Estimation ◽  
Asymptotic Covariance Matrix ◽  
Trait Locus

Abstract Positional cloning of gene(s) underlying a complex trait requires a high-resolution linkage map between the trait locus and genetic marker loci. Recent research has shown that this may be achieved through appropriately modeling and screening linkage disequilibrium between the candidate marker locus and the major trait locus. A quantitative genetics model was developed in the present study to estimate the coefficient of linkage disequilibrium between a polymorphic genetic marker locus and a locus underlying a quantitative trait as well as the relevant genetic parameters using the sample from randomly mating populations. Asymptotic covariances of the maximum-likelihood estimates of the parameters were formulated. Convergence of the EM-based statistical algorithm for calculating the maximum-likelihood estimates was confirmed and its utility to analyze practical data was exploited by use of extensive Monte-Carlo simulations. Appropriateness of calculating the asymptotic covariance matrix in the present model was investigated for three different approaches. Numerical analyses based on simulation data indicated that accurate estimation of the genetic parameters may be achieved if a sample size of 500 is used and if segregation at the trait locus explains not less than a quarter of phenotypic variation of the trait, but the study reveals difficulties in predicting the asymptotic variances of these maximum-likelihood estimates. A comparison was made between the statistical powers of the maximum-likelihood analysis and the previously proposed regression analysis for detecting the disequilibrium.

scholarly journals Directional Selection and the Site-Frequency Spectrum

Genetics ◽  
2001 ◽  
Vol 159 (4) ◽  
pp. 1779-1788 ◽  
Author(s):  
Carlos D Bustamante ◽  
John Wakeley ◽  
Stanley Sawyer ◽  
Daniel L Hartl
Keyword(s):  
Maximum Likelihood ◽  
High Power ◽  
Negative Selection ◽  
Likelihood Estimation ◽  
Directional Selection ◽  
Likelihood Ratio Tests ◽  
Maximum Likelihood Estimates ◽  
Likelihood Methods ◽  
Ancestral States ◽  
Asymptotic Variances

Abstract In this article we explore statistical properties of the maximum-likelihood estimates (MLEs) of the selection and mutation parameters in a Poisson random field population genetics model of directional selection at DNA sites. We derive the asymptotic variances and covariance of the MLEs and explore the power of the likelihood ratio tests (LRT) of neutrality for varying levels of mutation and selection as well as the robustness of the LRT to deviations from the assumption of free recombination among sites. We also discuss the coverage of confidence intervals on the basis of two standard-likelihood methods. We find that the LRT has high power to detect deviations from neutrality and that the maximum-likelihood estimation performs very well when the ancestral states of all mutations in the sample are known. When the ancestral states are not known, the test has high power to detect deviations from neutrality for negative selection but not for positive selection. We also find that the LRT is not robust to deviations from the assumption of independence among sites.

scholarly journals An Integrated Framework for the Inference of Viral Population History From Reconstructed Genealogies

Genetics ◽  
2000 ◽  
Vol 155 (3) ◽  
pp. 1429-1437
Author(s):  
Oliver G Pybus ◽  
Andrew Rambaut ◽  
Paul H Harvey
Keyword(s):  
Maximum Likelihood ◽  
Sequence Data ◽  
Demographic History ◽  
Population History ◽  
Maximum Likelihood Estimates ◽  
Viral Population ◽  
True Parameter ◽  
Subtype B ◽  
Exponential Growth Model ◽  
Parameter Values

Abstract We describe a unified set of methods for the inference of demographic history using genealogies reconstructed from gene sequence data. We introduce the skyline plot, a graphical, nonparametric estimate of demographic history. We discuss both maximum-likelihood parameter estimation and demographic hypothesis testing. Simulations are carried out to investigate the statistical properties of maximum-likelihood estimates of demographic parameters. The simulations reveal that (i) the performance of exponential growth model estimates is determined by a simple function of the true parameter values and (ii) under some conditions, estimates from reconstructed trees perform as well as estimates from perfect trees. We apply our methods to HIV-1 sequence data and find strong evidence that subtypes A and B have different demographic histories. We also provide the first (albeit tentative) genetic evidence for a recent decrease in the growth rate of subtype B.

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