The Asymptotic Behaviour of Tukey's General Method of Setting Approximate Confidence Limits (The Jackknife) When Applied to Maximum Likelihood Estimates

1964 ◽  
Vol 32 (3) ◽  
pp. 202 ◽  
Author(s):  
D. R. Brillinger
Keyword(s):  
Maximum Likelihood ◽  
Asymptotic Behaviour ◽  
Maximum Likelihood Estimates ◽  
Confidence Limits ◽  
General Method

Likelihood-based confidence intervals of relative fitness for a common experimental design

2005 ◽  
Vol 62 (3) ◽  
pp. 693-699 ◽  
Author(s):  
Steven T Kalinowski ◽  
Mark L Taper
Keyword(s):  
Maximum Likelihood ◽  
Experimental Design ◽  
Confidence Intervals ◽  
Maximum Likelihood Estimates ◽  
Relative Fitness ◽  
Literature Analysis ◽  
Confidence Limits ◽  
Sample Sizes ◽  
Statistical Inferences ◽  
Different Types

Statistical inferences concerning the relative fitness of different types of individuals in a population have not been well developed. We present a method for calculating confidence intervals for maximum likelihood estimates of relative fitness obtained from an experimental design that is common in the fisheries literature. Analysis and simulation show that these confidence limits are reliable. We also show that the bias of the estimates is low for realistic sample sizes.

A Selected Review of Risk Models: One Hit, Multihit, Multistage, Probit, Weibull, and Pharmacokinetic

1985 ◽  
Vol 4 (4) ◽  
pp. 271-278 ◽  
Author(s):  
B. Hanes ◽  
T. Wedel
Keyword(s):  
Maximum Likelihood ◽  
Risk Model ◽  
Maximum Likelihood Estimates ◽  
Model Parameters ◽  
Confidence Limits ◽  
Risk Models ◽  
Sufficient Detail ◽  
The One

This paper provides some of the underlying mathematical derivations for the one-hit, multihit, multistage, Weibull, and pharmacokinetic risk models. Our purposes are to remove for the nonmathematician some of the mystery as to the derivation of the formulas for each particular risk model and to discuss some of the assumptions contained in the risk models. Confidence limits and maximum likelihood estimates of the model parameters are not discussed, since they are not pertinent to our objectives. Rai and Van Ryzin(1) have outlined these procedures in sufficient detail.

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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