The Asymptotic Behaviour of the Maximum Likelihood Estimates for a Class of Diffusion Processes

1988 ◽  
pp. 205-213
Author(s):  
Kurt Helmes
Keyword(s):  
Maximum Likelihood ◽  
Asymptotic Behaviour ◽  
Diffusion Processes ◽  
Maximum Likelihood Estimates

Asymptotic likelihood theory for diffusion processes

1975 ◽  
Vol 12 (2) ◽  
pp. 228-238 ◽  
Author(s):  
B. M. Brown ◽  
J. I. Hewitt
Keyword(s):  
Central Limit Theorem ◽  
Maximum Likelihood ◽  
Limit Theorem ◽  
Continuous Time ◽  
Diffusion Processes ◽  
Maximum Likelihood Estimates ◽  
Stochastic Integrals ◽  
Ratio Test ◽  
Chi Squared ◽  
Asymptotic Likelihood

We investigate the large-sample behaviour of maximum likelihood estimates (MLE's) of the parameters of a diffusion process, which is observed throughout continuous time. The results (limit normal distribution for the MLE and an asymptotic chi-squared likelihood ratio test) correspond exactly to classical asymptotic likelihood results, and follow easily from a central limit theorem for stochastic integrals.

Asymptotic likelihood theory for diffusion processes

1975 ◽  
Vol 12 (02) ◽  
pp. 228-238 ◽  
Author(s):  
B. M. Brown ◽  
J. I. Hewitt
Keyword(s):  
Central Limit Theorem ◽  
Maximum Likelihood ◽  
Limit Theorem ◽  
Continuous Time ◽  
Diffusion Processes ◽  
Maximum Likelihood Estimates ◽  
Stochastic Integrals ◽  
Ratio Test ◽  
Chi Squared ◽  
Asymptotic Likelihood

We investigate the large-sample behaviour of maximum likelihood estimates (MLE's) of the parameters of a diffusion process, which is observed throughout continuous time. The results (limit normal distribution for the MLE and an asymptotic chi-squared likelihood ratio test) correspond exactly to classical asymptotic likelihood results, and follow easily from a central limit theorem for stochastic integrals.

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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