有限差分近似法在數量性狀基因座定位上最大概似估值變 異矩陣估算上之應用
Date Issued
2003-07-31
Date
2003-07-31
Author(s)
劉清
DOI
912313B002365
Abstract
For mapping and analysis of quantitative trait loci (QTL), the maximum
likelihood (ML) estimates of parameters of mixture model can be calculated via EM,
ECM, IRLS or other methods, whereas the asymptotic dispersion matrix of ML
estimates requires the second order derivative of likelihood function which is
generally complicated and not easily derivable. The calculation of asymptotic matrix
of ML estimates is important in that it enables us to evaluate the plausibility of our
statistical inference based on ML estimates. This study proposes calculating the
asymptotic dispersion matrix of ML estimates by the finite difference approximation
method if the second order derivative of likelihood function is too complicate to
derive.
To verify the correctness of the asymptotic dispersion matrix calculated by the
finite difference approximation method, the asymptotic dispersion matrix of the
simulated normal, binary and Poisson distributed F2 intercross data are calculated by
analytical formula and the finite difference approximation of second order derivative.
Results from the simulated F2 intercross data indicate that the asymptotic dispersion
matrices calculated by the finite difference approximation method are very close to
that of the analytical formula. Therefore, if the second order derivatives of likelihood
functions under various kinds of mathematical model settings are too complicated to
derive, it is suggested to calculate the ML estimates via EM, ECM, IRLS or other
methods which do not require the second order derivative. Once the ML estimates is
available, the asymptotic dispersion matrix of ML estimates can be calculated by
finite difference approximation method.
Subjects
quantitative trait loci (QTL)
genetic marker
simple interval mapping(SIM)
composite interval mapping (CIM)
finite difference approximation
method
method
maximum likelihood estimates
the asymptotic dispersion matrix
Publisher
臺北市：國立臺灣大學農藝學系暨研究所
Type
report
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