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WfccmAlgorithmHu
(07 May 2009,
WillGray
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---+++ Hu Algorithm ==function 1 : log-likelihood to estimate logmu== <br> * ==f(logmu)== = %$\sum(\frac{1}{2}*logsigma2 + \frac{(X-exp(logmu))^2}{2*exp(logsigma2)})$%<br> * logsigma2 = beta0 + beta1 * logmu<br> ==function 2 : log-likelihood to estimate beta== <br> * ==f(beta)== = %$\sum(\frac{1}{2}*logsigma2 + \frac{(X-exp(logmu))^2}{2*exp(logsigma2)})$%<br> * logsigma2 = beta[1] + beta[2] * logmu<br> ---+++ Data Preprocessing 1 seperate the original data set to two matrix.<br> ==%$M_1$%== = data in group1 <br> ==%$M_2$%== = data in group2 2 calculate [[http://www.geo.umass.edu/courses/geo340/R/library/base/html/Chisquare.html][rchisq]] ==%$rchisq_1$%== for ==%$M_1$%==, ==%$rchisq_2$%== for ==%$M_2$%== based on 10^6 time runs 3 calculate variance ==%$Var_1$%== of ==%$rchisq_1$%== , ==%$Var_2$%== of ==%$rchisq_2$%== 4 calculate 1% quantile ==%$Quan_1$%==, mean ==%$Mean_1$%==, variance ==%$Variance_1$%== of %$M_1$%, ==%$Quan_2$%==, mean ==%$Mean_2$%==, variance ==%$Variance_2$%== of %$M_2$%without NAN and negative values<br> n is sample of population, x is value corresponding to each sample<br> (a) ==mean== = %$\sum x $%/ n <br> (b) ==variance== = %$\frac{n*\sum {X}^2-(\sum X)^2 }{n*(n-1)}$% <br> (c) ==1% quantile== = value at (pos-1) + diff_v*diff_p<br> position = 1 + (n-1)*0.01<br> pos = integer part of position<br> diff_p = position - pos<br> diff_v = ceiling of value at (position - 1 ) - value at (pos-1)<br> 5 replace NA and negative values in %$M_1$% with %$Quan_1$%, %$M_2$% with %$Quan_2$% ---+++ Estimate MLE 1 calculate coefficients and residuals based on log values of %$M_1$% and %$Var_1$%, %$M_2$% and %$Var_2$%<br> x are values in M, y are values in Quan<br> ==coefficients== : <br> (a) intercept of coefficient = %$\frac{n\sum{xy}-\sum x \sum y}{n\sum {x}^2 -(\sum X)^2 }$% <br> (b) slope of coefficient = y - intercept * x<br> ==residuals== = y - (intercept + slope * x) <br> 2 ==xd2hat== = variance of residuals - Var <br> 3 calculate initial values ==xinitial== = estimate value of ==nlm== 4 lkdsumsloop loop 3 times to calculate ==lkdinitial== <br> %GRAY% if lkdinf-lkdsumsloop[3] >= 1 <br>then lkdsumsloop== lkdsumsloop[-1] %ENDCOLOR%<br> (a) calaulate ==min== and ==estimate== of xinitial<br> (b) lkdinitial = %$\sum{min}$%<br> 5 calculate ==lkdinf== <br> lkdinf = lkdsumsloop[1]+%BEGINLATEX{inline="1" density="160"}% \begin{displaymath} \frac{1}{(1-\frac{lkdsumsloop[3]-lkdsumsloop[2]}{lkdsumsloop[2]-lkdsumsloop[1]})*(lkdsumsloop[2]-lkdsumsloop[1])} \end{displaymath} %ENDLATEX% 6 calcualte mle estimate of mean expression, mle estimate of variance of each gene<br> (a) ==xbeta.mle== = xinitial[(m+1):(m+2)]<br> (b) ==xbar.mle== = exponent of xinitial<br> (c) ==xs2.mle== = exponent of xbeta.mle * xbar.mle ^ xbeta.mle <br> ---+++ calculate Hu score score = |%$\frac{xbar1.mle - xbar2.mle}{\sqrt{xs1.mle+\frac{xs2.mle}{6}}}$%| ---+++ Remarks * Details of nlm calculation have been skipped.
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Topic revision: r13 - 07 May 2009,
WillGray
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