### Hu Algorithm

function 1 : log-likelihood to estimate logmu
• f(logmu) =
• logsigma2 = beta0 + beta1 * logmu
function 2 : log-likelihood to estimate beta
• f(beta) =
• logsigma2 = beta[1] + beta[2] * logmu

### Data Preprocessing

1. seperate the original data set to two matrix.
= data in group1
= data in group2
2. calculate rchisq for , for based on 10^6 time runs
3. calculate variance of , of
4. calculate 1% quantile , mean , variance of , , mean , variance of without NAN and negative values
n is sample of population, x is value corresponding to each sample
(a) mean = / n
(b) variance =
(c) 1% quantile = value at (pos-1) + diff_v*diff_p
position = 1 + (n-1)*0.01
pos = integer part of position
diff_p = position - pos
diff_v = ceiling of value at (position - 1 ) - value at (pos-1)
5. replace NA and negative values in with , with

### Estimate MLE

1. calculate coefficients and residuals based on log values of and , and
x are values in M, y are values in Quan
coefficients :
(a) intercept of coefficient =
(b) slope of coefficient = y - intercept * x
residuals = y - (intercept + slope * x)
2. xd2hat = variance of residuals - Var
3. calculate initial values xinitial = estimate value of nlm
4. lkdsumsloop loop 3 times to calculate lkdinitial
if lkdinf-lkdsumsloop[3] >= 1
then lkdsumsloop== lkdsumsloop[-1]

(a) calaulate min and estimate of xinitial
(b) lkdinitial =
5. calculate lkdinf
lkdinf = lkdsumsloop[1]+
6. calcualte mle estimate of mean expression, mle estimate of variance of each gene
(a) xbeta.mle = xinitial[(m+1):(m+2)]
(b) xbar.mle = exponent of xinitial
(c) xs2.mle = exponent of xbeta.mle * xbar.mle ^ xbeta.mle

score = ||

### Remarks

• Details of nlm calculation have been skipped.
Topic revision: r13 - 07 May 2009, WillGray

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