Conditional Log-Likelihood of the Dispersion for a Single Group of Replicate Libraries
Derivatives of the negative-binomial log-likelihood with respect to the dispersion parameter for each gene, conditional on the mean count, for a single group of replicate libraries of the same size.
condLogLikDerSize(y, r, der=1L) condLogLikDerDelta(y, delta, der=1L)
y |
matrix of counts, all counts in each row having the same population mean |
r |
numeric vector or scalar, size parameter of negative binomial distribution, equal to 1/dispersion |
delta |
numeric vector or scalar, delta parameter of negative binomial, equal to dispersion/(1+dispersion) |
der |
integer specifying derivative required, either 0 (the function), 1 (first derivative) or 2 (second derivative) |
The library sizes must be equalized before running this function. This function carries out the actual mathematical computations for the conditional log-likelihood and its derivatives, calculating the conditional log-likelihood for each gene.
Derivatives are with respect to either the size (r) or the delta parametrization (delta) of the dispersion.
vector of row-wise derivatives with respect to r or delta
Mark Robinson, Davis McCarthy, Gordon Smyth
y <- matrix(rnbinom(10,size=1,mu=10),nrow=5) condLogLikDerSize(y,r=1,der=1) condLogLikDerDelta(y,delta=0.5,der=1)
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