Rewrite the BINOMHPDEL procedure to work correctly in this s

Rewrite the BINOM-HP-DEL procedure to work correctly in this situation.

It should still take O(lg n) steps. Dos it?

( Please write down each detail steps)

Solution

A)

Data generated by the nCounter system have to be normalized prior to being used to quantify gene expression and compare expression rate between different experimental conditions.Data normalization includes adjustment for sample preparation variation, background noise and sample content variation.Denote the observed count from gene g in sample i by Ygi, and the unobserved expression rate by gi.We assume a Poisson model for Ygi given gi:equation.we can decompose Ygi into Zgi + Bgi, where Zgi|gi Poisson(cidigi) denotes the count from the expression of gene g and Bgi Poisson(i) denotes the background noise. Gamma distribution is used to characterize the variation.Gamma distribution is parameterized with mean ugi and log dispersion g, where g is the negative of logarithm of the shape parameter in the common parameterization. Let vgi = cidiugi, then based on the hierarchical model, the marginal distribution of Zgi given vgi and g is negative binomial with mean vgi and variance.The hyper-parameters are empirically estimated using expression data for endogenous genes . Specifically, for each endogenous gene, we get the MLE of the log dispersion parameter. Because data contain background noise and endogenous genes with very low read counts cannot provide effective information, we only use equation M18 from endogenous genes with read counts larger than the the maximum value of negative controls to estimate the hyper-parameters.