The model applies to a cluster of cells representing a putatively homogeneous population. In this cluster, we have measured gene expression in n cells, and for each cell we have either detected the gene, or not. Given detection in k out of n cells, we want to know the underlying population frequency of expression, Θ. The observed fraction of expressing cells can be expressed conditional on the number of cells and the population expression frequency. By providing a prior on Θ, we can derive the posterior distribution of Θ given the observed number of detections:k|n,θ∼Binomial(θ,n)θ∼Beta(a,b)θ|n,k∼Beta(a+k,b+n−k)
