local.model.prior: Computes a prior to be used for edge-wise model inference

Description

The function pairwise.posterior infers a phenotypic hierarchy edge by edge by choosing between four models (unconnected, subset, superset, undistinguishable). For each edge, local.model.prior computes a prior distribution over the four models. It can be used to ensure sparsity of the graph and high confidence in results.

Usage

local.model.prior(size,n,bias)

Arguments

size

expected number of edges in the graph.

number of perturbed genes in the dataset, number of nodes in the graph

bias

the factor by which the double-headed edge is preferred over the single-headed edges

Value

a distribution over four states: a vector of four positive real numbers summing to one

Details

A graph on n nodes has N=n*(n-1)/2 possible directed edges (one- or bi-directional). If each edge occurs with probability $p$, we expect to see $Np$ edges in the graph. The function local.model.prior takes the number of genes (n) and the expected number of edges (size) as an input and computes a prior distribution for edge occurrence: no edge with probability size/N, and the probability for edge existence being split over the three edge models with a bias towards the conservative double-headed model specified by bias. To ensure sparsity, the size should be chosen small compared to the number of possible edges.

Examples

Run this code

# uniform over the 3 edge models
local.model.prior(4,4,1)
# bias towards <->
local.model.prior(4,4,2)