analytical edge prior formula citation

content/02.body.md

@@ -124,10 +124,12 @@ The edge prior is a numerical value that can be computed for every pair of nodes
 
 Because network permutation can be computationally intensive, we also considered whether the probability of an edge existing across permuted networks has a simple closed-form expression.
 We were unable to find a closed-form solution giving the edge prior without assuming that the probability of any given edge existing is independent of all other potential edges, which, in general, is not valid.
-Nonetheless, we discovered a good analytical approximation to the edge prior that is particularly good for networks with many nodes and fewer edges (Figure {@fig:approx-quality}).
-Further discussion of this approximate edge prior and an derivation are available in [the supplement](#approx-prior-supp).
+Nonetheless, we discovered a good analytical approximation to the edge prior, offering much improvement over a past attempt [@10.15363/thinklab.d201].
+The new approximation is particularly good for networks with many nodes and fewer edges (Figure {@fig:approx-quality}).
+Further discussion of this approximate edge prior and its derivation is available in [the supplement](#approx-prior-supp).
+
 Let $m$ be the total number of edges in the network, and $u_i$, $v_j$ be the source and target degrees of a node pair, respectively.
-An approximation of the edge prior is
+Our approximation of the edge prior is
 
 $$
   P_{i,j} = \frac{u_i v_j}{\sqrt{(u_i v_j)^2 + (m - u_i - v_j + 1)^2}}.
@@ -144,8 +146,6 @@ fig:approx-quality created by
 https://github.com/greenelab/xswap-analysis/blob/4f06bdaf1f034af9136e25c03f9891a145b9bf91/nb/8.fig6.prior_exact_vs_approx/plot_prior_exact_vs_approx.ipynb
 -->
 
-
-
 ### Prediction tasks {#tasks}
 
 We performed three prediction tasks to assess the performance of the edge prior.

content/manual-references-2023-12-21.yaml

@@ -1568,3 +1568,23 @@
     source_bibliography: manual-references.yaml
     standard_id: raw:laplacian
   id: 1E6tdJtDz
+- publisher: ThinkLab
+  DOI: 10.15363/thinklab.d201
+  source: Crossref
+  title: 'Network Edge Prediction: Estimating the prior'
+  author:
+  - given: Antoine
+    family: Lizee
+  - given: Daniel
+    family: Himmelstein
+  issued:
+    date-parts:
+    - - 2016
+      - 4
+      - 14
+  URL: https://doi.org/f3qbmg
+  id: 19OyKPQ4M
+  note: |-
+    This CSL Item was generated by Manubot v0.5.5 from its persistent identifier (standard_id).
+    standard_id: doi:10.15363/thinklab.d201
+  type: entry