From 46d7cf71b168657cbdbd04e1be813c2007cf322d Mon Sep 17 00:00:00 2001
From: Thibaut Horel <thibaut.horel@gmail.com>
Date: Fri, 19 Jun 2015 21:40:26 -0700
Subject: First draft of the (almost) full specification of the probabilistic
 model

---
 theory/main.tex | 10 +++++++---
 1 file changed, 7 insertions(+), 3 deletions(-)

diff --git a/theory/main.tex b/theory/main.tex
index 505f722..a20a140 100644
--- a/theory/main.tex
+++ b/theory/main.tex
@@ -251,9 +251,13 @@ $V = R\cup T$ where $R$ are the victim nodes and $T$ the non-victim nodes
 ($R\cap T=\emptyset$), then \emph{the violence cascades form a random forest
 spanning $R$ in $D$}.
 
-Given a random forest $(T_1,\dots T_r)$ spanning $R$, where $T_i, 1\leq i\leq
-n$ are trees, we can compute the probability of this forest occurring according
-to the model
+\paragraph{Likelihood.} Given the set of victim nodes $R$ and their infection
+times, which we denote by the vector $\textbf{t}$, we can compute the
+probability that the violence cascades propagated along the random forest
+$(T_1,\dots, T_r)$ spanning $R$, where $T_1,\dots,T_r$ are trees:
+\begin{displaymath}
+    \P\left[(T_1,\dots, T_r)|\mathbf{t}\right]
+\end{displaymath}
 
 \section{Maximum Likelihood Inference}
 
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