Analysis of Competing Hypotheses



Analysis of Competing Hypotheses

Introduction

We imagine that an analyst who is a specialist on terrorist activities related to the oil infrastructure of Iraq and Iran has to evaluate hypotheses in the Abadan region of Iran. The interest in evaluating the hypotheses is high, because of the recent interception of a message between terrorists. We emphasize that this is a fictitious example, devised to illustrate our techniques.

Question: Will terrorists try to create conflict in Iran by attacking the oil infrastructures in Abadan region?

Hypotheses

H1: Terrorists will bomb the oil refineries in Abadan.

H2: Terrorists will bomb the oil pipelines in Abadan.

H3: Terrorists will bomb the oil wells in Abadan.

H4: Terrorists will bomb the oil facilities in Shiraz.

H5: Terrorists will not launch an attack.

Evidence (fictitious for this example):

E1: A phone wiretap on a suspected terrorist cell in Beirut records a discussion about crippling the Iranian economy by destroying oil production facilities within the Abadan region.

E2: The oil refinery in Abadan can produce 0.37 million barrel per day. Oil is transported through pipeline.

E3: the oil refinery in Shiraz can produce 0.04 million barrel per day.

E4: There is an oil pipeline with from Abadan to Basra, which crosses the border. The capacity of this pipeline is over 0.2 million barrel per day.

E5: Historical analysis allows us to conclude that the affected oil industry will cripple the Iranian economy, which will lead to the conflict with its neighbors.

E6: The area near a border is easier for terrorist to infiltrate.

E7: Terrorists prefer a target that is near a road.

The preceding question, hypotheses, and items of evidence lead to the ACH matrix presented in the following table.

Bayesian Network Representation of ACH Tables

Bayesian networks are a space-efficient representation of multivariate probability distributions that exploits independence information and supports the time-efficient computation of posterior probabilities. The expressiveness and efficiency of Bayesian networks make them the decision support systems of choice in situations where uncertainty needs to be modeled. More precisely, a Bayesian network consists of a directed acyclic graph (DAG), called a Bayesian network structure, prior marginal probability tables for the nodes in the DAG that have no parents, and conditional probability tables for the nodes in the DAG given their parents. The network and the probability tables define a joint probability distribution on all variables corresponding to the nodes, with the defining property that the conditional probability of any variable v given any set of variables that includes only the parents of v and any subset of nodes that are not descendant of v is equal to the conditional probability of v given only its parents.

From this property, it follows that the joint probability of the variables in a Bayesian network decomposes in a multiplicative fashion; more precisely, if V is the set of the nodes in the DAG, the following equality (the chain rule for Bayesian networks) holds:

In turn, this decomposition allows for the very efficient computation of marginal posterior probabilities upon observation of evidence.

We illustrate this definition with a fictitious example from the medical domain ...