Bayesian Intelligence Analysis

Davide Barbieri

Summary

The author shows how Bayes’ method work for intelligence analysis firstly by defining the other probability measurements. The study’s objective is to give a general idea of Bayes’ method by showing the logical overlap and differentiated points with other mathematical measurement.

The author mentions about the simple probability approach which  was made famous by French mathematician Laplace: it says that the probability P of an event E is the number of favorable cases m divided by the total number of possible cases n:  P(E)=m/n

This classic definition can be applied when all the possible elementary outcomes of a random trial (or experiment) are known and each of them has the same chances of happening. For example, the probability that the roll of a die will give an even number is 3/6=1/2.

If things become less obvious then the conditional probability technique can be used which defined as: P (A | B) = P (A and B) / P (B) Chances that an event will occur given another event, that is the imposed condition: P(A|B), which can be read as the probability of A given B. For example, the probability of any given number in a fair die is 1/6. The joint probability that the roll of a die will give an even number n greater than 3 is P(A∩B), where A is the event “n is even” corresponding to the following outcomes: {2, 4, 6}, and B is the event “n>3” corresponding to {4, 5, 6}. Therefore, their intersection is (A∩B) = {4, 6}, and the corresponding joint probability is calculated as 2 favorable cases out of 6 possible: P(A∩B) =2/6=1/3. Since the probability of B is P(B)=3/6=1/2, then the conditional probability that n is even given B is P(A|B)=P(A∩B)/P(B)=(1/3)/(1/2)=2/3. In fact there are 3 numbers which are greater than 3 in a die: {4, 5, 6}, 2 of which are even: {4, 6}

Joint probability

Finally, the author comes to the Bayes’ rule. And, he suggests that “In science, and in medicine in particular, researchers want to know the probability of an event given some evidence.” This sentence actually forms the foundation of what Bayes’ method seeks for. Regarding the intelligence perspective, in a paper by Zlotnick (1970), Bayes’ rule is defined in the following way: R = PL where R is the estimate of the conditional probability of hypothesis H after revising the latest evidence E. R is equal to P, the prior estimate (which is given) times L, the likelihood ratio of event E in case hypothesis H is true:

 L=P(E|H)/P(E)

The author mentions about some example studies that the analysts utilized Bayes method to have an estimate. The first one is: In August 1969 the CIA had to evaluate the hypothesis that the USSR would attack China within the following month, in order to destroy its alarming nuclear capabilities. Analysts were asked to make an estimate, that is to evaluate the probability of a war. A list of intelligence items (Evidence) was collected such as E_1, E₂ … E_n. Then the analysts evaluated from their past experience the likelihoods P(Ei|H) of E1, E2... En in case of a war. They were asked to revise their estimates every week as the new evidence were available. Eventually, Bayesian probabilities always fell below conventional probabilities, demonstrating a better predictive accuracy. 


Conventional and Bayesian probabilities (Adapted from Fisk 1972)


Another example: There are two hypotheses. Israel was not going to attack Syria (H0, the null hypothesis) or that Israel was actually going to attack (H1, the alternative hypothesis). Being two complementary events, the sum of their probabilities had to be 1.

The prior probabilities of the two competing hypotheses were set to P(H0)=0.9 and P(H1)=0.1, with war being unlikely. An additional piece of information was then revealed: “Israeli finance minister Rabinowitz stated that the nation’s economic situation is one of war and scarcity, not one of peace and prosperity”. After hearing the minister’s statement on the radio, the two likelihoods of such an event were estimated by the analysts as P(E|H0)=0.8 (in case of no war) and as P(E|H1)=0.99 in case of war. Then they applied Bayes’ rule and revised the probability of an attack accordingly:

P (H₀|E) = P(E|H₀)P(H₀) / P(E) = 0.8 x 0.9 / 0.819 = 0.88
P (H₁|E) = P(E|H₁)P(H₁) / P(E) = 0.99 x 0.1 / 0.819 = 0.12
where
P(E) = P(H₀)P(E|H₀) + P(H₁)P(E|H₁) = (0.9 x 0.8) + (0.1 x 0.99)=0.72+0.099= 0.819

The perceived risk increased consistently according to the analysts’ view.


To sum up, we find the revised probability of the previously stated probability in case of additional available information by applying the rule.

The study asserts that the Bayes’ approach can give strategic warnings, can force analysts to quantify their estimates in numerical values, it may reduce cognitive bias. Since analysts are usually better at evaluating a single piece of evidence at a time rather than at drawing 
inferences from a large body of evidence, the method can enable them to focus thoroughly on one single evidence each time. 


Critique

The technique is very useful in terms of taking into account many different evidences that seemingly aren’t related with each other, whereas the classical probability approach deals with mainly related events (e.g. rolling a dice: you always roll the same dice and already every dice has the same features). Moreover, we use WEPs while articulating our estimates. But, Bayes’ approach enables analysts to give more accurate estimates rather than giving a range. On the other side, the method itself requires some talent in statistics and learning and applying the method is tough. The technique still requires analysts’ perceptions and experiences at the inception and while forming the formula (as assessed in article, there is a given probability which is the evaluation of the analyst about the topic. And then, after applying the rule we find the revised probability of the previously stated one). Therefore, to some extent, we can say that if the confirmation bias is present while weighting the evidences, the results shall not reflect a %100 ( or almost) accurate estimate.

Source:

http://www.researchgate.net/profile/Davide_Barbieri/publication/257933578_Bayesian_Intelligence_Analysis/links/540d6e1d0cf2f2b29a384931.pdf