How true is your memory: why is Bayes’ theorem necessary
We encounter probability everyday just as we face our own memory. How was my lunch? What was the person sitting next to me wearing? How true is my “vivid” memory? The one of TED’s invited speaker shared his speech on mainly two events where people’s “reconstructed memory” doesn’t actually give out the truth. In both events, when the teenagers testified someone guilty without sufficient evidence but enough confidence and when people logically assumed that the second tower fell soon after the first on 911, the brain, “abhor to vacuum,” filled holes in memory up with assumptions and post-scene information, and it made us believe in our memory.
This chance of recalling the false information in our brain is why Bayes’ theorem is very important. Having broader application than just on memory, the function describes the relationship between the prior probability of event A, the prior probability of event B, the posterior probability of A given B, and the posterior probability of B given A when a universe can be divided into two separate parts. The specific example given in the book about eyewitness testifying the color of the cab in a hit-and-run accident and related calculation actually said that when a witness provides his/her testimony in this case, the actual color of the cab still has equal chance (50:50) of either being yellow or black, assuming no outside effect was introduced during the testimony. This should suggest the court to be cautious towards eyewitness testimony because of the equal chance in this case. This also adds to the characteristics of information cascade: 1) can easily occur; 2) can lead to non-optimal outcomes; 3) can be fundamentally very fragile. The information cascade of wrong testimony can begin easily after the first two witnesses if they witnesses are to be asked sequentially. Even during separate interrogation, people who have already talked to other people about certain event at the first scene can be potentially influenced and thus provide similar information like he/she would as if he was the second person in the information cascade. Bayes’ theorem that calculates the probability of correctness of certain statements in this case thus become really important to show the judges whether a witness’s testimony should be considered the primary evidence in court. However, since all the probability should be less than or equal to 1, the fallibility of eyewitnesses should be taken into account even if the calculation did give report statement more than 50% of credibility according to Bayes’ theorem.
Sources:
Scott Fraser: Why eyewitnesses get it wrong URL: http://www.ted.com/talks/scott_fraser_the_problem_with_eyewitness_testimony.html
Valentina