1. A Statistical Analysis of the Trial of Adnan Syed
Tim manning

2. Outline Background of ‘Serial’ The Trials: All things Considered
Bayes’ Theorem and it’s Application to Law
Example of Bayes’ Theorem in a possible court case
Using Bayes’ Theorem in the trial of Adnan Syed
R code and output

3. First off, some general facts about the case
Podcast “Serial” by Sarah Koenig: Koenig, a journalist, investigates the 1999 murder of an 18 year old high school student Hae Min Lee
Location: Western suburb of Baltimore, Maryland
Main players: Hae Min Lee (murder victim), Adnan Syed (former boyfriend of Hae who was convicted of killing her), Jay Wilds (key witness at Syed’s trial), Cristina Guitierrez (Syed’s attorney), Asia McClain (Syed’s alibi)
Minor players: Nisha, Mr. S, Don, Jenn, Stephanie, Cathy
Hard evidence: Cell phone towers and cell phone records
Soft Evidence: Asian McClain as an alibi, Jay’s telling of events, Syed’s telling of events, character witnesses, Syed’s motive to kill

4. The Actual Trials: All things considered
Prior to the trial, Syed’s attorney, Christina Guitierrez, was accused of corruption when hundreds of thousands of dollars of client money went missing
Similar to a past trial, Guitierrez did not present a potential plea bargain to Syed
Guitierrez did not investigate Syed’s main alibi, Asia McClain, which would have contradicted the prosecution’s timeline of events
The first trial seemingly was going towards an acquittal of Syed, but Guitierrez requested and received a mistrial after she got in a heated fight with the judge and the opposing counsel in a bench conference. There is speculation as to Guitierrez causing the mistrial to make more money off of a second trial
The key witness in the case, Jay Wilds, had been secured a lawyer, pro bono, by the prosecutor. An unheard of allowance in any trial

5. The Actual Trials: All things considered
The job of the prosecution is to convict the defendant, not to present the truth
The timeline presented by the prosecution, while illogical, was believed to be the best prosecution to convict Syed
Sarah Koenig’s podcast uses objective journalism to search for the truth (as opposed to pursuing a verdict) no matter what the truth may be
Conclusion: My goal in this statistical analysis of the trial of Syed Adnan is not to prove he was guilty or innocent in the eyes of the court, but to show my subjective opinion on his guilt or innocence based on the evidence portrayed by Sarah Koenig. i.e. ‘Serial’ is the prosecutor and the defense, and I am the jury.

6. Bayes' Theorem and it’s Application to Law
In probability theory and statistics, Bayes’ Theorem relates current probability to prior probability
In the Bayesian interpretation, probability measures a degree of belief. Bayes' theorem then links the degree of belief in a proposition before and after accounting for evidence.
Bayes’ Theorem may be applied a number of times. Each time we observe a new event, we update the odds between the events of interest by taking account of the new information.
From a standpoint of a juror, an assessment of guilt or innocence can be calculated by using the odds for Bayes' Theorem which can be broken down to the following:
P(G|E) = P(G|E) X P(E|G) Where the first term on the right side of the equal sign is the
P(I|E) P(I|E) P(E|I) prior odds of guilt to innocence given prior evidence, and the second term is the probability according to the new evidence

7. An example: The life and death of Lizet’s pen
Hien has be brought to the court of Justice Manning for the theft of Lizet's pen.
Evidence 1: Hien was seen and heard by two witnesses complimenting Lizet’s pen during a statistical conference
P(G|E) = 0.6 While this gives Hien motive, Justice Manning does not think it is
P(I|E) that meaningful, because the pen is in fact very nice
Evidence 2: Hien was the president of his high school calligraphy club
P(G|E) = 0.42= 0.6 X With such a strong passion for penmanship, Hien looks more and
P(I|E) more guilty in the eyes of the court

8. The life and death of Lizet’s pen
Evidence 3: Lizet purchased a hefty insurance policy on her pen collection. Also, Lizet just had to renew her yearly yoga membership
P(G|E) = 0.084= X Lizette could be scamming her insurance provider so she can keep
P(I|E) appreciating the mindfulness practice of yoga
Final Evidence: Forensic evidence has linked the ink from Hien’s multivariate homework to that of a pen very similar to Lizet’s.
P(G|E) = = X Justice Manning is %=0.0798/( )100% positive
P(I|E) that Hien stole Lizet’s pen

9. A Breakdown of Statistical Analysis and an Asterisk to the Entire Process
I have broken down my statistical analysis into three main categories:
Motive: includes perception from witnesses
Character: includes judgement of what is the truth and overall moral fiber
Timeline: includes cell phone calls, tower pings, and coincidences
Asterisk: “…when you have eliminated the impossible, whatever remains, however improbable, must be the truth” –Sherlock Holmes
In a recent judgement The English Court of Appeal has not only reject the Sherlock Holmes doctrine shown above, but also denied that probability can be used as an expression of uncertainty for events that have either happened or not. i.e. This would not be admissible in the UK

10. Episode 1: The Alibi
Motive: Adnan maintained a secret relationship with Hae that didn’t work out due to religious constraints which angered him. This topic was barely touched upon.
Character: Can Adnan be a psychopath? He comes across as well spoken, polite, and conscientious, but is that a facade?
Timeline: Asian McClain maintains a detailed account of the day Hae was killed, and claims Adnan was at the library at 2:30 pm, which disproves the states case. But does this prove his innocence when the entirety of the day is taken into account
Conclusion: Way too early to calculate an odds for Bayes’ Theorem considering the three major categories of motive, character, and timeline

11. Episode 2: The Breakup
Motive: Adnan was “possessive,” and would get upset if Hae didn’t message him back after calls or pages. He would have many impromptu visits when it was a girls outings. Most of Adnan’s friends and teachers considered it a normal teenage break up. Adnan started dating multiple girls, and Hae started falling for an older guy. P(G|E)=0.35
Character: Adnan was not that religious despite the pressure from his family to have strong Muslim values. Adnan had sex regularly, drank, and smoked weed. All in all, he was a teenager which doesn’t say much about his guilt or innocence.
Timeline: Adnan purchased a cell phone 2 days before Hae was killed, and called her to give her his number the night before she was killed. Was the purchase of the phone for flirting with girls or for coordinating Hae’s murder? Adnan asked for a ride from Hae the day she was killed. Witnesses say Adnan was fine with not getting a ride, but why ask if he has practice after school? P(G|E)=0.67

12. Episode 3: Leakin Park
The majority of this episode was about a strange person, “Mr. S,” who stumbled upon Hae’s body in the woods. Hae could hardly be seen due to being buried, and Mr. S found her while going in the woods to pee after drinking a tall boy before going back to work. Mr. S called the police, and then was questioned by police only to be let go after two polygraph tests. Nothing incriminating was found against Mr. S, but he had a criminal record for streaking. One police report described a scenario in which he stood naked in front of a female police officer jumping up and down...yup. While this is a strange detail to be added to the case, it does not indicate the guilt or innocence of Adnan.

13. Episode 4: Inconsistencies
Motive: Jenn and her friend Jay, the key witness, claims that Adnan wanted to kill Hae because she broke his heart. Nothing new here, and from two unreliable witnesses.
Character: The only noteworthy item about character concerns Jay’s character. Jay is constantly changing his story; sometimes to make his friends look less guilty, sometimes to make him less guilty, and sometimes for seemingly no reason. With Jay being the main witness who is a drug dealer that works at a porn shop, and who changes his story for the cops over and over again, I’m going to take his account of events with little to no accuracy.
Timeline: For Adnan to kill Hae in the described time period presented by the state, would be extremely difficult, but not impossible. Nonetheless, there are other timelines in which Adnan could have killed Hae. The rest of the timeline is based off of Jay’s telling of the story, which has minimal accountability thus far. P(E|G)=0.54

14. Episode 5: Route Talk
Timing: While Jay is suppose to have Adnan’s phone from lunch until after track practice, there are two calls to a person that only Adnan knows; one call at 3:26 and one call at 5:36. Track practice started at 4, nobody can claim Adnan wasn’t at practice. If someone didn’t show up to practice or was late, wouldn’t it be noticeable? If someone was late or absent without an excuse, extra laps would ensue. Running is a spring sport, not a winter sport, maybe it’s not as important therefore not as noticeable. On the other hand, it was a Friday, and practice may have ended early around 5:30, but the 3:26 call is extremely suspicious. Jay’s account of the events aligns with cell phone records and cell phone towers in one spot, and that is at Cathy’s house at 6:36. While Jay’s accounting of the story doesn’t add up, Adnan does have his phone after 6, and his cell phone is located near Leakin Park at 7:09 and 7:13, where Hae’s body is buried. P(E|G)=0.82

15. Episode 6: The Case Against Adnan Syed
Motive: A note passed back and forth between Adnan and a classmate prior to the murder described some heart break, and later had the words “I’m going to kill.” The classmate did not recognize those words, and the context is inconclusive along with no mention of hand writing analysis. Still doesn’t look good for Adnan P(E|G)=0.64
Character: Adnan describes the day as normal despite being called by the police that day. How is that a normal day? Adnan doesn’t call Hae to see where she is, but is still in the loop with people who may know. Cathy, an acquaintance of Jay, describes Adnan showing up randomly, and acting strange while being stoned. He receives a call from the police, and according to Cathy, acts worried and suspicious. But Adnan is stoned and doesn’t know anybody in the apartment except for Jay, I’ve acted weird under the circumstances. P(E|G)=0.70

16. Episode 7: The Opposite of the Prosecution
Most of this episode concerned the misconduct and mishandling of the actual trials, so as stated before, it plays no relevance in my specific search for the truth with the exception of a couple anecdotes concerning character
Character: Adnan has claimed his innocence before his trial, and for 15 years after his trial. That is very uncommon in a murder case. The lead attorney for “The Innocence Project” has claimed that she never deals with charming sociopaths, the chances that Adnan is such is very slim. P(E|G)=0.13

17. Episode 8: The Deal with Jay
Character: Jay’s friends describe him as a liar, but not as a person that would lie “about this.” Jay seems genuinely remorseful about playing any role in the burying of the body of Hae, but all of his story doesn’t add up when considering all the fact. An outside detective talks about the law enforcement coaching Jay for the interviews. Did they coach him to give the right interview as opposed to the truth. With all of Jay’s shady acts, and unconventional behavior, it is hard for me to disprove him, or believe him. He did know where Hae’s car was hidden, and supposedly Adnan threatened Jay’s girlfriend, Stephanie, in order to keep control of the situation. I consider this episode close to a wash in the probability of guilt or innocence. P(E|G)=0.52

18. Episode 9: To be suspected
Character: After Hae is found dead, Adnan is in disbelief. He was seen in emotional pain by acquaintances, friends, and teachers. Despite this, a school nurse claimed he was faking it, but he still helped to plan a memorial for Hae. He kept correspondence with several friends, and even people that testified against him. The letters were heart felt, and showed signs of empathy and concern for others. What was a suspicious call received at Cathy’s, is now possibly a call from a friend letting him know that the police were interested in speaking with him. He was high, and that may have been the reason to show suspicion. He is considered an exemplary prisoner, and has achieved awards saying such. P(E|G)=0.22

19. Episode 10: The Best Defense is a Good Defense
Most of this episode concerned the trial, and Adnan’s attorney’s personality. While Guiterrez put forth a strong effort to defend Adnan, there were bouts of incompetence. After she lost the case, Guiterrez fell into a deep depression and passed away 4 years after the trial.
Motive: There was underlining's of anti-Muslim sentiment within the community. The idea of how Muslims treat women, and Arabic culture promoting pride and honor. This sort of prejudice is unfounded considering he was a Pakistani-American. Adnan was born and raised in the United States. P(E|G)=0.45

20. Episode 11: Rumors
Character: Adnan stole a few hundred dollars from the Mosque, but does that equate to murder? Teenagers play along the line of morality. Many members of the Mosque, including those that accused Adnan of stealing, claimed he was a wonderful person. Also, a subject similar to past episodes, Adnan being a psychopath seems unlikely, but it is a small possibility. P(E|G)=0.54

21. Episode 12: What We Know
Timing: Adnan had bad luck. With all of the coincidences and timing, it seems far fetched for all of that to happen on the day Hae was murdered.
Character: Why would Adnan do the story if he was guilty?
Motive: There was much speculation concerning other suspects, but is this pure speculation with no evidence? Time will tell with DNA tests that were not presented in the trial.

22. Justice Manning’s Conclusion
Motive / Character: 7.7% chance of Adnan being guilty
Timeline: 91.6% chance of Adnan being guilty
Combined Motive/Character and Timeline: 47.5% chance of guilt
When timeline is weighted by a factor of 2 and combining Motive/Character and Timeline: % chance of Adnan being guilty

23. R code library(dplyr) library(ggvis) library(shiny)
load("serial_data.rda")
shinyServer(function(input, output) {
# Change the colour of the points when selected
lb <- linked_brush(keys = 1:nrow(calls), "red")
ttip <- function(x) {
if (!is.null(x$min)) {
with(calls[x$id, ], paste(format(time, "%H:%M"), "-", min, "min", sec,
"sec, tower", Name)) }
# call timeline
timeline <- ggvis(calls, x = ~ time, y = ~ Called, fill = ~ Called,
size = ~ minutes, key := ~ id) %>%
add_axis("x", title = "Time") %>%
layer_points(size.brush := 400) %>%
hide_legend("fill") %>%
lb$input() %>%
add_tooltip(ttip)
# construct map
basemap <- combined_map %>%
filter(lat < & lat > & long < & long > ) %>%
group_by(group, type) %>%
ggvis(~ long, ~lat) %>% layer_paths(strokeOpacity := .15) %>%
add_axis("x", title = "Longitude", grid = FALSE) %>%
add_axis("y", title = "Latitude", grid = FALSE)
# add places of interest
desc <- function(x) {
if (!is.null(x$location_id) && POI$Description[x$location_id] != "") {
POI$Description[x$location_id]

24. Call log output

25. Cell phone output

26. Time for Quiet Judgement