DNA..... that tiny sample that apparently had Dr Vincent Tabak's name written all over it.... I am trying to understand how probabilities and matches work when deciding if someone has contributed to a DNA sample and especially one as small as the sample used to arrest and convict Dr Vincent Tabak....
1000/1 chance.... hopelessly small... pointless even not conclusive... But when trying to read about DNA and different theorems and of course understand such theorems, I find some interesting ways in which it can be determined how to calculate if a person is the contributor of said DNA sample....
And I think that CJ is the key here.... (again no finger pointing... he is an example)
Bayes's Theorem
The likelihood ratio and the match probability, being reciprocals, contain the same information. The LR, however, has a property that makes it especially useful, provided that prior odds are available on the hypothesis that the two DNA profiles have the same source. (Prior odds are the odds that the two DNA samples came from the same person on the basis of information other than the DNA. Posterior odds are the odds when the DNA information is included in the analysis.) That property can be stated this way:
The posterior odds are the prior odds multiplied by LR.4
In everyday words: Whatever are the odds that the two samples came from the same person in the absence of DNA evidence, the odds when the DNA evidence is included are LR times as great. That statement is an instance of Bayes's theorem.
For example, if there is reason to think that the prior odds that two DNA samples came from the same person (however this is determined) are 1:2, and the LR is 10,000, the posterior odds are 5,000:1. Many statisticians and forensic scientists prefer to use the likelihood ratio rather than the match probability (Berry 1991a; Berry et al. 1992; Evett et al. 1992; Balding and Nichols 1994; Collins and Morton 1994) because it admits an inferential interpretation that the simple match probability does not. Odds can be converted into a probability by the relation Prob = Odds/(Odds + 1), or Odds = Prob/(1-Prob). Thus, a likelihood ratio, which is not a probability, can be used to obtain a probability.
Extremely confusing... But It had me thinking..... Did the DNA Forensic examiners use Bayes's theroem?? Or did they use something else to determine what they probability of a match to Dr Vincent Tabak would be??
They talked of searching the DNA data base for a match...
The move will also be seen as controversial – especially as the Daily Mail understands that the sample has already been run through the national DNA database without finding a match.
The date of that article is in itself Interesting.... 14th January 2011
Now this is the part where Dr Vincent Tabak talking about the sample being dodgy holds water (imo).... They have already taken a sample from him... It should have been put through the national data base, they didn't find a match!!! Therefore his second sample shouldn't find a match either....(IMO).. But they apparently match Dr vincent Tabak's sample to this tiny DNA profile... How I don't know .. But I will carry on with my theory...
But if we go back to the idea of theorms and have more than one sample from a particular suspect, then that sample would therefore generate a greater hit... And the percentages would change.....
So they have 2 samples from Dr Vincent Tabak at this point and one sample from CJ.....
If I apply logic to the idea that 1000/1 chance that the sample belonged to Dr Vincent Tabak... The same should have applied to CJ realistically,.... It's a minute detail... I have said before that I believed the fact that someone was male in a sample group consisting mainly of females would give that sample a probability of 1000/1 .... we need to know what the sample was tested against... And if we are looking at odds as low as 1000/1.. CJ should in reality have matched some of the same characteristics as Dr Vincent Tabak.... That being Male and White.... Yet CJ's sample was not a match... And the sample should have at least shown that it came from a male...
Suspect Identified by a DNA Database Search
Thus far, we have assumed that the suspect was identified by evidence other than DNA, such as testimony of an eyewitness or circumstantial evidence. In that case, the DNA is tested and the match probability or likelihood ratio is computed for the event that a person selected at random from some population will have the genotypic profile of the evidence sample. There is an important difference between that situation and one in which the suspect is initially identified by searching a database to find a DNA profile matching that left at a crime scene.
The point I am making is the difference between CJ and Dr Vincent Tabak was that they had 2 samples from Dr Vincent Tabak in which to apply any type of probability... Couple that with other purported evidence and for an unsuspecting Jury it sounds compelling...
For instance we have....
* 1000/1 DNA
* Lived at the same address
* Could come into contact with Joanna Yeates at the communal hall
* Had a black coat
* Was apparently home alone
* Their two firms had a connection to each other
* Used the same exit (small gate)
* Had apparently been told by CJ that Greg was away
* His girlfriend was away for the evening
* He ate pizza
* He drove a car
* Made a second witness statement
We now have circumstantial evidence that adds weight to the useless DNA sample and gives weight to that sample...
Two Fallacies
Two widely recognized fallacies should be avoided (Thompson and Schumann 1987; Balding and Donnelly 1994b). The "prosecutor's fallacy"—also called the fallacy of the transposed conditional—is to confuse two conditional probabilities. Let P equal the probability of a match, given the evidence genotype. The fallacy is to say that P is also the probability that the DNA at the crime scene came from someone other than the defendant. An LR of 1,000 says that the match is 1,000 times as probable if the evidence and the suspect samples that share the same profile are from the same person as it is if the samples are from different persons. It does not say that the odds that the suspect contributed the evidence DNA are 1,000:1. To obtain such a probability requires using Bayes's theorem and a prior probability that is assumed or estimated on the basis of non-DNA evidence. As stated earlier, only if that prior probability is 1/2 will the posterior odds equal the LR.
The "defendant's fallacy" is to assume that in a given population, anyone with the same profile as the evidence sample is as likely to have left the sample as the suspect. For example, if 100 persons in a metropolitan area are expected to have the same DNA profile as the evidence sample, it is a fallacy to conclude that the probability that the suspect contributed the sample is only 0.01. The suspect was originally identified by other evidence, and such evidence is very unlikely to exist for the 99 other persons expected to have the same profile. Only if the suspect was found through a search of a DNA database might this kind of reasoning apply, and then only with respect to other contributors to the database, as we now discuss.
That sums it up in lots of ways ..
For example, if 100 persons in a metropolitan area are expected to have the same DNA profile as the evidence sample, it is a fallacy to conclude that the probability that the suspect contributed the sample is only 0.01. The suspect was originally identified by other evidence, and such evidence is very unlikely to exist for the 99 other persons expected to have the same profile. Only if the suspect was found through a search of a DNA database might this kind of reasoning apply, and then only with respect to other contributors to the database, as we now discuss.
The suspect be identified by other evidence and such evidence is very unlikely to exist for the 99 other persons.
only if the suspect was found through a search of a DNA DATA BASE might this kind of reasoning apply..... Well...
Again I will say that we are only too well aware that Dr Vincent Tabak had given the Police a DNA sample whilst he was in Holland, so naturally that would have been put through a DNA DATA BASE.... added to that the circumstantial evidence and they have themselves a case and a suspect.... OMG
They realistically could have applied the same evidence to CJ... But his lawyers knew it was a crock of s*** that the Police were saying... And he was released....
But we now have a baying public wanting an answer to this crime... So they can apply the same logic to Dr Vincent Tabak...(imo) this time it sticks.... It is not evidence... there is NO EVIDENCE... But a set of circumstances and a sample that exclude other people when marrying the two together....
The DNA sample should have been thrown out... It's ridiculous that it was not challenged... The only way in which that sample might have had any clout was if there had been other Forensic evidence of Dr Vincent Tabak being inside Joanna Yeates Flat and Joanna Yeates being inside Dr Vincent Tabak's Flat.... And that couldn't be enough really either... I say this because again CJ....
He should have hit one marker on the DNA, that being male.... And I could apply the same Circumstances to him
* Lived in the building
* Made a second witness statement
* Was The landlord
* Had access to Joanna Yeates Flat
* Knew Greg was away
* Heard people by the small gate
* Used the same communal area
These married together are really no different than that of Dr Vincent Tabak in many ways..... The only difference was that Dr Vincent Tabak had supplied an extra DNA sample....
CJ's solicitors put a stop to that idea quick sharp.... Because it is not enough to determine guilt... There has to be solid evidence to support any claim .... And where is the solid evidence to support that Dr Vincent Tabak killed Joanna Yeates ??
Where was the proper investigation into the 200 plus contacts that Joanna Yeates had on facebook, where was the DNA sampling of all her friends and associates?? Where was the viewing of CCTV footage from other days of her week to check she hadn't been followed... Whos' was the other DNA profile they found?? What motive was there for this Murder? Why would Joanna Yeates let a complete stranger into her home when not totally happy about being left alone?? Why the rush to arrest?? Why not check the college she had attended and anyone she may have come into contact... Why did the Police not leave that building alone!!
There were more people that had a profile that would fit just as easily as Dr Vincent Tabak's but they were never considered suspects... People whom she had told she would be alone... People who knew her routine on a Friday..People who had attended the Halloween party at the Flat at Canygne Road who DNA must surely have been left there.... Don't misunderstand me I am not saying any of these people are responsible... what I am saying if you marry the small DNA sample with circumstantial evidence they too should come up as 1000/1 at the very least..
* DNA Male
* Knew she would be home alone
* Worked at the same company
* Knew her routine
* Knew her plans
* Knew Greg was away all weekend
* Knew what time she left the pub
* Knew where she lived
* Knew her phone habits
Basically any circumstance could be applied to a tiny DNA sample.... But I personally believe that the DNA sample was a fallacy... It has to be, every male that Joanna Yeates knew could have be a candidate purely because they were male (imo) And they realistically should have tested everyone male that Joanna Yeates had been in contact with or knew... But i don't believe that they tested any of them, that why i think the sample is a fallacy... Because being a white male should have come up high on the 1000/1 sample.. And they manage to get only Dr vincent Tabak to register, and I believe the reason for this is that he gave two samples, which made him stand out from any other possible suspect and they ran with what they had....
So what real proof is there that Dr Vincent Tabak killed Joanna Yeates????
Oh Yes... That crock of unsupported S*** that was spoken on the witness stand by a man whom did not have The Presumption of Innocence as a basic right, and a media circus that told us all what a very bad man he was indeed...
And a defence team that was about as much use as a chocolate teapot.....
I do not know what probabilities or theorems The Forensic Firm use... But If I can argue a theory as to how it should have been thrown out as evidence, then why didn't the Defence have it thrown out??
Because 1000/1 is an extremely small and useless sample, far too small to arrest someone and certainly far too small to have someone convicted with murder...
Edit... If Dr Vincent Tabak's first DNA sample he gave on the 31st December 2010 hadn't show in the National Data base by the 14th January 2011.... Does that mean that the sample was put into the system after the 14th January 2011...
Did they put the two samples in on the same day?? Or a few days apart?
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