Wednesday, March 27, 2013

Are Two Heads Better than One? Mathematics and the Amanda Knox Case

In yesterday’s New York Times, “Leila Schneps, a mathematician and mystery writer, and her daughter Coralie Colmez” wrote an op-ed entitled “Justice Flunks Math.” They gave this failing grade to an Italian judge who declined to order a second DNA test in the notorious murder case against the American student, Amanda Knox and her Italian boyfriend, Raffaele Sollecito.

If only the judge understood probability theory, they suggest, he might have ruled in favor of the prosecution's request for another DNA test. In their words:
Whatever concerns the judge might have had regarding the reliability of DNA tests, he demonstrated a clear mathematical fallacy: assuming that repeating the test could tell us nothing about the reliability of the original results. In fact, doing a test twice and obtaining the same result would tell us something about the likely accuracy of the first result. Getting the same result after a third test would give yet more credence to the original finding.
This claim of a mathematical fallacy in the judge’s reasoning, however, rests on an important assumption — that the test results are statistically independent (at least in substantial part). To illustrate their point, Schneps and Colmez explain:
Imagine, for example, that you toss a coin and it lands on heads 8 or 9 times out of 10. You might suspect that the coin is biased. Now, suppose you then toss it another 10 times and again get 8 or 9 heads. Wouldn’t that add a lot to your conviction that something’s wrong with the coin? It should.
But consider this example instead:
You test the surface of a gold coin and test it to make sure it is gold. The test is 90% certain to indicate gold when the metal is gold, so following the advice of Schneps and Colmez, you repeat the test three times and strike gold each time. When you try to sell the coin, however, a more astute buyer weighs it and finds that it does not have the density of gold. It is, in fact a thickly gold plated, lead coin.
Which example is more apt in the Knox case? A Nature blog explained that "[v]ery small amounts of Knox’s DNA were found on a knife located at the crime scene 46 days after Kercher’s murder," but this is not correct. The knife came from Sollecito's kitchen, and a more informed account in the New York Times states that "the court-appointed experts concluded that ... Ms. Knox's DNA was in fact on the handle" -- hardly a surprise given that she may have used it to cook dinner in her boyfriend's apartment. The only thing that made the knife incriminating was a police laboratory finding of DNA from the victim, Meredith Kercher, on the blade. But there was evidence that the knife could not have produced all the wounds, and the court-appointed experts were skeptical of the finding about the blade as well the police laboratory's analysis of "a bra clasp that belonged to the victim found on the floor at the scene 46 days after her murder" said to show Sollecito’s DNA.

Returning to Nature's account:
Speaking at the request of the defence, two forensic scientists, Stefano Conti and Carla Vecchiotti from Sapienza University in Rome, said police investigators failed to follow international protocols for collecting and handling evidence and conducting tests on small genetic samples known as low-copy-number (LCN) DNA analysis. For example, officers were not wearing protective masks or hair caps at the crime scene. ... In addition, Conti said police often used plastic bags, rather than paper, to wrap evidence, heightening the risk of contamination. ... “There are various circumstances do not adhere to protocols and procedures,” Conti told the court.

Consequently, the independent experts concluded that they could not rule out the possibility that the knife and bra had been contaminated by other sources of Knox’s and Sollecito’s DNA, such as other evidence at the crime lab where forensic testing was taking place.
If these experts’ concern — that the original DNA test was simply detecting traces of Kercher's and Sollecito’s DNA that investigators inadvertently transferred to the knife and bra clasp, respectively — then repeating the tests could well continue to detect that DNA — and prove nothing more than the original tests did. If the bra clasp sample showed a mixture of DNA from the victim and Sollecito (and nothing else), for example, then repeating it over and over would not reinforce the prosecution case in the slightest. It would be no different than retesting the surface of the lead coin with its gold plated contamination. The inability of the DNA evidence to demonstrate a convincing link to the defendants would remain after even an infinity of new tests.

Consequently, it is hard to judge Schneps' and Colmez's suggestion that "[t]he judge’s rejection of the retest — at least based on the notion that a confirming retest could tell us nothing about the likelihood that the DNA was a match — was a serious error, one that scuppered an opportunity to get at the truth of Ms. Kercher’s murder."

The judge’s decision may have been mathematically sound, or it may have been as naive and fallacious as Schneps and Colmez propose. They have a nice theory but it is fair to assume that there were uncontaminated samples for new testing? Without some specification of precisely what made the initial testing problematic and whether those problems could be reduced sufficiently with retesting, it seems precipitous to convict the judge who overturned the guilty verdict of "bad math."

Indeed, Schneps and Colmez seem to believe that the judge ignorantly opposed retesting of the small sample of DNA on the blade despite an improvement in the technology of testing low template DNA. They wrote that
Even though the identification of the DNA sample with Ms. Kercher seemed clear, there was too little genetic material to obtain a fully reliable result — at least back in 2007. By the time Ms. Knox’s appeal was decided in 2011, however, techniques had advanced sufficiently to make a retest of the knife possible, and the prosecution asked the judge to have one done. But he refused.
Yet, the judge clearly was open to new methods. He asked the two university experts to ascertain "whether it is possible, by means of a new technical analysis, to identify the DNA present on items 165b (bra clasp) and 36 (knife)." The Conti-Vecchiotti Report, Assignment. Finding "no evidence of cellular material in the samples analyzed," however, his experts concluded that "no DNA suitable for further laboratory investigations (amplification, electrophoresis) was present either on the swabs [tamponature] (A-B-C-D-E-F-G-H-I) taken from Exhibit 36 (knife) or on those (L-M) taken from Exhibit 165B (hooks of the bra)." Id. Conclusions (1). They based this conclusion on the absence of cellular material and the failure of "quantification of the extracts ... conducted via Real Time PCR [to] reveal the presence of DNA." Id. Conclusions (2).

The prosecution disagreed. It asked for still more testing. But Judge Claudio Pratillo Hellmann had had enough. Rather than prolong the appeal -- and the imprisonment of the defendants -- still longer to await tests that his experts told him would be useless, he and the jurors returned their not-guilty verdict. It remains to be seen why this verdict now has been overturned, but it is hardly obvious that "bad judicial math" is the reason.

Later Postings


  1. Leila Schneps appears to be an active participant in the anti-Knox movement, which seems to be a sort of a hate group these days. I believe she misrepresented Judge Hellmann's argument in her NYT op-ed. She accused him of a math error he did not commit, and blamed him for not ordering new tests. But Hellmann, not being a DNA expert, relied on the Conti-Vecchiotti report for his conclusions, not his own "math" - as you point out correctly. It was C&V who claimed the futility of further testing of DNA from the blade, as there was too little material left. A prosecution expert (Novelli) challenged that saying there were methods even for that, by in "uno stato di avanguardia," sort of cutting-edge but not quite established technology. Given that Italy is barely managing traditional DNA testing (the Pruem convention ratified only in 2009; chain of custody protections poor), no wonder Novelli's suspicious methods were rejected.

  2. The problem with your criticism is that Meredith's DNA could not be the result of contamination or innocent transfer.

    Lets consider the three possibilities.

    Innocent Transfer -- the sample was not a mixed sample and for innocent transfer to happen would require tertiary transfer. As such we can rule out innocent transfer.

    Contamination during collection: The knife was collected at Sollecito's apartment -- a residence Kercher had never been to. None of the technicians who processed Knox's residence worked on the collection at Sollecito's apartment. This rules out contamination during collection.

    Contamination at the laboratory -- this would have been a concern until we learned that no items related to this case were tested for the six days prior to the knife. This makes contamination at the lab also impossible. The independent experts themselves admitted this during cross-examination.

    I think the last point is where you made your error. You likely relied on the C&V report unaware that at trial C&V contradicted most of what their report contained. This is not your fault as the reporting on this case has been horrible and you would have no way of knowing this unless you read the transcripts.

    1. Edward, You are making assumptions that are not valid. One, tertiary transfer is quite possible, as Taylor and Johnson showed some years ago. Two, suppose that Meredith hugs Amanda and Amanda touches the knife: that would be secondary transfer. Three, the knife was repackaged at the police station for no apparent reason, and the person who handled the knife (Gubbiotti) had been to the women's flat earlier in the day. Four, the forensic police kept poor records, and they have failed to turn over the electronic data files to the defense; therefore, their claim of a six-day gap is suspect. Five, even if there were a gap, we are talking about low template DNA, which is especially problematic. Six, the egram had two extra alleles; therefore, your point about the sample's not being mixed is not entirely true.

    2. What Leila Schneps and James Raper propose is simply (and simplistically) to turn up the dial. What they fail to acknowledge is that proper work in the low template region of DNA forensics requires a complete rethinking of the whole system, right from the starting point (evidence collection) all the way through the system. With respect to showing how contamination happens, this sometimes requires intensive study years after the fact (Farah Jama case) and even this is not always enough to pin it down (Jaidyn Leskie case).

    3. I don't think the analogy of turning up the dial, that is, of making more noise, is a helpful one.

      I was not making more noise but simply using a different perspective - one that you refuse to countenance. Since my approach is juridical rather than scientific, and our arena is in fact a court case, mine is the more relevant IMO.

      By all means let the scientists improve the effectiveness of LCN DNA evidence. I have no problem with that.

      The Farah Jama case is interesting within it's own parameters. Here there was no evidence other than the DNA and I would certainly be inclined to agree that convicting solely on the basis of DNA warrants extreme caution, particularly as Jama had alibi evidence that was rock solid and consistent throughout. Contrast with Amanda Knox.

      "Jama's DNA sample was taken for another unrelated matter and then the same person coincidentally took DNA from the woman found unconscious at the nightclub the next day."

      This does NOT show how contamination happens, or happened in this case, but clearly there is a cause for concern given the lack of any other evidence for the prosecution, and in this case the prosecution sensibly backed down.

      Source, mobility of host substance, time frame for transfer, and route of transfer are all relevant indicators to be evaluated. In the Jama case these at least seem, even if still hypothetically, somewhat clearer and more likely than in the Meredith Kercher case where you postulate all sorts of unlikely possibilities.

    4. I suggest that you have misunderstood the analogy. Turning up the amplitude increase both signal and noise. That is akin to doing more cycles of PCR or removing inhibitors of the reaction. This is exactly what should not be done in this instance. This analogy comes from Making the Invisible Visible in the New Zealand Herald 28 October 2006. “’LCN is not just about turning up the dial in the DNA lab, or about a tweak to the DNA system,’ says Bedford, ‘it is a reworking of the the whole process.’” The intent of the article was to show that LCN forensics require even greater precautions against contamination than conventional DNA forensics. That is why Ms. Stefanoni was wrong to proceed and why the knife is now hopelessly compromised as evidence. It never should have been opened in the police station, nor should it have been opened in anything less than a facility equipped especially for true low copy number work.

      Your personal incredulity is a poor indicator of what is or is not a likely pathway of secondary/tertiary transfer or contamination. Moreover, it is not up to the defense to provide a route of contamination; it is up to the prosecution to put forward evidence that was handled properly and to draw conclusions that make sense. Positing that a knife could be cleaned completely of blood but not DNA is magical thinking.

      What about Mr. Jama’s alibi was “rock solid” in your mind?

    5. No, I don't think I misunderstood your analogy.

      But moving on, the graph produced by the electropherogram was a near perfect match for Meredith's profile, so much so that none of the experts, albeit with a carping comment here and there from the defence, really disagreed with this. It is also obvious simply by transposing the one graph over the other.

      This is difficult for the defence to explain other than by bringing up contamination.

      The fact that it was LCN may direct one's mind to the possibility of contamination, but that is all.

      As with the bra clasp Hellmann accepted (without any evaluation) C&V's conclusion that contamination, in the laboratory or on collection, could not be ruled out. This merely leaves us with the possibility of contamination which as a theoretical abstract is pointless in a court of law.

      So we are back to a re-evaluation (there having been one, and the only one, at the first instance trial) at the next appeal.

      I prefer not to indulge in magical thinking. I don't know why Gubiotti (who, as you say, was at the cottage the same day the knife was collected) decided to transfer the knife from the bag to the box, but I do know that he (inter alia) wore gloves at the cottage which were not the same as were used to transfer the knife.

      If the knife was "hopelessly compromised" by that action then one has to ask whether it is ever possible to collect a sample without it likewise being compromised. That would be a reductio ad absurdum.

      "Rock solid alibi"? Yes, well OK, perhaps the alibi witnesses were lying.

    6. Professor Kekule suggested secondary transfer from Knox's hands as another possible route, and that is not the same as contamination. I think either one is roughly equally possible. Yet, unless someone can explain how a knife may be cleaned of blood but not DNA, either one is far more likely than that this ordinary kitchen knife was used in a murder. It doesn't matter why Gubbiotti transferred the knife; he had no business doing so, even if the item in question had been one in which ordinary DNA profiling were to be performed.

      I have no idea what you are talking about with respect to contamination as a "theoretical abstract." It was quite real for Mr. Jama (convicted in spite of a "rock solid" alibi), for Ms. P (Australian), for Mr. N (New Zealand), for Gregory Turner (Canada), and for others who were suspected or even convicted of crimes on the basis of this quite real phenomenon. If you wish to keep yourself ignorant of the fact that DNA forensics in the low template region is even more prone to the problems of innocent transfer of DNA, that is your choice. However, that difference is why the knife was compromised.

      A competent forensic technician does not transpose (superimpose) one graph over the other. However, if one did so, one would notice two extra alleles in the egram. I am sure you and the prosecution would like to sweep them under the rug, but facts are stubborn things.

    7. I can't begin to imagine why Knox would have been running her fingers over the sharp edge of the knife except perhaps whilst washing it in water. It's a possible route I suppose but rather fantastical.

      Drop-ins and drop-outs are a known phenomenon of the LCN amplification process.

      If we are talking of a mixture then I would have thought that there would have been more than two extra alleles which I suspect could also be explained by stutter - but then again, perhaps not.

      Controlled experiments have shown that drop-ins occur when there is a known single donor sample.

      So the two extra alleles don't tell us much and don't affect the interpretation.

      The possibility that this is a mixture is very unlikely.

      Even Vecchiotti accepted that Meredith's profile was there. Chance?

      It seems perfectly possible to me that the DNA sample was not blood but we will never know because it was not tested for blood.

      You have not explained why a sample of DNA this small could not survive washing, or bleaching for that matter. Have you got to hand the results of exhaustive experiments with a similar knife?

      Anyway, getting back to Schneps and Kaye, are you seriously going to argue that another positive result on an entirely different sample adds nothing, even if the analysis is carried out by a modern machine calibrated to deal with the LCN? If so then I would suggest that you, and Professor Kaye do not so much as flunk a maths test, as flunk a common sense test.

    8. Both Ms. Stefanoni, and Drs. Conti and Vecchiotti obtained a negative results for blood using a presumptive test for blood. The latter wrote, “both the generic blood test and the human species test were negative,” which suggests that Ms. Stefanoni did an additional (probably confirmatory) test. Thus the knife does not have blood.

      If it were used in the crime, the knife would have blood on the surface. What substance can remove all traces of blood but not DNA? IMO the burden of answering this question lies with the prosecution, not the defense, but it does not hurt to examine the issue further. Bleach is known to be effective in destroying DNA (Prince and Andrus, 1992, Biotechniques, 12(3), 358-360). Detergent will dissolve membranes, which might anyway rupture due to osmotic shock. This would release DNA, rendering it more susceptible to nucleases in the environment. DNA that is subject to random degradation shows a pronounced decrease in the peak heights as one proceeds from left to right in an egram; the profile in question does not appear to do so.

      The extra peaks are not in the right place to be stutters. Drop in is very different from drop out. This particular drop in had to come from DNA that did not belong to Ms. Kercher. Its importance is perhaps in the eye of the beholder.

      The most fundamental problem is that the first test should never have been done in the Rome lab and not with a protocol that had not been peer-reviewed. Just to point out one problem, Ms. Stefanoni concentrated the samples. Assuming that she used a Speed Vac to do so, she would have had to open the plastic tubes during this step, raising the odds of contamination. Yet she never produced negative controls (certainly not in the form of electronic data files), even though control experiments might have helped to show whether or not the concentration step was a problem.

      The original finding of DNA was supposedly in the groove of the knife, which I thought was along the side of the blade, not along the edge (too bad Ms. Stefanoni was the only person to observe it). Therefore, I don’t see your point with respect to secondary transfer involving Amanda. Retesting would not eliminate the possibility of secondary transfer or contamination during handling. Given these circumstances, redoing the test would produce little of value. Moreover, the fact that the pro-guilt community focuses only on retesting and not on the lack of discovery of the forensic files or the lack of controls, suggests a biased outlook on the case.

  3. Since the Italian Supreme Court nullified Hellmann's
    judgement and the Judge himself has been retired I
    think we can conclude that his judgements were wrong.

    It is much like your own judgement. Repeating a test
    assumes a valid test each time. Taking a sample from
    the surface of a coin is completely useless, ergo,two
    bad tests will give a bad result.

    The DNA on the knife was in two significant areas...a
    microscopic scratch on the blade and at the hilt.
    A knife used in a stabbing action can have traces in these areas, as the forensic people knew.
    The DNA was contested on two issues. Compatability
    and contamination, retesting would have clarified one
    of these
    Contamination should be proven not merely asserted and
    since the defence did not prove it the DNA should have
    been admitted.
    Incidently one of the 'experts' made a significant error in a previous case. The other was an acquaintance of the second judge. The experts cited
    obscure American police manuals from a 'True crime'
    website and they were seen ,out of court ,with the defence.
    No one with knowledge of the case was suprised when
    the whole appeal was thrown out.

    1. This reply demonstrates several common fallacies. It assumes that, if one thing happened and then another thing happened, one caused the other. In fact, we don't know why the judges annulled the acquittal. You are jumping to the conclusion you want to reach.

      What difference does it make that the judge retired afterward? Another example of faulty logic.

      Significant location. Were you able to write that without laughing? It doesn't matter where the DNA was found if it isn't the victim's and if the blade couldn't have caused the wounds.

      And this is just something you made up. "No one with knowledge of the case was suprised when the whole appeal was thrown out."

      How on earth would you know?

  4. Dear Professor Kaye,
    Let me say first that I greatly admire your work on mathematics in court, which was one of the inspirations for Coralie and my work on our book, Math on Trial.

    I believe your take on our analysis of the judge's comments on the knife DNA, however, is not right. This may be partly due to the fact that we have access to many court documents which you probably are not aware of.

    Information about the quantity of DNA that Conti and Vecchiotti found on the knife in their own tests was given in court. In particular, it was determined that there was one swab that contained a quantity that could not only be quantified, amplified and tested properly in today's new generation equipment, but that was even sufficient to be divided into two separate samples for such testing (albeit with the risk that each sample would give an electropherogram containing greater difficulties of interpretation due to low peaks). This rich sample came from the place where the blade joins the handle of the knife.

    Professor Vecchiotti decided single-handedly not to test this new knife blade sample. She explained in her court testimony that that was her decision to make, and justified it on the grounds that the quantity was significantly lower than the quantity *advised* by the kit, although the kit's website shows many examples of tests on smaller samples, some even smaller than the knife blade DNA, that gave positive and accurate results.

    To retest DNA from the knife blade would not have been akin to testing only the surface of a gold coin for gold. If positive for Meredith Kercher, it would have correctly settled two of the questions left outstanding in the courtroom: was the first electropherogram showing the DNA on the knife correctly interpreted as Meredith's, and was Meredith's DNA actually on the knife? These questions being settled, the court could have concentrated on the debate about the actual possibilities of contamination. Of course these questions were discussed at length, but the issue was confused by the issue of disagreement over the answers to the previous two questions.

    It would be nice if these issues will be clarified in the new appeal trial, but I have heard that it is unlikely that new testing will be ordered (and even if it is, there is always the possibility of a null result). It may be that the new appeal will proceed on the basis of other evidence.

    I hope that my explanation will add some nuance to your take on what happened at the original appeal trial, and make it clearer where I am coming from when I state that a retest should have been done.

    Best wishes
    Leila Schneps

    1. Here is an interesting quote from a Jan-2011 article in USA Today:

      "But they might look to go a bit further. Conti, one of the independent experts, asked if he could open up the handle of the knife, to determine if blood or other traces might have seeped through. This led prosecutors and a lawyer representing the Kercher family to argue that such an analysis would go beyond the boundaries of the experts' mandate."

      I question whether Leila Schneps has the background to speak as an expert in this case. She may well be an expert in statistics but that doesn't have any significant application to this case. Determination of probability in DNA testing is all about organic chemistry and physics. Garbage in, garbage out.

      I am also intrigued by her claim that she has access to court records that aren't available to the public. Barbie Nadeau (a controversial and highly biased journalist who has written extensively about the case) has made similar claims. One underrated aspect of this case is that the trial record is NOT available to the public. Some favored journalists have documents but they are not permitted to publish this information to the Internet in its original unaltered form. The result is that the important public debate about the case has been defined by Internet blog hearsay -- just how the prosecution wanted it.

      Here are some statistical questions that Ms. Schneps should consider:

      (1) How common is female participation in sexually motivated homicides? Granted, this doesn't prove guilt or innocence but it is an important starting point. This type of crime is in almost all cases committed by a troubled male just like Rudy Guede. In those rare cases where females do participate, you find a long term dysfunctional relationship with a manipulative male and a woman who is an empty shell.

      (2)How common is it for crime scene involving a violent struggle to have no DNA of one of the killers? No DNA of Amanda Knox was found in the room. What is that probability that she could have participated in the struggle and left no biological evidence of her presence?

      (3) What is the probability of police accidentally destroying three hard drives important to the case? It's not that hard to remove a hard disk and make a bit by bit copy of it. Kits that only cost about $30 can connect a removed disk to a USB port on a computer. How could this have happened.

      (4) How does the existence of other male DNA on the bra clasp affect the probability that the DNA was not actually from Sollecito (as claimed by his attorneys) of whether it got there through innocent means. Sollecito's DNA was probably on a door knob that Meredith touched. If one looks closely enough it's probably not that unusual to find non-host DNA on a woman's bra clasp transferred there from the woman's fingers. We all touch things that other's have touched.

      The trial of Amanda Knox and Raffaele Sollecito was a travesty of justice. Meredith's murder was tragic but it was a very simple crime. Rudy Guede's DNA is everywhere; he flees; he admits being there, and he has a story that is believed by no one. He did it.

  5. Interesting but having given an alternative analogy to Schneps' tossing of a coin you do not examine why your analogy is the better of the two.

    Of course your analogy depends on an assumption that turns out to be false. The false assumption is that the gold coin is gold throughout. No amount of testing the surface only and discovering that the surface is gold is going to establish that the coin is gold throughout. Quite true.

    So how does this analogy work when applied to the DNA from the blade? It must be that whilst the DNA matches Meredith's, it is not "gold standard", it's not Meredith's through and through, in the same way that the coin looks gold throughout but is not. Nice, but what on earth does this mean and how is this supposed to help?

    In short, your analogy is deployed to support the assumption of an established fact (though far from established - that the Meredith DNA reading is unreliable because the sample cannot be re-tested) and has nothing to do with, except as a diversion, the maths of probability that Schneps was considering.

    The repetition testing in your analogy bears no comparison to what is being proposed anyway. What is not being proposed is that the same LCN sample be tested again. That repetition has already been done (to check the reliability of that particular machine). There is in fact a new sample of DNA in a different location (near to the handle whereas the other was further up the blade). Again it is Low Copy Number. Hellmann refused a testing of that sample on the basis that if LCN is unreliable then the testing of a further LCN sample does not increase the reliability of any finding.

    Incidentally, no analogy is likely to be flawless. Schneps' analogy has a problem simply because testing two different samples is not analogous to flipping a single coin. More like flipping separate coins and adding the maths together. But the same results with two separate coins would indicate something interesting about the minting of that type of coin.

    I think it's very difficult to construct an adequate model for the maths and indeed I am not sure that maths helps.

    But at least her analogy illustrates what we understand instinctively about probability, in this case that if the same result (using more modern machines) were to be obtained from the fresh sample as was obtained from the first (and the reading on the first very clearly Meredith's profile, as Vecchiotti had to concede on cross-examination) then not only does the probability of Meredith's DNA being on the blade increase exponentially but so also does the reliability of LCN testing.

    Probability is evidence.

    On the question of contamination you've swallowed Conti and Vecchiotti's erroneous logic, fact finding and conclusions wholesale direct from their report although some of fact finding was later modified in court.

    If you have not already read it I recommend my own article about the bra clasp contamination issue on the True Justice for Meredith Kercher website (I'd put a link in but I am not that computer savvy). Contamination of the knife was even less of an issue which is why I did not bother with it.

    In future please read up on all the material available before comment.

  6. What I find incredulous about this whole affair is this. If Amanda Knox and Rafaelle Sollecito were indeed at the scene of the crime (inside Meredith's bedroom) there would have been thousands of samples of DNA not just one molecule on a bra clasp (found weeks later) which clearly happened because of cross contamination. It would have been impossible for them to clean up their DNA (which you can't see with the naked eye) and leave only Rudy Guede's DNA. Science is on the side of truth, and the truth is Amanda Knox and Rafaelle Solecito are innocent.

  7. After a long period of inactivity in this response to my questions about the analysis in the op-ed, I was surprised to find a slew of comments awaiting my approval for posting. Not a Poisson process, I dare say. I nixed four because they merely said nasty things about people without giving any reasoning or facts to support the aspersions or the view of the case.

  8. @Julie,

    The crime scene isn't limited to Meredith's bedroom. The Scientific Police collected DNA and forensic evidence from the bathroom, the hallway, Filomena's room, the kitchen and the other toilet.

    I can't think of any crime scene where an offender has left thousands of samples of DNA and I'm pretty sure you can't too.

    There were only four instances of Rudy Guede's DNA in Meredith's room. Surprisingly, there was only one instance of his DNA on Meredith's body. In total, there were five instances of Guede's DNA at the crime scene.

    In comparison, there was a total five pieces of incriminating pieces of DNA evidence against Amanda Knox at the crime scene. According to the prosecution's experts, Knox's blood and Meredith's blood were found in different locations in the cottage. In other words, they were both bleeding at the same time.

    Amanda Knox's DNA was found on the handle of the double DNA knife and a number of independent forensic experts - Dr. Patrizia Stefanoni, Dr. Renato Biondo, Professor Giuesppe Novelli, Professor Francesca Torricelli and Luciano Garofano - categorically stated that Meredith’s DNA was on the blade.

    An abundant amount of Raffaele Sollecito's DNA was found on Meredith's bra clasp. His DNA was identified by two separate DNA tests. Of the 17 loci tested in the sample, Sollecito’s profile matched 17 out of 17. Professor Novelli pointed out there's more likelihood of meteorite striking the courtroom in Perguia than there is of the bra clasp being contaminated by dust.

    According to Sollecito's forensic expert, Professor Vinci, and Luciano Garofano, Knox's DNA was also on Meredith's bra.

    In light of the above, Knox and Sollecito clearly didn't clean up all the DNA and forensic evidence against them.