tag:blogger.com,1999:blog-1754053998399059707.post3948335643419439447..comments2017-06-10T05:54:19.578-05:00Comments on Invariances: Please Help / Real Criminal CaseJeff Rouderhttp://www.blogger.com/profile/12042232118911308833noreply@blogger.comBlogger20125tag:blogger.com,1999:blog-1754053998399059707.post-63368614903221199982017-06-10T05:54:19.578-05:002017-06-10T05:54:19.578-05:00Thanks for the nice compliment and for bringing yo...Thanks for the nice compliment and for bringing your post<br /><br /><br /><a href="https://www.golden-slot.com/" rel="nofollow">goldenslot slot games</a><br /><a href="http://www.gtzlg.com/" rel="nofollow">gclub casino</a><br /><a href="http://www.gtzlf.com/" rel="nofollow">gclub</a><br />smey valentinehttps://www.blogger.com/profile/07159047406612580657noreply@blogger.comtag:blogger.com,1999:blog-1754053998399059707.post-13181159410544156652017-03-15T12:44:51.030-05:002017-03-15T12:44:51.030-05:00This comment has been removed by the author.Bart Kolendowskihttps://www.blogger.com/profile/00789698878419034707noreply@blogger.comtag:blogger.com,1999:blog-1754053998399059707.post-20517470752538316002017-03-14T09:16:49.969-05:002017-03-14T09:16:49.969-05:00> the likelihood ratio for that case will domin...> the likelihood ratio for that case will dominate the probability of guilt<br /><br />Actually, on thinking it over, this is not correct. The correct method is to compute the likelihood ratio for the single hypothesis of cross contamination with two terms in the denominator: one for the case of a single cross-contamination event, and one for the case of two cross-contamination events. With the numbers as we have them, the sum of those two terms is basically equal to the first, since its probability is three orders of magnitude higher. But information about how cross-contamination events happen could lower that difference and therefore possibly raise the probability of guilt. However, I think it's highly unlikely that information about cross-contamination events could raise the probability of guilt anywhere close to the value of 0.373 that I computed just for the case of two cross-contamination events. (And even that probability is still less than 50-50, which should equate to reasonable doubt at the very least.)<br />Peter Donishttps://www.blogger.com/profile/09122769947782402203noreply@blogger.comtag:blogger.com,1999:blog-1754053998399059707.post-41290909796954337672017-03-14T07:12:11.532-05:002017-03-14T07:12:11.532-05:00I do work involving DNA analysis for research purp...I do work involving DNA analysis for research purposes, but it is sequencing-based. I have no specific knowledge about CODIS but I have considerable difficulty believing that the 13 (now 20) loci in it are really completely "independently assorted" as claimed. This assumption is used to claim that the probability of a false positive is the product of the population frequencies of each allele.<br /><br />If we were talking about a SNP chip or DNA sequencing, I would agree that the FPR is truly negligible because there are so many loci being measured. With CODIS, the FBI acknowledges that "near matches" can be obtained by relatives, but even that is possibly understating the case. After a moderate amount of Googling and PubMed searching, I could not find evidence for the assertion that the CODIS alleles are completely independent. It is puzzling to me that this would be taken as a given since, because of how genetics works, few alleles really are independent. What is certain is that using a "product rule" to calculate the FPR is the most optimistic possible way to do it, and the unfortunate result would be prejudicial to defendants if in fact the FPR is considerably higher.<br /><br />I am sure that whatever the FPR of CODIS is, it is small, certainly far below 1%. But with the large prior probabilities involved, even a small FPR may become quite important. So that is another possibility to consider. And of course if it is true that, as one commenter suggests, that the match against Leiterman was only partial, then the FPR potential skyrockets.Cory Gileshttps://www.blogger.com/profile/04730303915073488448noreply@blogger.comtag:blogger.com,1999:blog-1754053998399059707.post-86630074856011201742017-03-13T23:44:30.966-05:002017-03-13T23:44:30.966-05:00> It is not so much that I think there were two...> It is not so much that I think there were two x-contamination events<br /><br />I think you need to consider both possibilities: the possibility that one cross-contamination event occurred and resulted in both DNA traces being put into the sample, and the possibility that there were two separate cross-contamination events, each of which put one DNA trace into the sample.<br /><br />> we need to compute the probability of a single x-contamination event with two separate contaminating profiles (Ruelas and Leiterman)<br /><br />You already estimated that: it's 1.85x10^-11 (1 in 1500*6000^2).<br /><br />If you're thinking there should be an extra factor in there, i.e., that the probability of that single cross-contamination event containing both Ruelas' and Leiterman's DNA samples is less than 1 in 6000^2, I don't think that's significant unless you think that extra factor should be on the order of 1 in 1500 or smaller. The reason is simple: the probability of two independent cross-contamination events, one containing Ruelas' DNA and one containing Leiterman's DNA, is 1.23x10^-14 (1 in 1500^2*6000^2). So the likelihood ratio for that case will dominate the probability of guilt unless there is a small enough extra factor in the probability of a single cross-contamination event to bring it down to the same order of magnitude.<br />Peter Donishttps://www.blogger.com/profile/09122769947782402203noreply@blogger.comtag:blogger.com,1999:blog-1754053998399059707.post-41077618805318699452017-03-13T21:20:03.207-05:002017-03-13T21:20:03.207-05:00Here's a simple analysis:
If the same lab ask...Here's a simple analysis:<br /><br />If the same lab asked all 2.5M people in Detroit to come in to be swabbed, how many matches would there be against the evidence in this case? You can estimate this using the number of samples the lab took in the few months around the time of the analysis. Suppose they acquired 10k samples in that time; then the odds of a match are at least 1 in 10k (because of the 1 false match, Ruelas, out of the 10k the lab acquired in this time).<br /><br />So if the lab swabbed 2.5M people in Detroit, they would find that 250 people matched (1 in 10k). Of these, at most 1 is guilty. So the probability of guilt given a match is less than 1 in 250.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-1754053998399059707.post-60070803004169506512017-03-13T19:59:05.892-05:002017-03-13T19:59:05.892-05:00Peter, you write, "I'm not sure I would m...Peter, you write, "I'm not sure I would make that assumption." I agree. It is the one I am quite unhappy with. It is not so much that I think there were two x-contamination events, but that we need to compute the probability of a single x-contamination event with two separate contaminating profiles (Ruelas and Leiterman). That is a challenge.Jeff Rouderhttps://www.blogger.com/profile/12042232118911308833noreply@blogger.comtag:blogger.com,1999:blog-1754053998399059707.post-53653368245460188032017-03-13T19:00:09.994-05:002017-03-13T19:00:09.994-05:00Ahh, the DNA expert testimony shows that the DNA m...Ahh, the DNA expert testimony shows that the DNA matches were partial matches (2 to 7 alleles out of 13). What this would seem to indicate is that the person who matched the DNA is contained in a group that may be a blood relation of Leiterman.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-1754053998399059707.post-50172440655951424942017-03-13T18:41:20.862-05:002017-03-13T18:41:20.862-05:00You say the DNA tests matched? How much of a match...You say the DNA tests matched? How much of a match? How many alleles matched?Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-1754053998399059707.post-29007737455844660462017-03-13T18:28:21.387-05:002017-03-13T18:28:21.387-05:00The prosecution suffers from a deeply unprofession...The prosecution suffers from a deeply unprofessional lack of curiosity to find out how Ruelas got his DNA on the victim or the crime scene. <br /><br />Ockham's knife points the finger at the lab. <br /><br />Sloppiness is a hallmark of forensic labs as has been documented countless times. <br /><br />Credulous juries enable prosecutorial fantasies. George Haehhttps://www.blogger.com/profile/06368585073962056838noreply@blogger.comtag:blogger.com,1999:blog-1754053998399059707.post-22151148351705939342017-03-13T17:13:31.545-05:002017-03-13T17:13:31.545-05:00Was John Ruelas present at the crime scene or was ...Was John Ruelas present at the crime scene or was his identification a guarantee that cross-contamination happened in the lab at least once?Morganhttps://www.blogger.com/profile/13224060788731876893noreply@blogger.comtag:blogger.com,1999:blog-1754053998399059707.post-7676382547939757262017-03-13T16:55:12.917-05:002017-03-13T16:55:12.917-05:00> I think you have to assume two separate cross...> I think you have to assume two separate cross-contamination events<br /><br />That assumption, by my calculations, when it is figured into the Fourth Pass calculation (including the fluids and the second sample), gives odds of guilt of 0.595 to 1, or a probability of guilt of 0.373.<br /><br />(The calculation is the same as your Second Pass calculation, but dividing the numerator by 3 to account for the fluids and dividing the denominator by 1500 to account for the second cross-contamination event.)Peter Donishttps://www.blogger.com/profile/09122769947782402203noreply@blogger.comtag:blogger.com,1999:blog-1754053998399059707.post-70961272847665603462017-03-13T16:44:46.948-05:002017-03-13T16:44:46.948-05:00> I assumed it was the same cross-contaminatio...> I assumed it was the same cross-contamination event that captured each.<br /><br />I'm not sure I would make that assumption. I think you have to assume two separate cross-contamination events, since that's the assumption that gives the lower probability of cross-contamination being the reason for the match. Or at least, if you're going to assume one cross-contamination event, I think you need to justify that assumption based on knowledge of how DNA labs work and how likely it is that a single cross-contamination event would include two DNA profiles.Peter Donishttps://www.blogger.com/profile/09122769947782402203noreply@blogger.comtag:blogger.com,1999:blog-1754053998399059707.post-37181408769091264912017-03-09T21:05:15.543-06:002017-03-09T21:05:15.543-06:00The following is not a statistical suggestion but ...The following is not a statistical suggestion but nevertheless is relevant: I am far from sure that the method of analysis used in DNA matching is infallible. It all comes down to the number of markers used for comparison, which markers, how good AND relevant for a criminal investigation/comparison are they and what method was used for processing the sample. <br /><br />May be this from Andrew Gelman's blog of use: http://andrewgelman.com/2007/05/18/the_prosecutors/<br /><br />I cant remember when but Andrew recently (within last year) wrote an invited paper for a criminology journal which decided not to publish it, so he wrote about it in his blog. That would be useful for you. Sorry for the memory hole there.<br /><br />Good luck with the case. I am curious now.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-1754053998399059707.post-31823828618836828072017-03-09T18:52:05.016-06:002017-03-09T18:52:05.016-06:00My answer at https://github.com/rouderj/leiterman,...My answer at https://github.com/rouderj/leiterman, see the pdf.Jeff Rouderhttps://www.blogger.com/profile/12042232118911308833noreply@blogger.comtag:blogger.com,1999:blog-1754053998399059707.post-84280689057336631422017-03-09T18:35:05.115-06:002017-03-09T18:35:05.115-06:00Matt, that is key, isn't it. I assumed it was...Matt, that is key, isn't it. I assumed it was the same cross-contamination event that captured each. But who knows. I did it with and without Ruelas, but when I did, I used this assumption.Jeff Rouderhttps://www.blogger.com/profile/12042232118911308833noreply@blogger.comtag:blogger.com,1999:blog-1754053998399059707.post-25122630023109327602017-03-09T16:32:33.552-06:002017-03-09T16:32:33.552-06:00Hi Jeff and John,
I'm struggling with this on...Hi Jeff and John,<br /><br />I'm struggling with this one, but one thing that I am wondering about it is the probability of cross-contamination involving more than one spuriously introduced DNA profiles. E.g., if we know that a particular sample includes at least one DNA profile introduced by contamination, what is the probability that there will be one or more *additional* profiles present in the sample that were introduced by contamination?Matthttps://www.blogger.com/profile/15143483413289978878noreply@blogger.comtag:blogger.com,1999:blog-1754053998399059707.post-57426106892918383252017-03-09T15:40:59.196-06:002017-03-09T15:40:59.196-06:00Astonishing case. Really a hard one, I couldnt fig...Astonishing case. Really a hard one, I couldnt figure out how to start. I tried to used Bayes for P(Guilty | Positive Test) for a random Inhabitant of Detroit and tried modifying P(Positive Test | Not Guilty) for the chance of crosscontamination. I got a Number with five zeros as endresult, so its probably far from being right...really interested how you solve itTimnoreply@blogger.comtag:blogger.com,1999:blog-1754053998399059707.post-70505559983304252572017-03-09T02:09:14.582-06:002017-03-09T02:09:14.582-06:00Wow, the evidence underlying this conviction is ab...Wow, the evidence underlying this conviction is about the flimsiest I have ever seen. The DNA of a 4-yr old showing up in the same place inexplicably? huh? really? Stephan Lewandowskynoreply@blogger.comtag:blogger.com,1999:blog-1754053998399059707.post-48526356200890734892017-03-08T19:13:59.028-06:002017-03-08T19:13:59.028-06:00Thank you, Jeff. I tried this analysis myself and ...Thank you, Jeff. I tried this analysis myself and discovered it was harder than I thought. I really appreciate your help. I hope others can help as well.John Wixtedhttps://www.blogger.com/profile/17003418348569625262noreply@blogger.com