Continuation Part 20: Amanda Knox/Raffaele Sollecito

[Bill Williams]

Exactly. It's not that "a priori probability" is wrong per se - it's that one always refers to a Bayesian prior, and not a "Bayesian a priori (probability)".

It's a bit like saying that Novak Djokovic won the All England Lawn Tennis Club Single Handed Championship of the World in 2015. Nobody would say that, even though it's technically "correct". Rather, they'd say that he won Wimbledon

Ok then. One-half point Vixen.

 

[Desert Fox]

The way that Steve Novella explains Bayesian statistics is as such

We have had hundreds of [Good] studies which show that acupuncture does not work.
There is then one new well controlled study which indicates that acupuncture works.
One should not change your conclusion based on that one study but based on prior evidence. Now if enough new evidence was to come through, then one changes ones mind.

Based on that, I am not sure that Bayesian statistics is even really usable in this case. There was never any actual good evidence of guilt.

 

[NotEvenWrong]

It is useful in the sense that we know the prior probability of Amanda and Raffaele teaming up with Rudy Guede for a vampire manga murder orgy is incredibly low. We can take the total number of people that could possibly have committed the murder (the ~total population of Perugia would be a good start), call it N, and the probability that Amanda committed the murder would be 1/N, the probability that Raff did it 1/N, and the probability that Rudy did it 1/N.

The probability that all three of them ganged up to do it would then be 1/(N^3). Then adjust down (way, way.... waaaaay) down for the fact that they didn't really know Rudy (other than Amanda being in the vicinity of him once or twice due to mutual acquaintances) and adjust down further for the implausibility of the entire scenario presented by the prosecution. It rapidly shrinks towards zero when you take Mignini's vampire manga orgy as the proposed scenario (although it was Halloween and this is what college students do! Thanks Vixen). Honestly I think they should modify Bayesian statistics to include negative infinities for this level of stupid. But right now zero is the lowest it can go, so we'll say it shrinks to zero.

Then of course, we analyze the evidence to see if it changes our beliefs. We have incompetent investigators who contaminate everything and go back to the crime scene to find evidence of the people who they beat the confession out of. We have a lab tech (sorry! doctor with a 3 year community college degree) who didn't follow any known forensic science protocols for LCN analysis but voila! found a tiny bit of Amanda and Raf's DNA when she tested it enough times. And no evidence aside from a contaminated bra clasp of either of them in the murder room. None of Amanda whatsoever. Crazy people may think that the obvious explanation is that Amanda is a sex crazed witch who spot cleaned invisible DNA, but intelligent people know otherwise.

 

[Desert Fox]

I do not think the probably of Amanda murdering Meredeth would be as low as you appear to be arguing. People are most often murdered by somebody they know.

Based on that, Amanda would start as a reasonably high priority along with her other roommates, "the virgins", her boyfriend, etc. Amanda would still be a relatively low probability but nothing like what you argue.

I did not pay much attention to the headlines at first except that some American woman was accused of murdering her roommate in Italy. I shock my head, figuring that they just got into a fight over a boyfriend or something. That happens more often than one would like.

 

[acbytesla]

I do not think the probably of Amanda murdering Meredeth would be as low as you appear to be arguing. People are most often murdered by somebody they know.

Based on that, Amanda would start as a reasonably high priority along with her other roommates, "the virgins", her boyfriend, etc. Amanda would still be a relatively low probability but nothing like what you argue.

I did not pay much attention to the headlines at first except that some American woman was accused of murdering her roommate in Italy. I shock my head, figuring that they just got into a fight over a boyfriend or something. That happens more often than one would like.

While it is true that most homicides by far are committed by someone acquainted with the victim, it is much less so when the acquaintance is brief. I think your going to find this is in fact extremely rare when they have known each other less than 2 months.

 

[Desert Fox]

While it is true that most homicides by far are committed by someone acquainted with the victim, it is much less so when the acquaintance is brief. I think your going to find this is in fact extremely rare when they have known each other less than 2 months.

I agree but it still would be more likely (in theory) of Amanda being the murderer than a random person in the population of the city. There is nothing wrong with at least considering her a person of interest initially. Of course even there, they were so heavy handed it was bad comedy - such as wiretapping.

 

[Zephyrgeist]

Who's leg do I need to dry-hump to get kicked outa' here? Clive, just WHAT did you and Dan-O do? You musta' been REAL bad...

 

[Bill Williams]

Who's leg do I need to dry-hump to get kicked outa' here? Clive, just WHAT did you and Dan-O do? You musta' been REAL bad...

LOL! A bit of an impossible request by definition. But on the other side, apparently slow-flooding the thread doesn't work either. I'm stumped.

 

[acbytesla]

I agree but it still would be more likely (in theory) of Amanda being the murderer than a random person in the population of the city. There is nothing wrong with at least considering her a person of interest initially. Of course even there, they were so heavy handed it was bad comedy - such as wiretapping.

I agree with that in principle. But you can pretty much eliminate her when Raffaele says they were together. There is little reason for Amanda to kill Meredith and so much less for Raffaele. And then it gets truly absurd and stupid with Guede's involvement.

I mean seriously. This is really the dumbest most unlikely scenario. Yet some people keep arguing it.

 

[Desert Fox]

I agree with that in principle. But you can pretty much eliminate her when Raffaele says they were together. There is little reason for Amanda to kill Meredith and so much less for Raffaele. And then it gets truly absurd and stupid with Guede's involvement.

I mean seriously. This is really the dumbest most unlikely scenario. Yet some people keep arguing it.

If I was the police, I don't think I would eliminate her based on just Raffaele's say-so. Once you get a few witnesses such as the woman who he was going to give a ride, I would make her a very low possibility suspect.

The big thing is that they should have done a good job at the crime scene and simply waited on the physical evidence. Then there would have been no issues.

 

[NotEvenWrong]

I do not think the probably of Amanda murdering Meredeth would be as low as you appear to be arguing. People are most often murdered by somebody they know.

Based on that, Amanda would start as a reasonably high priority along with her other roommates, "the virgins", her boyfriend, etc. Amanda would still be a relatively low probability but nothing like what you argue.

I did not pay much attention to the headlines at first except that some American woman was accused of murdering her roommate in Italy. I shock my head, figuring that they just got into a fight over a boyfriend or something. That happens more often than one would like.

I only meant 1/N as a starting point. You could (should) adjust up based on the fact they knew each other and lived together. But you would also have to adjust way way down for the team-up murder scenario with the random burglar they didn't know. This is solely for the prior.

The inference updates based on the evidence comes after and would dramatically changes the posterior probability. (adjusted up for the Rudy by himself hypothesis since he was the only person to leave actual empirical [non-contaminated] evidence behind. Down for Amanda/Raf since it is impossible to commit a violent murder as described by the prosecution and not leave evidence behind of two people yet leave tons for the third; i.e. the "selective cleanup" is impossible in practice because you can't see DNA deposits.)

 

[NotEvenWrong]

Oh and just for clarity, I am only comparing the scenarios of Rudy by himself vs. Rudy team-up murder/rape/manga vampire orgy with Amanda and Raf.

You could of course (initially, prior to looking at any evidence) consider the Amanda by herself and Raf by himself as separate possibilities. That's a separate analysis though and one the prosecution didn't put forth as the competing hypothesis is Rudy+Amanda+Raf together. The priors for these (as you said) would be much higher. It was just ruled out early on because of Amanda's alibi and the fact they found evidence of Rudy everywhere. So they had to postulate the team-up scenario, otherwise they had to (gasp!) admit they were wrong and not jail two innocents.

 

[Grinder]

While it is true that most homicides by far are committed by someone acquainted with the victim, it is much less so when the acquaintance is brief. I think your going to find this is in fact extremely rare when they have known each other less than 2 months.

I believe if we were to apply Bayesian logic where 1/n is the formula and n = infinity the chance of the statement being obviously wrong is a priori.

 

[Vixen]

Deleted.

 

[acbytesla]

If I was the police, I don't think I would eliminate her based on just Raffaele's say-so. Once you get a few witnesses such as the woman who he was going to give a ride, I would make her a very low possibility suspect.

The big thing is that they should have done a good job at the crime scene and simply waited on the physical evidence. Then there would have been no issues.

I pretty much would have. Raffaele had known Amanda a week. He has no history that would make you think he'd cover for a killer. Amanda is an unlikely killer and Raffaele makes it doubly so. In fact, when you think about it, it is far more likely that Filomena's long time boyfriend would cover for Filomena than Raffaele covering for Amanda.

Sure, if some real evidence comes to light then you revisit it, but there was none really.

 

[query grind]

Exactly. It's not that "a priori probability" is wrong per se - it's that one always refers to a Bayesian prior, and not a "Bayesian a priori (probability)".

It's a bit like saying that Novak Djokovic won the All England Lawn Tennis Club Single Handed Championship of the World in 2015. Nobody would say that, even though it's technically "correct". Rather, they'd say that he won Wimbledon

As far as it goes a search across google books finds around 50 mentions of the phrase "Bayesian a priori probability" and around 400 mentions of "Bayesian prior probability". The Google scholar ratio is similar. So it seems Anglicised version has not totally pushed out the Latin usage yet.

Vixen comes across as something of an intellectual name-dropper, but I don't feel any reason to doubt her claim to statistical literacy - for what its worth.

And since my great grandmother was the love child of Charles Babbage and Ada Byron and once beat 7 chess grandmasters in parallel blindfolded and using only extra-sensory perception, I think you can take my word for it.

As far as it goes, I don't think Sollecito's DNA on the bra clasp can be securely considered LCN - and LCN is generally applied to the entire sample and not individual components.

The quantification for the sample was 110 pg/microliter - assuming resuspension in 50 microliters, that makes 5.5 micrograms. I don't think one can safely conclude that Sollecito's DNA makes up less than 1/30th of the mixture, particularly if you consider the possibility his DNA was spiked in after quantification (which if you accept falsification would have been when such an event took place)!

On the Y profile his peaks are by far the strongest and reach quite respectable RFU heights.
Professor Budowle makes the point that these definitions are a bit arbitrary and that don't really capture when LCN issues become concerning:

The value will change with technology and genetic markers typed and the 200-pg threshold therefore will not necessarily apply to all systems. More likely, a heterozygote peak height imbalance ratio may be a better criterion for a stochastic threshold. The stochastic threshold values need to be determined within the laboratory through proper validation studies for each system

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2702736/
And on the Y profile Sollecito's peaks are well out of the zone where heterozygote peak height imbalance is a concern - although obviously there is heterozygosity on the Y chromosome.
Sollecito's peaks are lower on the autosomal typing because there is competition for primers with Kercher's DNA, but this isn't grounds for calling it either LCN or unreliable.
For example, on the vaginal or misreported oral swab, Guede's autosomal peaks are non-existent, but are perfectly strong on the Y profile and we don't say that is LCN or unreliable.

 

[Zephyrgeist]

As far as it goes a search across google books finds around 50 mentions of the phrase "Bayesian a priori probability" and around 400 mentions of "Bayesian prior probability". The Google scholar ratio is similar. So it seems Anglicised version has not totally pushed out the Latin usage yet.

Vixen comes across as something of an intellectual name-dropper, but I don't feel any reason to doubt her claim to statistical literacy - for what its worth.

And since my great grandmother was the love child of Charles Babbage and Ada Byron and once beat 7 chess grandmasters in parallel blindfolded and using only extra-sensory perception, I think you can take my word for it.
As far as it goes, I don't think Sollecito's DNA on the bra clasp can be securely considered LCN - and LCN is generally applied to the entire sample and not individual components.

The quantification for the sample was 110 pg/microliter - assuming resuspension in 50 microliters, that makes 5.5 micrograms. I don't think one can safely conclude that Sollecito's DNA makes up less than 1/30th of the mixture, particularly if you consider the possibility his DNA was spiked in after quantification (which if you accept falsification would have been when such an event took place)!

On the Y profile his peaks are by far the strongest and reach quite respectable RFU heights.
Professor Budowle makes the point that these definitions are a bit arbitrary and that don't really capture when LCN issues become concerning:

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2702736/
And on the Y profile Sollecito's peaks are well out of the zone where heterozygote peak height imbalance is a concern - although obviously there is heterozygosity on the Y chromosome.
Sollecito's peaks are lower on the autosomal typing because there is competition for primers with Kercher's DNA, but this isn't grounds for calling it either LCN or unreliable.
For example, on the vaginal or misreported oral swab, Guede's autosomal peaks are non-existent, but are perfectly strong on the Y profile and we don't say that is LCN or unreliable.

Blindfold. Not Blindfolded. Wow.

7 GMs? Whom? I've probably played them, or [maybe] know someone who has. I will ask.

Whom? (7 GMs) I can't call Vixen a liar ... even though he is. Okay. I won't.

Vixen is just being funny now (easy stuff to refute).

Oh, I get it now. It is a joke. Damn, I swung, and whiffed. I accept your apology.

 

[Planigale]

As far as it goes a search across google books finds around 50 mentions of the phrase "Bayesian a priori probability" and around 400 mentions of "Bayesian prior probability". The Google scholar ratio is similar. So it seems Anglicised version has not totally pushed out the Latin usage yet.

Vixen comes across as something of an intellectual name-dropper, but I don't feel any reason to doubt her claim to statistical literacy - for what its worth.

And since my great grandmother was the love child of Charles Babbage and Ada Byron and once beat 7 chess grandmasters in parallel blindfolded and using only extra-sensory perception, I think you can take my word for it.

As far as it goes, I don't think Sollecito's DNA on the bra clasp can be securely considered LCN - and LCN is generally applied to the entire sample and not individual components.

The quantification for the sample was 110 pg/microliter - assuming resuspension in 50 microliters, that makes 5.5 micrograms. I don't think one can safely conclude that Sollecito's DNA makes up less than 1/30th of the mixture, particularly if you consider the possibility his DNA was spiked in after quantification (which if you accept falsification would have been when such an event took place)!

On the Y profile his peaks are by far the strongest and reach quite respectable RFU heights.
Professor Budowle makes the point that these definitions are a bit arbitrary and that don't really capture when LCN issues become concerning:

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2702736/
And on the Y profile Sollecito's peaks are well out of the zone where heterozygote peak height imbalance is a concern - although obviously there is heterozygosity on the Y chromosome.
Sollecito's peaks are lower on the autosomal typing because there is competition for primers with Kercher's DNA, but this isn't grounds for calling it either LCN or unreliable.
For example, on the vaginal or misreported oral swab, Guede's autosomal peaks are non-existent, but are perfectly strong on the Y profile and we don't say that is LCN or unreliable.

To be a pedant 50 x 110pg = 5500pg = 5.5ng = 0.0055 mcg.

However only 10mcl is used in the actual amplification, so the DNA content of the sample amplified would be 10 x 110pg = 1.1ng.

it is difficult to be exact about the ratio of Sollecito (and I accept Sollecito's DNA was detected) to Kercher DNA. Certainly less than 20% and greater than 10%. So the quantity of Sollecito DNA amplified and typed lies in the range 220 - 110pg.

You are correct the definition LCN DNA varies. Accepting a definition of less than 200pg then this would be LCN.

You are correct that there are particular issues around dealing with mixed DNA samples, particularly when one is greater than another. This makes the issue of LCN in the minority sample greater not less. However I repeat I accept the profile found was that of Sollecito.

This issue arose because Vixen said that the quantity of DNA was too great for the DNA to have been the result of secondary or greater transfer but must be the result of direct contact. This is an arbitrary claim by Vixen, there is no evidence in the literature that the quantity of DNA found in trace samples can define primary secondary or tertiary transfer. This is untrue. Certainly this level of transmission has been demonstrated in studies. Transfer during simulated crime scene examination has been demonstrated e.g. on gloves.
DNA transfer by examination tools – a risk for forensic casework? Forensic Science International: Genetics Volume 16, May 2015, Pages 246–254

 

[query grind]

To be a pedant 50 x 110pg = 5500pg = 5.5ng = 0.0055 mcg.

However only 10mcl is used in the actual amplification, so the DNA content of the sample amplified would be 10 x 110pg = 1.1ng.

it is difficult to be exact about the ratio of Sollecito (and I accept Sollecito's DNA was detected) to Kercher DNA. Certainly less than 20% and greater than 10%. So the quantity of Sollecito DNA amplified and typed lies in the range 220 - 110pg.

But my understanding was that your concern with LCN was not the amplification (which you can see from the EPGs was perfectly satisfactory), but because of the ease of inadvertent transfer.

Hence you have to consider the entire sample, not the fraction that Stefanoni chose to amplify. In which case there was somewhere between 0.5 ng and 1 ng of Sollecito's DNA.

 

[Planigale]

But my understanding was that your concern with LCN was not the amplification (which you can see from the EPGs was perfectly satisfactory), but because of the ease of inadvertent transfer.

Hence you have to consider the entire sample, not the fraction that Stefanoni chose to amplify. In which case there was somewhere between 0.5 ng and 1 ng of Sollecito's DNA.

Yes.

We will never know the absolute amount of Sollecito's DNA on the bra hook. If we exclude the possibility of laboratory contamination, and that the DNA was never on the hook, and assume the DNA was on the hook. The amount of DNA is defined relative to the amount extracted and typed. If a larger amount of DNA was present initially, then a larger amount would be extracted and the amount typed would not be LCN. That the amount typed (admittedly only a fraction of the total DNA on the hook) was small, means the amount originally present was small. In the studies of trace DNA transfer, this would fit with the amounts found by secondary or greater transfer. There is a standard process of extraction to 50mcl, quantifying, then typing if DNA present. The concentration of Sollecito DNA in the extract would be about 10 - 20mcg/l. (I use these units as easier to imagine, a grain of sugar is about a milligram, so imagine the DNA is the equivalent of 1/50 th of a grain of sugar in a litre (or for our US colleagues say in a quart). Then 10mcl of this extract is used in typing. This is fairly standard and so quantities found can be compared by the amount in the proportion assayed as the proportion is the same.

Anyway the point is the original amount was relatively small.