Continuation Part 14: Amanda Knox/Raffaele Sollecito

[katy_did]

I don't understand your argument here at all.

I am saying that while I think it's possible to construct a mathematical model that could output a "correct" verdict in a criminal trial, it would require an astonishingly complex set of inputs in order to replicate human reasoning. Therefore, for practical purposes as of 2015, I believe it's impossible to construct a sufficiently robust mathematical model to do this job (and I suggest that the modelling may have to be so complex as to require the use of things such as AI, fuzzy logic and quantum computing.

Look: you can build a mathematical model that will accurately tell you the real-world probability (and standard deviations etc) of pulling three blue balls in a row out of a sack that originally contained 20 blue balls and 20 red balls. And if you actually conduct that experiment in the real world a whole bunch of times, the real-world results you get will converge towards the results predicted by the model.

But imagine another scenario. If you're a heterosexual male, you probably glance at women sometimes in the street or in a store or on public transport, and you make a pretty instant assessment of whether you find that woman physically attractive. Your input into that process is usually no more than your vision. For the sake of this argument, imagine that in your head you might be grading any particular woman on a scale from 1 to 5, with 1 being not at all attractive to you, and 5 being wow, super attractive to you.

So imagine now that you are trying to build a computer model that could take the same input - a still or moving image of a woman - and accurately model whether or not you would find that woman physically attractive and where on the 1-5 scale you would place her. Stop and think about that. This is something that you can do in your head pretty instantly. But even though you don't realise it, there are a truly astonishing number of highly nuanced (and often abstract) thought processes going on in that split second before you reach your decision. The precise (and minutely differing) position and size of the woman's eyes, nose, mouth etc. The way she wears her hair. What you can discern of her physical body type (which would include complex understanding of how clothes hang on a body, how they reflect the underlying body type, how they can disguise body type). More abstract things still, such as the way the woman "carries herself". A comparison between the woman and other women whom you find attractive (or not). Society's definitions of what constitutes "physical attractiveness" in a woman*

This is an incredibly complex set of operations being carried out inside your mind in a split second. Most of these operations are extremely difficult to translate into a mathematical form, and some of them are mind-blowing difficult to translate into a mathematical form. I therefore propose that it would be nigh-on impossible for anyone today to build a mathematical model that came anywhere even close to accuracy in mirroring/predicting how you would rate the physical attractiveness of any given woman, based on the single input of a still or moving image of that woman.

That's what I'm trying to say here.



* For example, in Europe during the Renaissance, the prevailing cultural norm among the higher social classes was that the most beautiful women had a body type that we would now classify as very overweight or obese (i.e. "Rubenesque"). And that would have obviously impacted heavily on how a given person at that point in history would have rated the physical attractiveness of a given woman that he saw.....

LJ, I think you're both missing the point and over-complicating things here. Any decision to convict or acquit someone, or to accept or reject a piece of evidence, should be possible to explain logically. You should be able to state your reasons and the weight you attached to each particular factor. One of those factors might be that a witness came across well when they testified, and there's nothing to stop you adding that factor into the mix and assigning it a particular level of importance - although given that people are notoriously bad at detecting when someone is lying, it probably should be given a pretty low level of importance.

We're not trying to create a theory of everything here; there's no need to set out all the various factors in your history and genetics that have led you to the point where you decide a particular witness is lying or telling the truth. But if your argument is largely based on subjective impressions, then that should be taken into account when deciding how much weight to give it.

You keep mentioning translating things into "mathematical form" but that's not really the issue you're addressing, is it? You're suggesting these things are too complex to address in any form, whether it be language or figures or whatever. I disagree that in the context of a court case, the reasoning behind whether to convict or acquit can't be expressed in clear, logical terms, that it shouldn't be based on things which are concrete and measurable rather than subjective impressions.

 

[LondonJohn]

LJ, I think you're both missing the point and over-complicating things here. Any decision to convict or acquit someone, or to accept or reject a piece of evidence, should be possible to explain logically. You should be able to state your reasons and the weight you attached to each particular factor. One of those factors might be that a witness came across well when they testified, and there's nothing to stop you adding that factor into the mix and assigning it a particular level of importance - although given that people are notoriously bad at detecting when someone is lying, it probably should be given a pretty low level of importance.

We're not trying to create a theory of everything here; there's no need to set out all the various factors in your history and genetics that have led you to the point where you decide a particular witness is lying or telling the truth. But if it's largely based on subjective impressions, then that should be taken into account when deciding how much weight to give it.

You keep mentioning translating things into "mathematical form" but that's not really the issue you're addressing, is it? You're suggesting these things are too complex to address in any form, whether it be language or figures or whatever. I disagree that in the context of a court case, the reasoning behind whether to convict or acquit can't be expressed in clear, logical terms, that it shouldn't be based on things which are concrete and measurable rather than subjective impressions.

No - the entire background to this issue was whether it was possible to use Bayesian maths within a mathematical model to accurately model an overall verdict in a criminal trial. Not language. Cold, hard maths. Numbers.

And my opinion is that yes it's possible in principle. But in practice the astonishing size and amount of complexity (including fuzzy logic, almost certainly) that would be necessary to translate much of human reasoning into cold, hard numbers make it practically impossible.

The reason I'm "complicating it" is the whole point. It's too complicated to model accurately with mathematical concepts.


So let's get back to the actual question here. Do you think that it is practically possible to translate all the factors driving human reasoning into numbers and associated mathematical equations, to the degree that you can build a model capable of accurately outputting the "correct" verdict to a trial (or the correct relative probabilities of various possible outcomes to a trial)? Let's start with whether you think the answer to that question is yes or no. If it's no, then we agree. If it's yes, I then invite you to consider how difficult it would be to mathematically model many concepts and thought processes involved in human reasoning. And as a starting example, I'd ask you to consider the example I gave earlier: how could one build a mathematical model to predict how I (or any given person) would rate the physical attractiveness of (in my case) any given women I saw?

 

[LondonJohn]

I might also point out, by the way, that I'm a big fan of (and very familiar indeed with the use of) maths and numerical reasoning to solve problems. I am scientific by training and by thinking.

But when mathematicians, computer scientists and engineers can only barely find a way in 2015 to model the processes necessary to enable a human-body-shaped form to run and jump in proper balance, I propose that it's currently practically impossible for anyone to model the processes necessary for a human to decide the guilt or non guilt of another human being (unless there is a very small number of essentially binary decisions involved in that process - e.g. the suspect's DNA from his semen was found all over the victim's body, and the suspect claimed he'd never even met the victim....).

 

[carbonjam72]

"In Italy, if no one dies, no one is held accountable" - M

Not going to happen. While I think Mignini is despicable, a creep and certainly guilty of over reaching, I don't see how anyone can prove that he committed a crime.

Rudy's case file is still under seal. Suppose its opened, and Rudy's interview with Mignini when he first got back from Germany (Dec 2007 - before he interviewed Amanda in Dec 2007)) is on tape or video, and Rudy says again, "Amanda wasn't there", and "Raf who?".

Shouldn't Mignini have turned that over to the defense?

I think this is one of the points of disagreement we have, and it relates purely to point of view of how things actually work in Italy, and indeed, many places.

You're suggesting the only basis for charges being brought, is by strict adherence to the letter of the law. I'm suggesting the law is a vehicle to accomplish the objectives of the people who wield it.

When Mignini and Giuttari were brought up on charges for abuse of office, was that the worst of their crimes? Is that really WHY they were prosecuted?

Or was it because Mignini and Giuttari had just made fools out of the entire judiciary by imprisoning Mario Spezi, drawing international condemnation in a campaign initiated by Douglas Preston, and joined in by the whole of the Italian media. It was an absolute fiasco. And someone had to pay.

With Mignini and Giuttari, they picked the right two guys. Because these Narducci trail charges which ensnared Spezi, was all about the two of them pursuing Giuttari's fraudulent hoax that a satanic sect was responsible for the Monster of Florence killings.

So I think the nature of the charges placed, were incidental to the fact that they were going to be charged with something.

I think when they decide to charge someone, there are any number of charges to choose from. One gets the sense it could happen to any official when their number comes up.

So, one more prediction to be tested. This is harder to predict, whether Mignini actually winds up in jail.

I'd be surprised if no one ends up going to jail. Because if no one ends up in jail, it means the system worked fine.

I guess we'll see. I just think you're underestimating the need to "make someone pay". An earthquake killed people, someone had to pay, so they convicted scientists for failing to predict it. Mach says that in Italy, if no one dies, no one is held accountable.

 

[carbonjam72]

By the way, was the charge in the recent April 27 2015 verdict, of staging a break-in, found AK/RS to not have committed the crime, because the crime does not exist?

If so, then it implies Rudy committed an actual break-in. I would suggest that means cassation will find Rudy acted alone.

 

[Kaosium]

delete

 

[Planigale]

Wow. "Thoughtful" has just given an excellent demonstration of why maths can have massive shortcomings in the real world of assessing guilt. I urge everyone to read her example.

To summarise, she's imagining a man accused of murdering a woman. At this point (although she's coy about clarifying this), there might as well be zero evidence pointing to the man. And she posits that the imaginary jurors will have formed their own probabilities of the guilt of the man (which logically could range from 0% to 100%).

Now she imagines a single new piece of evidence emerging. A bloody handprint, which clearly was made by the killer. She imagines that this print matches 1 in 100 of the population, including the accused man.

She then uses Bayesian maths to show that this single piece of evidence should (by sheer statistical calculations alone....) serve to raise every juror's assessment of the probability of the guilt of the man to something not far off certainty: someone who previously adjudged the probability of guilt at 10% "should" now judge it at 91%!! Someone who had previously judged guilt at 50% "should" now judge guilt at 99%!!

If ever a single post served to illustrate the massive shortcomings of pure Bayesian reasoning in this sort of real-word situation, it's this post of "Thoughtful's". It takes no account whatsoever of many crucial factors that also go into the real-world assessment of guilt. What about the potential for the absence of evidence that "should" be there if this man is the real killer? What about population spreads? After all, if the murder happened on a tiny remote island of 50 inhabitants, this would affect the value of the handprint evidence dramatically compared with the murder happening in a city of 5 million inhabitants. And what about the sheer basic stupidity of the mathematical outcomes here in a real-world assessment? Really? One single item of evidence that is shared by 1 in every 100 people, including the accused man, can serve - all on its own - to raise an assessed probability of guilt from 10% to 91%?! Really?!!!!!

Seriously. Read it. And weep. But not in the way that "Thoughtful" would like you to weep..............

not read the post. But it makes a real difference whether the accused was suspected prior to finding the evidence, in which case she is right. What is wrong is using the evidence to identify a suspect amongst a group, then saying this is the chances of not being guilty. So if you have a characteristic say red hair only present in 1:100 of the population, picking on the nearest gingertop and saying there is only 1:100 chance that they're innocent is wrong.

The problem with Bayesian maths is your priors. The problem with the red hair (or equivalent) is how strong the association is with the murderer. So was the red hair on the victim incidental or associated with the murderer. If the red hair was in the hair ribbon used to strangle the victim that is one thing, on her skirt when she'd been to the hairdresser earlier that day is completely different.

 

[LondonJohn]

not read the post. But it makes a real difference whether the accused was suspected prior to finding the evidence, in which case she is right. What is wrong is using the evidence to identify a suspect amongst a group, then saying this is the chances of not being guilty. So if you have a characteristic say red hair only present in 1:100 of the population, picking on the nearest gingertop and saying there is only 1:100 chance that they're innocent is wrong.

The problem with Bayesian maths is your priors. The problem with the red hair (or equivalent) is how strong the association is with the murderer. So was the red hair on the victim incidental or associated with the murderer. If the red hair was in the hair ribbon used to strangle the victim that is one thing, on her skirt when she'd been to the hairdresser earlier that day is completely different.

I think the real problem with Bayesian maths is in getting it to represent the real world accurately in complex scenarios.

As I said earlier, a relatively simple problem, such as the probability of pulling four blue balls in a row out of a bag of 20 red and 20 blue balls, can be easily modelled using Bayes and conditional logic. The model will indeed predict with very high accuracy the real-world probability. But this is obviously a self-contained problem with no "soft" factors. When it comes to problems where there are a large number of impacting variables and situational factors, some of which are abstract, then it gets exponentially more difficult to build an accurate mathematical model.

And incidentally, all of those things you mention in your complicating factors to your "red hair" could be factored into the model - but the problem is that it would actually take a huge amount of mathematics to represent them accurately. In the same way, when I pointed out that a match that is shared by 1 per 100 of the population occuring in a closed community of ten people is far more significant than the same match occurring in a city of five million people, that can also be modelled. But it immediately becomes a much more complicated model as a result.

That's the problem. Bayes is just fine (in fact, it's perfect) for modelling problems with closed margins and pure (and preferably binary) sets of choices. But Bayes is absolutely not fine for modelling complex problems with myriad intricate and highly-nuanced choices, especially when some of those choices are based on abstract concepts such as human intuition, trust, learned behaviours, the vast accumulation of human observation, and so on.

 

[Planigale]

This is odd isn't it? Someone who lives by proof at work, rejects it in this case.

Isn't there an even odder poster at PMF - Greggy, I think - says he's a scientist who has a professional understanding of forensic evidence, actually rejects the probative value of the DNA evidence against Amanda and Raffaele, yet still thinks they are guilty!? Apologies to Greggy, if I've misrepresented him.

It is a mistake to assume that because people are intelligent and well educated, they always think logically. Einstein was clearly wrong on his views of quantum theory, he could not move on from classical deterministic physics. Jackie having read his CV is a well educated lawyer working for a respectable law firm. (Allbeit not a criminal lawyer).

This rather reminds me of HIV denialism. Pefectly sensible people for a variety of reasons often political denied the obvious. The Sidney group had a very specific set of criteria to 'prove' HIV caused AIDS. (Koch's criteria). This was reminiscent of Jackie's requirement to prove tertiary transmission. Even once this was proved, although a predefined criteria this failed to alter his view. Which is perfectly normal, humans defend their pre conceived views robustly. What i found interesting was when I said I saw similarities with Intelligent Design, Briars defended ID; Mach obviously favours the Sidney view of AIDS. Jackie I suspect will think Climate change is part of a neoliberal agenda (the latter is pure fantasy on my part and I apologise to Jackie if he is Prius driving vegetarian who votes Democrat).

 

[LondonJohn]

By the way, was the charge in the recent April 27 2015 verdict, of staging a break-in, found AK/RS to not have committed the crime, because the crime does not exist?

If so, then it implies Rudy committed an actual break-in. I would suggest that means cassation will that find Rudy acted alone.

Well, logically speaking, not necessarily. The court might have decided that Guede and others broke in.

I just have a suspicion that the SC will somewhat "fudge" this issue by adjusting the previous SC Guede ruling, to the effect that Guede could have committed the crime either alone or with others - that the evidence supports either alternative - and that it's not necessary to definitively rule which of the two it was in order to safely convict Guede.

And then in the Knox/Sollecito SC verdict, the SC will similarly be able to say that the crime may have been committed by Guede along, or by Guede with others (and that either alternative is compatible with the evidence), but that it finds no evidence that Knox or Sollecito comprised some or all of those "others" if there were indeed others.

 

[MichaelB]

Amanda Knox: Moving forward, with gratitude and a purpose

http://www.seattletimes.com/opinion/amanda-knox-moving-forward-with-gratitude-and-a-purpose/

 

[LondonJohn]

Amanda Knox: Moving forward, with gratitude and a purpose

http://www.seattletimes.com/opinion/amanda-knox-moving-forward-with-gratitude-and-a-purpose/

I think that comes across as a well-pitched, sincere and entirely appropriate letter. Thanks for posting it here.

 

[acbytesla]

I don't understand your argument here at all.

I am saying that while I think it's possible to construct a mathematical model that could output a "correct" verdict in a criminal trial, it would require an astonishingly complex set of inputs in order to replicate human reasoning. Therefore, for practical purposes as of 2015, I believe it's impossible to construct a sufficiently robust mathematical model to do this job (and I suggest that the modelling may have to be so complex as to require the use of things such as AI, fuzzy logic and quantum computing.

Look: you can build a mathematical model that will accurately tell you the real-world probability (and standard deviations etc) of pulling three blue balls in a row out of a sack that originally contained 20 blue balls and 20 red balls. And if you actually conduct that experiment in the real world a whole bunch of times, the real-world results you get will converge towards the results predicted by the model.

But imagine another scenario. If you're a heterosexual male, you probably glance at women sometimes in the street or in a store or on public transport, and you make a pretty instant assessment of whether you find that woman physically attractive. Your input into that process is usually no more than your vision. For the sake of this argument, imagine that in your head you might be grading any particular woman on a scale from 1 to 5, with 1 being not at all attractive to you, and 5 being wow, super attractive to you.

So imagine now that you are trying to build a computer model that could take the same input - a still or moving image of a woman - and accurately model whether or not you would find that woman physically attractive and where on the 1-5 scale you would place her. Stop and think about that. This is something that you can do in your head pretty instantly. But even though you don't realise it, there are a truly astonishing number of highly nuanced (and often abstract) thought processes going on in that split second before you reach your decision. The precise (and minutely differing) position and size of the woman's eyes, nose, mouth etc. The way she wears her hair. What you can discern of her physical body type (which would include complex understanding of how clothes hang on a body, how they reflect the underlying body type, how they can disguise body type). More abstract things still, such as the way the woman "carries herself". A comparison between the woman and other women whom you find attractive (or not). Society's definitions of what constitutes "physical attractiveness" in a woman*

This is an incredibly complex set of operations being carried out inside your mind in a split second. Most of these operations are extremely difficult to translate into a mathematical form, and some of them are mind-blowing difficult to translate into a mathematical form. I therefore propose that it would be nigh-on impossible for anyone today to build a mathematical model that came anywhere even close to accuracy in mirroring/predicting how you would rate the physical attractiveness of any given woman, based on the single input of a still or moving image of that woman.

That's what I'm trying to say here.



* For example, in Europe during the Renaissance, the prevailing cultural norm among the higher social classes was that the most beautiful women had a body type that we would now classify as very overweight or obese (i.e. "Rubenesque"). And that would have obviously impacted heavily on how a given person at that point in history would have rated the physical attractiveness of a given woman that he saw.....

In theory it may be possible, but in practice no. This is what I am arguing. Anything can be argued with math, but that doesn't mean it is accurate. Building so called mathematical models on arbitrary events always include speculation that cannot actually have any accuracy built In. It reminds me of that old axiom, there are liars, dam liars and statisticans.

 

[RoseMontague]

In theory it may be possible, but in practice no. This is what I am arguing. Anything can be argued with math, but that doesn't mean it is accurate. Building so called mathematical models on arbitrary events always include speculation that cannot actually have any accuracy built In. It reminds me of that old axiom, there are liars, dam liars and statisticans.

This case is about common sense. The Why, When, and How make no sense for AK & RS, but all the sense in the world for RG.

 

[LondonJohn]

This case is about common sense. The Why, When, and How make no sense for AK & RS, but all the sense in the world for RG.

I'd absolutely agree with that. But over and above that, there's ample evidence to safely convict Guede (I'd argue that as few as three reliable pieces of evidence - the bloody handprint, Guede's version of events, and the evidence of his visits to the clubs in Perugia and his travel to Germany - would be sufficient to convict him safely all on their own).

It's when the "why, when and how" make no sense yet the evidence appears to suggest involvement, that one ought to take particular care to look again at the evidence. More often than not, the "evidence" turns out not to be what it first appeared. And actually, that's pretty much my personal experience in this case. I read (apparent) evidence that looked like it proved Knox and Sollecito guilty, then as I looked into the case I began to realise that common sense suggested they had nothing to do with it, and then I delved deeper and realised that the "evidence" was unreliable, incredible, or just plain made up.

 

[acbytesla]

This case is about common sense. The Why, When, and How make no sense for AK & RS, but all the sense in the world for RG.

In my experience "good common sense" isn't always good and is rarely common.

From my perspective it has more to do with the fact that a great many people are just plain stupid and the inability for society to quash misinformation after it has permeated the public conciousness. I see it like the perception that vaccines cause Autism, that Iraq was involved in the 9-11 attacks, that Obama wasn't born in the US..etc. People believe what they want to believe and usually they want to believe what they think they already know. That the Sun revolves around the Earth, that God created the heavens and the Earth.

It started with that kiss. For whatever reason it gave people, me included the heebie jeebies. But the truth is that kiss wasn't in context. But it wrongly made everyone suspicious and from that moment on everyone was trying to prove what they thought they knew instead of taking an unbiased view of the evidence.

 

[carbonjam72]

This case is about common sense. The Why, When, and How make no sense for AK & RS, but all the sense in the world for RG.

Yup. What people want explains what they do and say. (That's what my writing teachers tell me!).

Last question I have is, was Mignini honestly mistaken in thinking the break-in was staged? Or did he seize two innocent people, just because he could, and it was convenient to his professional needs at the time?

Did Mignini or others cope there, know or suspect Rudy Guede was behind the break-in right away, by recognizing his MO from prior break-ins?

 

[NotEvenWrong]

Wow. "Thoughtful" has just given an excellent demonstration of why maths can have massive shortcomings in the real world of assessing guilt. I urge everyone to read her example.

To summarise, she's imagining a man accused of murdering a woman. At this point (although she's coy about clarifying this), there might as well be zero evidence pointing to the man. And she posits that the imaginary jurors will have formed their own probabilities of the guilt of the man (which logically could range from 0% to 100%).

Now she imagines a single new piece of evidence emerging. A bloody handprint, which clearly was made by the killer. She imagines that this print matches 1 in 100 of the population, including the accused man.

She then uses Bayesian maths to show that this single piece of evidence should (by sheer statistical calculations alone....) serve to raise every juror's assessment of the probability of the guilt of the man to something not far off certainty: someone who previously adjudged the probability of guilt at 10% "should" now judge it at 91%!! Someone who had previously judged guilt at 50% "should" now judge guilt at 99%!!

If ever a single post served to illustrate the massive shortcomings of pure Bayesian reasoning in this sort of real-word situation, it's this post of "Thoughtful's". It takes no account whatsoever of many crucial factors that also go into the real-world assessment of guilt. What about the potential for the absence of evidence that "should" be there if this man is the real killer? What about population spreads? After all, if the murder happened on a tiny remote island of 50 inhabitants, this would affect the value of the handprint evidence dramatically compared with the murder happening in a city of 5 million inhabitants. And what about the sheer basic stupidity of the mathematical outcomes here in a real-world assessment? Really? One single item of evidence that is shared by 1 in every 100 people, including the accused man, can serve - all on its own - to raise an assessed probability of guilt from 10% to 91%?! Really?!!!!!

Seriously. Read it. And weep. But not in the way that "Thoughtful" would like you to weep..............

Did Thoughtful then show mathematically that the most probable explanation for the murder and bloody handprint of a single person, was a sex game gone wrong involving 3 people that didn't know each other?

 

[MDDVS]

Did Thoughtful then show mathematically that the most probable explanation for the murder and bloody handprint of a single person, was a sex game gone wrong involving 3 people that didn't know each other?

One thing's for sure, in her scenario she's using very inflated priors. The prior probability according to her scenario should be very close to zero, not 10%.

 

[Bill Williams]

I might also point out, by the way, that I'm a big fan of (and very familiar indeed with the use of) maths and numerical reasoning to solve problems. I am scientific by training and by thinking.

But when mathematicians, computer scientists and engineers can only barely find a way in 2015 to model the processes necessary to enable a human-body-shaped form to run and jump in proper balance, I propose that it's currently practically impossible for anyone to model the processes necessary for a human to decide the guilt or non guilt of another human being (unless there is a very small number of essentially binary decisions involved in that process - e.g. the suspect's DNA from his semen was found all over the victim's body, and the suspect claimed he'd never even met the victim....).

With all due respect, LJ, I believe you are misrepresenting what this is all about - as is Thoughtful.

It's like criminal profiling. Criminal profiling does not solve crimes. What it does is help investigative agencies narrow avenues of inquiry when they are stuck. It is a way of focussing resources on the most probable of avenues - but, and there's a huge but, it is not meant to be determinative.

It's like the Myers-Briggs personality inventory. MBTI tests were developed mainly during WWII to help slot people into jobs somewhat related to their psychological temperments. However, this was an ass-backwards way of applying the Myers-Briggs/Jungian theories.... because "type" was not necessarily related to success or ability to do any one job.

The classic response, for instance, to someone who comes to an MBTI administrator with a question is never, ever to assume it is predictive. For instance if someone is a jazz-saxophonist, no reputable MBTI administrator would ever encourage/discourage someone from pursuing it based on type. However, a reputable MBTI administrator might make a good guess as to what each type might enjoy differently about being a jazz saxophonist.

With all due - I believe this is the basic mistake you are making with this Bayesian stuff. Expert systems always claim to be able to increase the likelihood of being able to short-track decision making. Whereas there can be some successes in very simple tasks, knowledge acquisition is the big stumbling block.

In short, behind Thoughtful's bogus application of Bayesian math to the overly complex reality of evidence in a murder... is the problem build in from the start - garbage in, garbage out.

http://en.wikipedia.org/wiki/Knowledge_acquisition