UK court rules against use of Bayes' Theorem

I'm a little surprised at the "trials shouldn't be decided on probabilities anyway" arguments. It's not as if all available data is plugged into an obscure equation and if the result is > 50% guilty, you get convicted.

As it is applied, like in the example case in the article, it's to judge the legitimacy of forensic evidence. Of course we don't have the numbers here, but it's possible that there is a comparatively high probability that someone else than the defendant might have left the same shoeprints, given the abundance of that shoe profile. This is in my opinion a completely valid way to cast reasonable doubt on this kind of evidence.

Now, such arguments are usually only used when there is a notably high probability involved, and I doubt that Nike's sales figures are that inaccurate to distort the result by whole magnitudes. Also, I don't think the consulted expert took Nike's sales figures for granted and immediately went to calculating - there are methods to deal with the insecurity here as well.
 
Almost every trial can be summed up as "is the probability that person A did it great enough that we can say they did it". It's almost impossible to say with complete certainty that a specific person committed a crime.

probable cause is not equivalent to moral certainty or proof beyond reasonable doubt. probably cause is a standard of proof used for preliminary matters like the issuance of warrants and indictments but not for arriving at a final criminal conviction.

if the best that a jury or a judge can come up with is that the accused is probably guilty of the crime...acquittal must follow necessarily.
 
probable cause is not equivalent to moral certainty or proof beyond reasonable doubt. probably cause is a standard of proof used for preliminary matters like the issuance of warrants and indictments but not for arriving at a final criminal conviction.

if the best that a jury or a judge can come up with is that the accused is probably guilty of the crime...acquittal must follow necessarily.

That's childish pretending. Since none of us are omniscient it always comes down to "almost certainly". This is just a bid to avoid quantifying "reasonable doubt".
 
probable cause is not equivalent to moral certainty or proof beyond reasonable doubt. probably cause is a standard of proof used for preliminary matters like the issuance of warrants and indictments but not for arriving at a final criminal conviction.

if the best that a jury or a judge can come up with is that the accused is probably guilty of the crime...acquittal must follow necessarily.

The probability that the person committed the crime needs to be extremely high to say they did it, but it's still a probability. The evidence used is intended to increase and decrease these probabilities in the minds of the judge and jury. It is practically impossible to completely prove that someone is guilty, hence the use of "beyond reasonable doubt".
Just for an example, 99% certainty that they did it is still an unacceptably high risk of making a mistake IMO.
 
The probability that the person committed the crime needs to be extremely high to say they did it, but it's still a probability. The evidence used is intended to increase and decrease these probabilities in the minds of the judge and jury. It is practically impossible to completely prove that someone is guilty, hence the use of "beyond reasonable doubt".
Just for an example, 99% certainty that they did it is still an unacceptably high risk of making a mistake IMO.

evidence does not increase and decrease the probability of a person's guilt, which is perfectly okay because probability of guilt is not what you should be after. the prosecutor's duty is to remove all reasonable doubt while the defense's is to sow any and all doubt.

technically evidence simply proves or makes less or more probable the existence of a disputed fact or the factum probans (Wigmore).

only after proof of the existence of these facts can the factum probandum or the ultimate fact/proposition i.e. the guilt of the accused be finally established. at this point, the judge or juror must travel that long road from proven facts to whatever inference can be made from these facts. and, relying solely on common human experience, reason and logic the judge or juror decides a person's guilt.

i think what happened here was that the judge rejected the statistics for the reason that its evidentiary value is low and the possible inferences of guilt that may be derived from it might be infirm.

but i think the judge was wrong to exclude statistics even when offered as circumstantial evidence only. his rejection is simply a result of his ignorance and perhaps hostility to good math, and a misstep in his duties as a judge.

also, the article did mention something about prosecutor's fallacy. as far as factum probans and factum probandum go, the judge mistook the statistics to be proof and probability of guilt of the accused, rather than as proof and probability of the truth respecting a certain fact in issue.
 
evidence does not increase and decrease the probability of a person's guilt, which is perfectly okay because probability of guilt is not what you should be after. the prosecutor's duty is to remove all reasonable doubt while the defense's is to sow any and all doubt.

technically evidence simply proves or makes less or more probable the existence of a disputed fact or the factum probans (Wigmore).

only after proof of the existence of these facts can the factum probandum or the ultimate fact/proposition i.e. the guilt of the accused be finally established. at this point, the judge or juror must travel that long road from proven facts to whatever inference can be made from these facts. and, relying solely on common human experience, reason and logic the judge or juror decides a person's guilt.

i think what happened here was that the judge rejected the statistics for the reason that its evidentiary value is low and the possible inferences of guilt that may be derived from it might be infirm.

but i think the judge was wrong to exclude statistics even when offered as circumstantial evidence only. his rejection is simply a result of his ignorance and perhaps hostility to good math, and a misstep in his duties as a judge.

also, the article did mention something about prosecutor's fallacy. as far as factum probans and factum probandum go, the judge mistook the statistics to be proof and probability of guilt of the accused, rather than as proof and probability of the truth respecting a certain fact in issue.

Ultimately, the judge or jury makes a decision on a person's guilt based on how probable it is that they did it. They cannot know with utmost certainty whether they did it or not, so they must reach a point in their thinking where they decide the probability that they did not do it is so low that it can be discarded.
 
Ultimately, the judge or jury makes a decision on a person's guilt based on how probable it is that they did it. They cannot know with utmost certainty whether they did it or not, so they must reach a point in their thinking where they decide the probability that they did not do it is so low that it can be discarded.

again, it's not about probability of guilt, but reasonable doubt of guilt. the judge could say "there's a 99% chance that the person is guilty", but if the judge remains 99% morally uncertain then there's nothing left to do but acquit. that's it.

to convict based on how probable it is that a person did it is to commit the prosecutor's fallacy. i think the article explains the issue in more detail, too bad the important parts were cut out in the OP.
 
I'm a little surprised at the "trials shouldn't be decided on probabilities anyway" arguments. It's not as if all available data is plugged into an obscure equation and if the result is > 50% guilty, you get convicted.

As it is applied, like in the example case in the article, it's to judge the legitimacy of forensic evidence. Of course we don't have the numbers here, but it's possible that there is a comparatively high probability that someone else than the defendant might have left the same shoeprints, given the abundance of that shoe profile. This is in my opinion a completely valid way to cast reasonable doubt on this kind of evidence.

Now, such arguments are usually only used when there is a notably high probability involved, and I doubt that Nike's sales figures are that inaccurate to distort the result by whole magnitudes. Also, I don't think the consulted expert took Nike's sales figures for granted and immediately went to calculating - there are methods to deal with the insecurity here as well.
There were apparently good reasons to suspect the conclusions reached by this particular "expert". The legal pundits seem to agree on that.

http://www.slaw.ca/2011/10/12/proba...r-uk-court-case-bars-bayes-and-raises-ruckus/

To put it shortly, the expert presenting this evidence did it badly, and the data he used to form his estimate of probability were less than precise. No commentator has suggested that the Court of Appeal’s conclusion in the instant case was wrong. However, the Court went further and anathematized the use of Bayes’ Theorem, the mathematical tool commonly used by scientists to calculate “likelihood ratios”. Paragraph 90 contains this fatal phrase:

It is quite clear therefore that outside the field of DNA (and possibly other areas where there is a firm statistical base), this court has made it clear that Bayes theorem and likelihood ratios should not be used.

As the recent story in The Guardian relates, barring Bayes has led to a strong reaction from the scientific and mathematics communities and the formation of a group of more than 60 members aimed at explicating and defending the use of probabilistic reasoning in the criminal courts. As they say on their main page:

Proper use of probabilistic reasoning has the potential to improve the efficiency, transparency and fairness of criminal trials by enabling the relevance of evidence – especially forensic evidence – to be meaningfully evaluated and communicated. If more widely and effectively used, it could lead to fewer cases being revisited by the Court of Appeal.
While it is interesting, while not very surprising, that a Court of Appeals doesn't understand all that much about statistics, I'm sure they will be properly educated and this part of the decision will be rectified.
 
again, it's not about probability of guilt, but reasonable doubt of guilt. the judge could say "there's a 99% chance that the person is guilty", but if the judge remains 99% morally uncertain then there's nothing left to do but acquit. that's it.

to convict based on how probable it is that a person did it is to commit the prosecutor's fallacy. i think the article explains the issue in more detail, too bad the important parts were cut out in the OP.

It's not the judge/jury assigning a probability to how likely the person did it, it's the judge/jury determining, based on the evidence given, how certain they are that the person did it. Reasonable doubt is there to discard alternatives that are extremely unlikely to have occurred. Making decisions based on incomplete information, which judges/juries do on a daily basis, relies on using probability, whether you like it or not.
 
It's not the judge/jury assigning a probability to how likely the person did it, it's the judge/jury determining, based on the evidence given, how certain they are that the person did it. Reasonable doubt is there to discard alternatives that are extremely unlikely to have occurred. Making decisions based on incomplete information, which judges/juries do on a daily basis, relies on using probability, whether you like it or not.

if a decision went that way, according to how you outlined it, i'd probably appeal the judgment and i probably will win.
 
Using your logic, no one could ever be convicted.

why not? my idea is not original. it has been around for at least 300 years and is still being used today. the modern rules of evidence have not changed, and Wigmore's idea are very much a staple currency in courts.
 
why not? my idea is not original. it has been around for at least 300 years and is still being used today. the modern rules of evidence have not changed, and Wigmore's idea are very much a staple currency in courts.

You're arguing that you must have complete certainty that someone committed the crime to convict them. That is practically impossible to attain. The inherent uncertainty means that you're using probabilities to make a decision, whether you realise it or not.
 
You're arguing that you must have complete certainty that someone committed the crime to convict them. That is practically impossible to attain. The inherent uncertainty means that you're using probabilities to make a decision, whether you realise it or not.

No, that's not what I said. you confuse complete certainty with moral certainty. moral certainty means that having convicted a person for a crime the judge or juror can still sleep at night peacefully so to speak.

like i said before, 100% probability of guilt of a person is not even enough to say that he is guilty based on a single piece of evidence alone. you have to be 100% sure that he is guilty and this could be based on logic, reason and common sense. it could be gut sure, instinct sure, or sure because you can sense the guilty demeanor of the person on the stand.

thus, even if the DNA evidence establishes a 99.9 probability of guilt of an accused, if the chain of custody was irregular, for instance, then the judge's mind cannot possibly rest easy on convicting the accused. but if the judge ignores the chain of custody principle and says that it is highly unlikely that someone else, with an identical DNA could have done the crime, that is clear error. this is basically the gist of the OP and what the judge did but only in reverse or the opposite.
 
While it is interesting, while not very surprising, that a Court of Appeals doesn't understand all that much about statistics, I'm sure they will be properly educated and this part of the decision will be rectified.
Okay, that puts things into a different light of course. If the statistician screws up, it's his fault, not his method's. It would be like stopping DNA tests because one sample was mixed up.
 
No, that's not what I said. you confuse complete certainty with moral certainty. moral certainty means that having convicted a person for a crime the judge or juror can still sleep at night peacefully so to speak.

like i said before, 100% probability of guilt of a person is not even enough to say that he is guilty based on a single piece of evidence alone. you have to be 100% sure that he is guilty and this could be based on logic, reason and common sense. it could be gut sure, instinct sure, or sure because you can sense the guilty demeanor of the person on the stand.

thus, even if the DNA evidence establishes a 99.9 probability of guilt of an accused, if the chain of custody was irregular, for instance, then the judge's mind cannot possibly rest easy on convicting the accused. but if the judge ignores the chain of custody principle and says that it is highly unlikely that someone else, with an identical DNA could have done the crime, that is clear error.

I suspect there is a difficulty in understanding each other here. What you refer to as moral certainty is what I'd refer to as being the lowest possible probability the judge/juror would accept to convict the person. I'm not talking about single pieces of evidence proving anyone did a crime.

You say in your last paragraph "even if the DNA evidence establishes a 99.9% probability of guilt". As far as I'm aware, DNA evidence cannot establish a 99.9% probability of guilt. It can put the accused at the scene of a crime, or establish a link between the accused and an object, but it alone cannot prove that someone committed a crime. What should be said is that the DNA evidence makes it highly likely that a person with that DNA was in that area/used that object/etc.
 
I suspect there is a difficulty in understanding each other here. What you refer to as moral certainty is what I'd refer to as being the lowest possible probability the judge/juror would accept to convict the person. I'm not talking about single pieces of evidence proving anyone did a crime.

You say in your last paragraph "even if the DNA evidence establishes a 99.9% probability of guilt". As far as I'm aware, DNA evidence cannot establish a 99.9% probability of guilt. It can put the accused at the scene of a crime, or establish a link between the accused and an object, but it alone cannot prove that someone committed a crime. What should be said is that the DNA evidence makes it highly likely that a person with that DNA was in that area/used that object/etc.

why the hang up on probability? if you're "not talking about single pieces of evidences proving anyone did a crime" then what's this talk on probability about?

the point of the article was that it was wrong for the judge to excluded the theorem as circumstantial evidence all because he did not believe or was not convinced that it was enough to show the probable guilt of the accused---can you see what's wrong there?
 
A person must never be convicted based on statistical probability.
All court cases are decided based on probability. There is no rule as to what probability determines resonable doubt, but every judge and/or juror makes the decision on their own based on what they believe it means and what is acceptable to the individual. On the other hand with civil cases, it simply comes downto which side has the greater probability.

Fingerprints are not statistical probabilities. They are flat out unique. Until they are shown to not be unique, it is fine to use them.
While they may be unique, the people comparing fingerprints use probability. They check a number of points of comparison and determine the probability that they are overall from the same person given that those points match. This is even more true when the samples aren't perfect (which is pretty common).

No, that's not what I said. you confuse complete certainty with moral certainty. moral certainty means that having convicted a person for a crime the judge or juror can still sleep at night peacefully so to speak.
So, to convict the probability that the individual is innocent must be small enough to giver the decision maker moral certainty.

It all comes down to probability.
 
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