I’m moderately familiar with the case (have read a few media articles on the case over the last few months).
10% (weak evidence, lack of motive, low prior probability of female on female sexually motivated violence)
30% (evidence not much better, higher prior probability of male on female sexually motivated violence)
50% (seems to fit profile of this type of offence, evidence of association with victim and opportunity and circumstantial evidence)
I expect your relative rankings to be the same, less confidence in absolute probabilities.
Fairly mainstream media sources, probably linked from blogs I read which will likely supply a selection bias, don’t remember exactly what the sources were.
After reading a bit more I’d revise my probabilities to:
5%
10%
90%
The evidence against Knox and Sollecito is very weak and there doesn’t seem to be clear motive. The evidence against Guede is strong and it seems clear that had he been identified initially as the primary suspect there would have been no reason for the police to suspect anyone else was involved in the attack.
I think there’s a very high probability Guede is the only guilty party. There is a small probability that all 3 conspired in some way and an even smaller probability that Knox and Sollecito conspired together.
The spread between the base prior for male on female sexual violence vs. female on female sexual violence is nowhere near enough to separate the percentages for Knox and Sollecito this widely, let alone as widely as in your first cut.
The general prior may be 2-3 times as likely, but that spread should not hold up after a lot of additional evidence to consider where they are essentially equal. Every piece of evidence that counts for or against them roughly equally should shrink that spread in ratio terms. And it should not expand it in absolute terms at all either. Given that these priors are extremely low (or should be), well under 1% for male or female, there shouldn’t be more than a 1% spread in those simply from that prior. Only evidence which would amplify the male v. female disparity in prior, or evidence that specifically argues in favor of S’s but not K’s guilt, should get you to a spread of more than 1% between them.
According to this page, only 6.4% of offenders in sex related homicides are female (lower than the 11.2% of all homicide offenders who are female). Of all homicides only 2.4% are female on female. I can’t see a simple way to derive the percentage of female offenders in sex related homicides with a female victim but it seems likely based on the other numbers to be lower than p(Female Offender|Female Victim) which I make to be 9.6%: p(FO|FV) = p(FV|FO)*p(FO)/p(FV) = 2.4 / (2.4 + 22.7) = 0.096.
So given no other information, if you know you have a female victim in a sex related homicide it would be reasonable to assume that it is at least 10 times more likely that the murderer is male. About 91% of female murder victims are killed by someone known to the victim so it is reasonable for the police to start with her close associates. Given no particular reason to favour Knox or Sollecito as the murderer you would put much higher odds on it being Sollecito purely based on his gender.
That was roughly the reasoning I used with my initial estimates. I hadn’t looked up any statistics at that point, I just knew that a female murder victim was significantly more likely to have been killed by a male than by a female, especially if there appeared to be a sexual motive to the murder. In light of the statistics I think if anything I should have put a wider gap on the estimates in the absence of other evidence implicating one over the other.
About 91% of female murder victims are killed by someone known to the victim so it is reasonable for the police to start with her close associates.
I don’t know anything about this specific case, but in general—we need to adjust this kind of statement for selection bias, and I would like to know how this is done.
When killers aren’t known to the victims, the police are less likely to find them both because they don’t look for them (as you said) and because there are too many people the victim didn’t know for the police to examine more than a small fraction.
Therefore I expect the just conviction rate in these crimes to be lower, and the false conviction rate to be higher (the police are always likely to accuse and help convict someone the victim knew, but in these cases we know such an accused is innocent).
However, your statistic (many murder victims knew their attacker) probably actually counts convictions. How should we revise this due to A) false convictions and B) a different-than-general rate of crimes solved (where conviction was achieved, or the primary suspect died or fled)? If the statistic already takes such considerations into account, how it this done?
5.Fairly mainstream media sources, probably linked from blogs I read which will likely supply a selection bias, don’t remember exactly what the sources were.
Do you happen to remember from what country or countries these sources were? (Obviously most stories about this case have been from the US, UK, or Italy—with, according to some, significantly different biases among them.)
I believe at least one of the articles was in the New York Times. Most of the blogs I read would link to US or UK sources and any coverage I saw on TV would likely have been from BBC World or from US sources.
I’m moderately familiar with the case (have read a few media articles on the case over the last few months).
10% (weak evidence, lack of motive, low prior probability of female on female sexually motivated violence)
30% (evidence not much better, higher prior probability of male on female sexually motivated violence)
50% (seems to fit profile of this type of offence, evidence of association with victim and opportunity and circumstantial evidence)
I expect your relative rankings to be the same, less confidence in absolute probabilities.
Fairly mainstream media sources, probably linked from blogs I read which will likely supply a selection bias, don’t remember exactly what the sources were.
After reading a bit more I’d revise my probabilities to:
5%
10%
90%
The evidence against Knox and Sollecito is very weak and there doesn’t seem to be clear motive. The evidence against Guede is strong and it seems clear that had he been identified initially as the primary suspect there would have been no reason for the police to suspect anyone else was involved in the attack.
I think there’s a very high probability Guede is the only guilty party. There is a small probability that all 3 conspired in some way and an even smaller probability that Knox and Sollecito conspired together.
The spread between the base prior for male on female sexual violence vs. female on female sexual violence is nowhere near enough to separate the percentages for Knox and Sollecito this widely, let alone as widely as in your first cut.
The general prior may be 2-3 times as likely, but that spread should not hold up after a lot of additional evidence to consider where they are essentially equal. Every piece of evidence that counts for or against them roughly equally should shrink that spread in ratio terms. And it should not expand it in absolute terms at all either. Given that these priors are extremely low (or should be), well under 1% for male or female, there shouldn’t be more than a 1% spread in those simply from that prior. Only evidence which would amplify the male v. female disparity in prior, or evidence that specifically argues in favor of S’s but not K’s guilt, should get you to a spread of more than 1% between them.
According to this page, only 6.4% of offenders in sex related homicides are female (lower than the 11.2% of all homicide offenders who are female). Of all homicides only 2.4% are female on female. I can’t see a simple way to derive the percentage of female offenders in sex related homicides with a female victim but it seems likely based on the other numbers to be lower than p(Female Offender|Female Victim) which I make to be 9.6%: p(FO|FV) = p(FV|FO)*p(FO)/p(FV) = 2.4 / (2.4 + 22.7) = 0.096.
So given no other information, if you know you have a female victim in a sex related homicide it would be reasonable to assume that it is at least 10 times more likely that the murderer is male. About 91% of female murder victims are killed by someone known to the victim so it is reasonable for the police to start with her close associates. Given no particular reason to favour Knox or Sollecito as the murderer you would put much higher odds on it being Sollecito purely based on his gender.
That was roughly the reasoning I used with my initial estimates. I hadn’t looked up any statistics at that point, I just knew that a female murder victim was significantly more likely to have been killed by a male than by a female, especially if there appeared to be a sexual motive to the murder. In light of the statistics I think if anything I should have put a wider gap on the estimates in the absence of other evidence implicating one over the other.
I don’t know anything about this specific case, but in general—we need to adjust this kind of statement for selection bias, and I would like to know how this is done.
When killers aren’t known to the victims, the police are less likely to find them both because they don’t look for them (as you said) and because there are too many people the victim didn’t know for the police to examine more than a small fraction.
Therefore I expect the just conviction rate in these crimes to be lower, and the false conviction rate to be higher (the police are always likely to accuse and help convict someone the victim knew, but in these cases we know such an accused is innocent).
However, your statistic (many murder victims knew their attacker) probably actually counts convictions. How should we revise this due to A) false convictions and B) a different-than-general rate of crimes solved (where conviction was achieved, or the primary suspect died or fled)? If the statistic already takes such considerations into account, how it this done?
Do you happen to remember from what country or countries these sources were? (Obviously most stories about this case have been from the US, UK, or Italy—with, according to some, significantly different biases among them.)
I believe at least one of the articles was in the New York Times. Most of the blogs I read would link to US or UK sources and any coverage I saw on TV would likely have been from BBC World or from US sources.