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# The birthday problem; aka why everything you know about DNA evidence is wrong.

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edited August 2009
Consider the following statistical conundrum. You may have seen it before, it's a mainstay of undergraduate statistics classes. If you have seen it before, you can safely skip past the first spoiler.

Anyway, the statistical problem is this: In a class of [N] people, what are the chances that any two people share the same birthday?

If N=2, the probability is simple. The chance that one person has the same birthday as another is 1 in 365 (roughly, ignoring leap years and seasonal trends).

If N>365, the probability is also simple. 100%. If you have more than 365 people in a classroom, then it is a foregone conclusion that somebody has the same birthday as somebody else.

But what if the class size is somewhere in between? Well, as the class gets bigger, the probability of a match increases very, very quickly. In fact, in class size of just 57, the probability of a match is over 99%.

What's the cause behind this unintuitive conclusion? Well, while you might think "hmmm, 57 people isn't very much, merely a fraction of the 365 days of a year," the problem is that we're not looking for a particular person or a particular birthdate... we're looking for a particular combination. When you think about it, the number of possible combinations in a class of 57 is 57-squared, or 3249. (That's why another name for this problem is "combinatorial explosion."

The exact math for this is behind the spoiler. Click only if you want a math lesson.
When figuring out a combinatorial problem like this, it's usually easier to work backwards. Basically, instead of looking for a probability of a match, you look for the probability of no match.

The probability of no match between any two people (let's call them Alice and Bob) is 364/365, or 99.7%.

Add a third person, Charlie, and now you need to figure out two things. First, the probability that Alice and Bob do not share a birthday. Second, the probability that Charlie does not share a birthday with either Alice or Bob. Then you figure out the probability that both cases are true at the same time. This works out to (364/365) * (363/365) = 99.1%.

Add a fourth person, David, and the calculation becomes (364/365) * (363/365) * (362/365) = 98.3%.

The easiest way to express this in a formula is this, blatantly stolen from Wikipedia:

Evaluate this for N = 57 and you get: 365! / [( 365^57) * 308!] = 0.009. In other words, the chance of no match is under 1%. This would imply that the chance of the inverse condition, any match, is 1-0.009, or 0.991. Roughly 99%.

A nice little rule of thumb to use on cases like this is the formula:

That formula tells you how big N has to be to get a match probability around 50%. H is the number of possible values. So for birthdays, H is 365. Plug that into the formula and you get 1.25 * sqrt(365) = 1.25 * 19.10 = 23.88. So in a class of 24 students, the probably of a match exceeds 50%.

What does this have to do with DNA evidence?

Nothing, as long as we're talking about suspects pulled from the general population, on account of some other cooborating evidence.

However, law enforcement agencies are starting to perform what are called "cold hits." A cold hit is where a piece of DNA evidence entered into a law enforcement database from an unsolved case is then searched against the entire database. In some cases, the entire database is searched against itself, and any match is flagged.

The issue here is that even though the chances of two samples matching by coincidence might be very small, the combinatorial explosion that occurs on sufficiently large databases can cause an alarming number of false positives, as an Arizona crime lab analyst discovered last year.

Now, part of the problem with DNA evidence is that nobody really agrees what the chances of a coincidental match really are. Prosecutors like to bandy around numbers like "1 in 100 billion;" but those numbers don't take into account laboratory error or common ancestry among community populations. In real world scenarios, the actual chances of a coincidental match are between 1/1,000 and 1/1,000,000. But let's give the prosecutors the benefit of the doubt and say that the chances of a coincidental match really are 1 in 100 billion. Even if that's the case, then in a database of 400,000 records the chances of a false positive between any two records exceed 50%.

Think about that for a second. The FBI runs the CODIS database with over 7 million records pulled from criminals and nearly 300,000 case samples - including arrestees who were never convicted, and missing persons. The UK has a similar database that is almost the same size. Cast a wide enough net in a database of that size, and you are guaranteed to find something, even if the similarity is completely coincidental.

This is not merely a theoretical problem. In 2005, John Puckett, a prior offender who had served his time, was arrested and convinced on no more evidence than a cold hit alone even though the chances of it being a false positive were 1 in 3. 33% is not "beyond a shadow of a doubt," but even today judges are averse to letting juries know about the birthday problem.

In 2008, the California courts ruled in People v. Nelson that the birthday problem is not an issue; that the chances of a false positive are still infinitesimally small even when a database is mined for cold hits. This conclusion has been thoroughly refuted by professional statisticians, yet the courts turn a blind eye to their objections.

It's hard to sympathize with people like Puckett or Dennis Nelson, both of whom were prior rapists - each one had been seperately convinced of rape charges in a different case without the use of DNA evidence. But the use of arrestee and missing persons DNA in forensic database mining means it's basically a matter of time until somebody truly innocent is standing trial while the prosecution lies to the jury about the reliability of this type of evidence.

every person who doesn't like an acquired taste always seems to think everyone who likes it is faking it. it should be an official fallacy.

the "no true scotch man" fallacy.
Feral on
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Registered User, ClubPA regular
edited August 2009
Sure, but DNA testing has also exonerated hundreds of convicts in the last few years. I'm seeing a problem with application and definitely a problem with inappropriate data retention (New Scientist did a feature on the UK laws about this a year or two ago, which was scary), along with the usual "juries suck" stuff, but I worry that your OP doesn't adequately state that you're not against the technology being used in the first place.

Do you have a proposed solution?

The Cat on
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Registered User regular
edited August 2009
This is one of those problems though where we could solve it by changing the DNA testing protocol, though it tends to depend on how much DNA you actually can reasonably recover from the crime scene.

electricitylikesme on
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edited August 2009
I'm not sure what I'm against, exactly, or what the best solution would be quite yet.

My gut instinct is to say that we shouldn't keep on file the DNA of nonconvicts, and we shouldn't let prosecutors tell juries that the chances of a false positive are virtually impossible.

But I'm not totally sure.

Feral on
every person who doesn't like an acquired taste always seems to think everyone who likes it is faking it. it should be an official fallacy.

the "no true scotch man" fallacy.
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Registered User regular
edited August 2009
Add another bit of unique DNA to decrease the odds of false positives? Is that even possible? It wouldn't help with the current database, but it should keep new suspects/criminals from being falsely accused through statistical shenanigans.

Stop doing cold hits? How good of a tool are they anyway? It seems to be they are a shot in the dark.

I know very little of statistics or DNA profiling. Disabuse me of my ignorance.

TeaSpoon on
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edited August 2009
I think as long as cold hits are treated like leads rather than conclusive evidence they're fine.

Perhaps if they were treated a little more like an anonymous tip, or a 911 caller's eyewitness report. Not enough to convict alone, but enough to lend probable cause.

Feral on
every person who doesn't like an acquired taste always seems to think everyone who likes it is faking it. it should be an official fallacy.

the "no true scotch man" fallacy.
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ALL minions Registered User regular
edited August 2009
I'm fine with a cold hit getting you like, a search warrant or something, but it shouldn't be any more than that on its own.

override367 on
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Registered User regular
edited August 2009
But the chances of a false positive are virtually impossible, if full scientific rigor is applied. The Puckett case is an anomaly, the DNA evidence from the crime was so degraded that only a partial match was possible (to simplify, he was a 100% match for the 2/3 of the evidence there was to be tested, giving the "1 in 3" false positive chance). That, plus the fact that Puckett was a convicted multiple rapist on trial for a rape and murder in an area where he was known to have been at the time, swayed the jury. It's certainly a close one but it's not a miscarriage of justice by any stretch of the imagination.

zilo on
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Registered User regular
edited August 2009
zilo wrote: »
But the chances of a false positive are virtually impossible, if full scientific rigor is applied. The Puckett case is an anomaly, the DNA evidence from the crime was so degraded that only a partial match was possible (to simplify, he was a 100% match for the 2/3 of the evidence there was to be tested, giving the "1 in 3" false positive chance). That, plus the fact that Puckett was a convicted multiple rapist on trial for a rape and murder in an area where he was known to have been at the time, swayed the jury. It's certainly a close one but it's not a miscarriage of justice by any stretch of the imagination.
Not really though. DNA testing is not a comparison of whole sequences, it's a comparison of 13 genetic loci which can be amplified by the polymerase chain reaction reliably. They then compare these sequences.

So while it is implausible that we have identical DNA between two unrelated people (nearly), it is certainly not implausible that amongst 13 sites we could get a coincidental match within a big population.

electricitylikesme on
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Registered User regular
edited August 2009
You say that in a database of 400,000 people, there is a 50% chance of any two people's DNA matching.... but what is the chance that there will be a match to the particular DNA sample that police have obtained? There is a 99% chance that two of a random group of 57 people will have the same birthday; but the chance that any one of them was born on January 3 is significantly lower.

Nibble on
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Registered User regular
edited August 2009
Yeah, but cold hits don't test a random set- if you test 400,000 random people for genetic matches you'd be bound to find a few "false positives". But the set of people in law enforcement databases is hardly random.

If this kind of technique was used to convict, say, a housewife who was never known to leave the state of Florida of a murder in California, then yeah. Bogus. But these "cold hit" matches don't exist in a vacuum.

edit: responding to electricitylikeme

zilo on
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edited August 2009
Nibble wrote: »
You say that in a database of 400,000 people, there is a 50% chance of any two people's DNA matching.... but what is the chance that there will be a match to the particular DNA sample that police have obtained? There is a 99% chance that two of a random group of 57 people will have the same birthday; but the chance that any one of them was born on January 3 is significantly lower.

We're talking about different problem spaces, in increasingly likely possibilities of coincidental match:

Problem 1: Single sample taken from crime scene matched against convict database. (One-to-many.)
Problem 2: All unsolved cases matched against convict database. (Many-to-many.)
Problem 3: Entire database searched against itself. (N-squared.)

Dennis Nelson and John Puckett were both more like problem space 2. (Although, in all honesty, Nelson was really more like problem space 1. Even though the search started as a cold-case vs. convict database search, the positive combination that turned up was a case that Nelson had previously been a suspect for. So there was additional non-DNA evidence that he may have been responsible for that crime, although I don't know what that evidence was.)

You're right, the probability of a false positive for problem space 1 is significantly lower. However, it's still higher than prosecutors report. Assuming a database of 7 million, with a 1 in a billion chance of false positive on a comparison of two single samples, the false positive probability on a single sample vs. 7 million large database search is roughly equal to 1 - [(999,999,999/1,000,000,00)^7,000,000 = .007, or less than 1%. Very small, but still some room for error - with the most conservative assumptions.

If the actual chance of a false positive on the comparison of two single samples is more like 1 in a million, then the probability of a false positive on a database search balloons to a nigh-inescapable 99.9%.

Feral on
every person who doesn't like an acquired taste always seems to think everyone who likes it is faking it. it should be an official fallacy.

the "no true scotch man" fallacy.
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Registered User regular
edited August 2009
Related, everybody's favorite http://en.wikipedia.org/wiki/Prosecutor%27s_fallacy.
Supreme Court weights in and I certainly don't fucking like it: http://www.deathpenaltyinfo.org/supreme-court-rejects-due-process-right-dna-testing-after-trial
Sure, but DNA testing has also exonerated hundreds of convicts in the last few years. I'm seeing a problem with application and definitely a problem with inappropriate data retention (New Scientist did a feature on the UK laws about this a year or two ago, which was scary), along with the usual "juries suck" stuff, but I worry that your OP doesn't adequately state that you're not against the technology being used in the first place.

Do you have a proposed solution?

Right now, I'm pretty much willing to support a radical and obviously bad decision like making DNA tests available to defense only if it would cut the current level of dna profiling and DNA retention.
Ideal case is probably to try and educate juries as much as possible about the method by which a specific DNA match was obtained and eventually forbid straight forward match queries on DNA databases.

zeeny on
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Registered User regular
edited August 2009
Feral wrote: »
Nibble wrote: »
You say that in a database of 400,000 people, there is a 50% chance of any two people's DNA matching.... but what is the chance that there will be a match to the particular DNA sample that police have obtained? There is a 99% chance that two of a random group of 57 people will have the same birthday; but the chance that any one of them was born on January 3 is significantly lower.

We're talking about different problem spaces, in increasingly likely possibilities of coincidental match:

Problem 1: Single sample taken from crime scene matched against convict database. (One-to-many.)
Problem 2: All unsolved cases matched against convict database. (Many-to-many.)
Problem 3: Entire database searched against itself. (N-squared.)

Dennis Nelson and John Puckett were both more like problem space 2. (Although, in all honesty, Nelson was really more like problem space 1. Even though the search started as a cold-case vs. convict database search, the positive combination that turned up was a case that Nelson had previously been a suspect for. So there was additional non-DNA evidence that he may have been responsible for that crime, although I don't know what that evidence was.)

You're right, the probability of a false positive for problem space 1 is significantly lower. However, it's still higher than prosecutors report. Assuming a database of 7 million, with a 1 in a billion chance of false positive on a comparison of two single samples, the false positive probability on a single sample vs. 7 million large database search is roughly equal to 1 - [(999,999,999/1,000,000,00)^7,000,000 = .007, or less than 1%. Very small, but still some room for error - with the most conservative assumptions.

If the actual chance of a false positive on the comparison of two single samples is more like 1 in a million, then the probability of a false positive on a database search balloons to a nigh-inescapable 99.9%.

Puckett was convicted because of 3 reasons: The DNA evidence, he was a previously convicted of sexual assaults and those assaults took place in the same area and time as the rape and murder.

What's the probability that a false positive would be a rapist who was operating in the same area and time as when the rape and murder took place?

Mr. Pokeylope on
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ski-bap ba-dapModerator mod
edited August 2009
Feral wrote: »
My gut instinct is to say that we shouldn't keep on file the DNA of nonconvicts, and we shouldn't let prosecutors tell juries that the chances of a false positive are virtually impossible.

In Sweden we have the PKU register - ever since the late 70s all newborns have a blood sample taken to test for PKU, and this sample is physically stored for research purposes. Somewhere down the line it got digital.

Then, a year or two back, someone had the bright idea that maybe the police should have access to this database! You know, to fight crime! And protect the children!

edit: in my 1st to 3rd grade class of ~25 kids we had three people born on March 21st (me being one).

Echo on
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Registered User regular
edited August 2009
Echo wrote: »
Then, a year or two back, someone had the bright idea that maybe the police should have access to this database! You know, to fight crime! And protect the children!

For what it's worth, the ECHR ruled that the UK Police retaining DNA taken from people arrested but not convicted was illegal. Having said that most of the English forces are still dragging their feet on destroying the samples they've taken (the Scottish Forces did it immediately, and had only been adding the samples to the database in certain circumstances anyway, most notably sex crimes, because they're notoriously hard to prosecute) and erasing the database entries. If you could get some political will behind it I'm fairly sure this could be challenged.

japan on
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ski-bap ba-dapModerator mod
edited August 2009
japan wrote: »
If you could get some political will behind it I'm fairly sure this could be challenged.

I'm gleefully waiting for some politician to talk about police access to the PKU database again so the Pirate Party can verbally decapitate them.

Because no other parties give a shit.

Echo on
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Registered User regular
edited August 2009
Feral wrote: »
If N>365, the probability is also simple. 100%. If you have more than 365 people in a classroom, then it is a foregone conclusion that somebody has the same birthday as somebody else.

edit: and it's me.

There's an interesting article in popular mechanics about forensics and the movement to reform it (link). Anyways, the numbers they quote for the best DNA match is 1 in 100,000,000,000,000 (1 in a Quadrillion). I wonder if that's enough to put your maths back on to a more sure footing.

Rook on
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Registered User regular
edited August 2009
It's depressing how little traction this gets.

In the UK, back in 1996, a guy called Adams was being tried for rape. The only evidence against him was DNA evidence, which the prosecution trumpted with a '1 in 200 million' statistic. In addition, the victim had failed to pick him out of a lineup, and later said he didn't look like the attacker. Adams also had an alibi in his girlfriend.

His defence guided the jury through Bayes theorem. He was convicted. He appealed, and was convicted again. On his second appeal, the appeal judges decided that
...to introduce Bayes theorem, or any similar method, into a criminal trial plunged the jury into inappropriate and unnecessary realms of theory and complexity deflecting them from their proper task/

Inappropriate and unnecessary? Are these synonyms for 'potentially difficult' of which I was previously unaware?

area on
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ski-bap ba-dapModerator mod
edited August 2009
area wrote: »
Inappropriate and unnecessary? Are these synonyms for 'potentially difficult' of which I was previously unaware?

I'll never stop finding new reasons for being pissed off at the trial by jury system, will I?

Echo on
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Registered User regular
edited August 2009
That's not really a problem with the jury system, so much as with the judge.

japan on
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Registered User regular
edited August 2009
Echo wrote: »
Feral wrote: »
My gut instinct is to say that we shouldn't keep on file the DNA of nonconvicts, and we shouldn't let prosecutors tell juries that the chances of a false positive are virtually impossible.

In Sweden we have the PKU register - ever since the late 70s all newborns have a blood sample taken to test for PKU, and this sample is physically stored for research purposes. Somewhere down the line it got digital.

Then, a year or two back, someone had the bright idea that maybe the police should have access to this database! You know, to fight crime! And protect the children!

edit: in my 1st to 3rd grade class of ~25 kids we had three people born on March 21st (me being one).

They don't see how the police using a database intended solely for scientific research and that they said would be used for just that could discourage people from wanting to give any of that crap again?

Couscous on
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ski-bap ba-dapModerator mod
edited August 2009
Couscous wrote: »
They don't see how the police using a database intended solely for scientific research and that they said would be used for just that could discourage people from wanting to give any of that crap again?

Give? You think they get asked?

It's a routine procedure. Weigh the baby, measure length, a pinprick on the heel of the foot to sample blood for the PKU database...

They might not do it if you ask them not to, but how many people will remember that while their kid is being born?

You can send a letter to whichever hospital it was that handles the database and request your DNA sample and database entry destroyed. When the PKU database was up in the news tons of blogs posted instructions and a sample letter, which lead to the politicians behind this going "Damnit, a loophole! Fast-track this law to make it impossible to have your data deleted!"

I don't think anyone will dare talk about that again for a long while after the results in the EU MEP election. The established parties crapped their pants at the support the Pirate Party got and went "holy shit, people care about privacy and integrity?"

Echo on
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Registered User regular
edited August 2009
area wrote: »
It's depressing how little traction this gets.

In the UK, back in 1996, a guy called Adams was being tried for rape. The only evidence against him was DNA evidence, which the prosecution trumpted with a '1 in 200 million' statistic. In addition, the victim had failed to pick him out of a lineup, and later said he didn't look like the attacker. Adams also had an alibi in his girlfriend.

His defence guided the jury through Bayes theorem. He was convicted. He appealed, and was convicted again. On his second appeal, the appeal judges decided that
...to introduce Bayes theorem, or any similar method, into a criminal trial plunged the jury into inappropriate and unnecessary realms of theory and complexity deflecting them from their proper task/

Inappropriate and unnecessary? Are these synonyms for 'potentially difficult' of which I was previously unaware?

I suspect that judges don't like dealing with statistics for two reasons: first, because it does confuse juries, even if it's absolutely pertinent to the case; second, because it comes awfully close to asking what "beyond reasonable doubt" really means. As regards the first point, they've actually abandoned trial by jury in certain complicated financial fraud cases in the UK on this basis. (Brought on by a big trial collapsing after two years: they were discussing such complex financial instruments that the jury just didn't understanding the proceedings.) I can see why the concept of the same happening to all cases involving DNA evidence would not please judges.

Sadly, the concept of involving statistics in a trial really doesn't agree with trial by jury and the adversarial system. Any change here really needs to be made at the forensics level, where there will be a lot less resistance.

Kester on
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edited August 2009
The DNA evidence, he was a previously convicted of sexual assaults and those assaults took place in the same area and time as the rape and murder.

What's the probability that a false positive would be a rapist who was operating in the same area and time as when the rape and murder took place?

John Puckett committed his sexual assaults over a 20 year period, and a 400-mile range from Long Beach to San Rafael. (He had been previously convicted of a sexual assault in 1973, but I can't find any info on where that occurred. It might have been San Francisco, or it might have been 400 miles away.) I don't think that these cases are as proximal as the prosecution represented them to be.

Obviously, he's a scumbag. Perhaps he should have been locked up for life in 1957. However, he wasn't; he did his time and he was a free man brought back into custody on flimsy circumstantial evidence. He's effectively been convicted twice for his criminal record.

Feral on
every person who doesn't like an acquired taste always seems to think everyone who likes it is faking it. it should be an official fallacy.

the "no true scotch man" fallacy.
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Registered User regular
edited August 2009
Feral wrote: »
The DNA evidence, he was a previously convicted of sexual assaults and those assaults took place in the same area and time as the rape and murder.

What's the probability that a false positive would be a rapist who was operating in the same area and time as when the rape and murder took place?

John Puckett committed his sexual assaults over a 20 year period, and a 400-mile range from Long Beach to San Rafael. (He had been previously convicted of a sexual assault in 1973, but I can't find any info on where that occurred. It might have been San Francisco, or it might have been 400 miles away.) I don't think that these cases are as proximal as the prosecution represented them to be.

Obviously, he's a scumbag. Perhaps he should have been locked up for life in 1957. However, he wasn't; he did his time and he was a free man brought back into custody on flimsy circumstantial evidence. He's effectively been convicted twice for his criminal record.

He was convicted of rape and sexual assault that took place in the Bay area in 1977. The prosecution was able to place him in Frisco close to where the victim worked in 1972. It is worrisome that the DNA evidence they did have was only able to match 5 1/2 loci with Puckett, but what is the chance that a rapist who was operating in the same area and time as the rape and murder is a false positive?

Mr. Pokeylope on
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Registered User regular
edited August 2009
Feral wrote: »
The DNA evidence, he was a previously convicted of sexual assaults and those assaults took place in the same area and time as the rape and murder.

What's the probability that a false positive would be a rapist who was operating in the same area and time as when the rape and murder took place?

John Puckett committed his sexual assaults over a 20 year period, and a 400-mile range from Long Beach to San Rafael. (He had been previously convicted of a sexual assault in 1973, but I can't find any info on where that occurred. It might have been San Francisco, or it might have been 400 miles away.) I don't think that these cases are as proximal as the prosecution represented them to be.

Obviously, he's a scumbag. Perhaps he should have been locked up for life in 1957. However, he wasn't; he did his time and he was a free man brought back into custody on flimsy circumstantial evidence. He's effectively been convicted twice for his criminal record.

He was convicted of rape and sexual assault that took place in the Bay area in 1977. The prosecution was able to place him in Frisco close to where the victim worked in 1972. It is worrisome that the DNA evidence they did have was only able to match 5 1/2 loci with Puckett, but what is the chance that a rapist who was operating in the same area and time as the rape and murder is a false positive?
Depends what the mean level of random hits with the rest of the population for 5 1/2 loci would be. I don't know - but you can't say "what are the chances?" without actually checking the number.

According to Feral the chances are pretty good - 1/3 is an absurdly high hit rate within the general population, if our null hypothesis is that another, unknown rapist is operating within the population.

electricitylikesme on
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edited August 2009
He was convicted of rape and sexual assault that took place in the Bay area in 1977. The prosecution was able to place him in Frisco close to where the victim worked in 1972. It is worrisome that the DNA evidence they did have was only able to match 5 1/2 loci with Puckett, but what is the chance that a rapist who was operating in the same area and time as the rape and murder is a false positive?

In a dense city with a relatively small surface area, the chances might be higher than they appear on the surface.

And, again, we're talking about a lag time of five years.

What I'd really like to find right now, and I can't seem to get any leads through Google, are the following:

- Crime rate statistics for San Francisco in the 1970s
- The exact locations where Puckett's 1973 and 1977 crimes occurred.

Again, I'm not saying that the guy is not the rapist. I'm not saying he's a nice guy. I'm saying this feels a little bit too much like double jeopardy; if the key piece of evidence here is that he committed a rape in the 1970s in the same general area, he's for all intents and purposes being put on trial for that rape twice.

Feral on
every person who doesn't like an acquired taste always seems to think everyone who likes it is faking it. it should be an official fallacy.

the "no true scotch man" fallacy.
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Cool Cat Registered User regular
edited August 2009
I got all outraged when I read this and then I actually got the math. Why would you worry about the police in the future, theoretically, fucking over innocent people when there are like 10000x more innocent people getting screwed over right now thanks to good old fashioned police work?

This is worth noting and planning around, but still...

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edited August 2009
Hoz wrote: »
I got all outraged when I read this and then I actually got the math. Why would you worry about the police in the future, theoretically, fucking over innocent people when there are like 10000x more innocent people getting screwed over right now thanks to good old fashioned police work?

This is worth noting and planning around, but still...

I find it intellectually interesting because I dig it when our intuition proves us wrong. See also: the Monty Hall problem.

Feral on
every person who doesn't like an acquired taste always seems to think everyone who likes it is faking it. it should be an official fallacy.

the "no true scotch man" fallacy.
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Cool Cat Registered User regular
edited August 2009
Just read up on that. Complete mindfuck until I saw the diagram.

Hoz on
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ＭＥＭＥＴＩＣＨＡＲＩＺＡＲＤ interior crocodile alligator ⇔ ǝɹʇɐǝɥʇ ǝᴉʌoɯ ʇǝloɹʌǝɥɔ ɐ ǝʌᴉɹp ᴉRegistered User regular
edited August 2009
Hoz wrote: »
Just read up on that. Complete mindfuck until I saw the diagram.

I didn't get it until I sat down with a deck of cards and simulated it on myself.

Feral on
every person who doesn't like an acquired taste always seems to think everyone who likes it is faking it. it should be an official fallacy.

the "no true scotch man" fallacy.
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Registered User regular
edited August 2009
Further proof of why probability and statistics should be required material in primary school.

I learned a little about probability in middle and high school. Took a basic stats course in college and a more focused stats course in graduate school. Ignorance truly is bliss because it pisses me off to no end to see the media, politicians, and big business totally abuse statistics to the detriment of the general populace. It is just baffling some of the things they claim by using scientific and mathematical phrases, and yet are so terribly wrong and founded on outright trickery.

travathian on
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I'm tired of being Batman, so today I'll be Owl.Registered User regular
edited August 2009
Feral wrote: »
Hoz wrote: »
I got all outraged when I read this and then I actually got the math. Why would you worry about the police in the future, theoretically, fucking over innocent people when there are like 10000x more innocent people getting screwed over right now thanks to good old fashioned police work?

This is worth noting and planning around, but still...

I find it intellectually interesting because I dig it when our intuition proves us wrong. See also: the Monty Hall problem.

Hi 5 me too.

I'm a person who used to basically run on intuition so my world view has been pretty heavily shaken n stirred the last few years. Instead of upsetting me, it fascinated me.

Morninglord on
(PSN: Morninglord) (Steam: Morninglord) (WiiU: Morninglord22) I like to record and toss up a lot of random gaming videos here.
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ski-bap ba-dapModerator mod
edited August 2009
Feral wrote: »
Hoz wrote: »
Just read up on that. Complete mindfuck until I saw the diagram.

I didn't get it until I sat down with a deck of cards and simulated it on myself.

Someone asked me that years ago and I got it at once. (lolautism)

You can switch from two goats to one car, but only from one car to two goats. Thus: 2/3rd chance to move from a goat to a car. One of the goats being revealed doesn't change the statistics.

Echo on
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I'm tired of being Batman, so today I'll be Owl.Registered User regular
edited August 2009
That is a fantastic problem.
I'd never heard of it before.

Morninglord on
(PSN: Morninglord) (Steam: Morninglord) (WiiU: Morninglord22) I like to record and toss up a lot of random gaming videos here.
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Registered User regular
edited August 2009
That is one of those ones I understand but haven't internalized as logical yet, although its growing on me.

electricitylikesme on
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ski-bap ba-dapModerator mod
edited August 2009
Echo wrote: »
You can switch from two goats to one car, but only from one car to two goats. Thus: 2/3rd chance to move from a goat to a car. One of the goats being revealed doesn't change the statistics.

...ok, from a mathematical perspective this is actually horribly incorrect, but damn if I knew how to explain my train of thoughts on it. :P

We pick one door, and a goat is revealed in another door. Our natural bias is to ignore the revealed door as irrelevant for the probabilities (and thus think there's a 50% chance that we picked the correct door), when in fact it's still very relevant.

If you picked the car door, switching can only move to the goat door that isn't revealed.

If you picked a goat door, switching can only move to the car, since the other goat door gets revealed.

There are two chances to pick a goat door, thus two chances to switch to the car door. Ergo, 2/3rds chance.

There we go, that made more sense.

Echo on
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Registered User regular
edited August 2009
In my experience the thing that tends to trip people up when it comes to the monty hall problem is that they do not actually consider the actions of the door opener, in that he will always open a door with a goat behind it.

Numi on
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Registered User regular
edited August 2009
Monty hall was easy for me, when someone changed it to 100 doors, and then telling me I only had a 1% chance that my first pick was right, makes the 99% change make a lot more sense.

Code on
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ski-bap ba-dapModerator mod
edited August 2009
Code wrote: »
Monty hall was easy for me, when someone changed it to 100 doors, and then telling me I only had a 1% chance that my first pick was right, makes the 99% change make a lot more sense.

Yeah, adding doors actually makes it easier - 100 doors, pick one. Then open 98 goat doors - leaving the one you picked, and one other door.

1% chance to have picked the correct door in your first choice... and there's one other door to switch to. Easy to understand that example.

Echo on