Patterico's Pontifications

5/3/2008

Statistical Probability in Cold Hit DNA Cases

Filed under: Crime,Dog Trainer,General — Patterico @ 10:20 pm

The L.A. Times has an interesting article about the application of probability measures to “cold hit” cases made from DNA databases. I find the statistical arguments made in the article to be unconvincing, but due to my lack of training in this area, I remain completely humble about my ability to properly analyze the issue. However, experts have widely divergent opinions on the matter — a fact you’d never learn reading the article.

The article begins by describing a 1970s rape/murder scene. A match was made from badly deteriorated DNA that bore only 5 1/2 of the possible 13 markers available. When all 13 markers are available for a match, the probability of a random person bearing the same profile can run to 1 in a quadrillion — thousands of times the number of people on the planet. Because of the lack of the 13 markers in this case, the chance was lowered to 1 in 1.1 million.

This is known as a “random match probability” and the article describes it as the “rarity of a particular DNA profile in the general population.”

At Puckett’s trial earlier this year, the prosecutor told the jury that the chance of such a coincidence was 1 in 1.1 million.

Jurors were not told, however, the statistic that leading scientists consider the most significant: the probability that the database search had hit upon an innocent person.

In Puckett’s case, it was 1 in 3.

The article restates the proposition again later in the article:

In every cold hit case, the panels advised, police and prosecutors should multiply the Random Match Probability (1 in 1.1 million in Puckett’s case) by the number of profiles in the database (338,000). That’s the same as dividing 1.1 million by 338,000.

For Puckett, the result was dramatic: a 1-in-3 chance that the search would link an innocent person to the crime.

It seems to me that the conclusion does not logically follow at all. The formulation simply can’t be right. The suggestion appears to be that the larger the database, the greater the chance is that the hit you receive will be a hit to an innocent person. I think that the larger the database, the greater the probability of getting a hit. Then, once you have the hit, the question becomes: how likely is it that the hit is just a coincidence?

An example makes it simpler.

Let’s say the random match probability for a DNA profile is one in 13.4 billion. In such a case, it seems very unlikely that the hit you get will come back to a different person than the person who left the DNA at the crime scene. Now assume that your database contains all 6.7 billion people on the planet. It’s virtually certain that you will get a hit, of course. But if you got a hit — only one hit — you would intuitively feel certain that you had the right person from that hit.

Yet the logic of the article would seem to say you take 13.4 billion and divide it by the size of the database (6.7 billion). making a 1-in-2 chance (50%) that you have the wrong person (an “innocent person”).

I say hogwash. And I think my example shows why it’s confusing and potentially misleading to use the word “innocent” in these calculations.

My off-the-cuff reaction — and keep in mind, I have no experience in statistics — is that the people who advocate this approach are measuring the question:

1. What are the chances that a search of this database will turn up a match with the DNA profile?

when the truly relevant question is, instead:

2. What are the chances that any one person whose DNA matches a DNA profile is indeed the person who left the DNA from which the profile is taken?

There is a third, rather silly question whose answer seems obvious, but which I will raise for the purposes of relating to an analogy I will make:

3. Once a match has been made through the database, what is the chance that the person whose DNA provided the match will match the DNA profile?

This last one is obviously almost 100%, the lack of complete certainty owing purely to human error; taking human error out of the equation for a theoretical analysis, it’s a tautology: a match is a match.

It seems to me that this is a useful analogy: everyone knows a coin has a 50/50 chance of coming up heads. If I give you a room that has 10,000 coins that were randomly tossed in the air and have landed on the ground, the chances that at least one of those coins landed heads are very nearly approaching 100% certainty (question 1). But the chances that any one of those coins was going to come up heads before it was tossed is still 50% (question 2).

Now, if I tell you to go find me a coin that has come up heads, then the chances it did come up heads are (absent human error) 100% (question 3). But, the chances that it was going to come up heads before it was tossed are still 50% . . . and always will be, no matter how many coins are in the room. You’re almost certain to find one with heads in a room with a larger database (thousands of coins), but the chances that it was going to come up heads always remain the same.

Applying the analogy to a DNA database, it seems to me that the size of the database increases your chances of a hit. But the chances that the profile obtained from your hit is a coincidence will always remain the same, and will always be a function of the number of loci and their frequency in the relevant populations.

The L.A. Times article makes it sound as though it’s quite well accepted that jurors are constantly being misled:

Jurors are often told that the odds of a coincidental match are hundreds of thousands of times more remote than they actually are, according to a review of scientific literature and interviews with leading authorities in the field.

. . . .

[B]ecause database searches involve hundreds of thousands or millions of comparisons, experts say using the general-population statistic can be misleading.

The closest you get to an acknowledgement that not everybody agrees is a passing reference to the fact that this assertion “has been widely but not universally embraced by scientists.”

“Not universally” is quite the understatement. Apparently, there is a debate raging about this among statisticians. Law professor David H. Kaye explains that, while many agree with the analysis described in the L.A. Times article, there is a theory out there that the use of the database “actually increases the probative value of the match.” (I have an e-mail in to Professor Kaye to ask him for further comment.)

The argument to which Professor Kaye refers was made in a Michigan Law Review article by Peter Donnelly, Professor of Statistical Science and Head of the Department of Statistics at the University of Oxford, and Richard D. Friedman, a law professor at the University of Michigan. The first page of their law review article is here. An earlier version of the argument was apparently made by Donnelly with David Balding in a paper titled “Evaluating DNA Profile Evidence When the Suspect is Identified Through a Database Search,” according to mathematician Keith Devlin of Stanford.

Devlin appears to agree with the approach described in the L.A. Times article. However, he says:

Personally, I (together with the collective opinion of the NRC II committee) find it hard to accept Donnelly’s argument, but his view does seem to establish quite clearly that the relevant scientific community (in this case statisticians) have not yet reached consensus on how best to compute the reliability metric for a cold hit.

You’d never know that reading the L.A. Times article, which implies that all but the most rabid pro-law enforcement shills agree that jurors are being given bogus statistics.

[UPDATE: For proof as to how conclusively the paper portrays this point of view, look at this image of what appears on the front page of today’s Sunday paper:

dna-on-front-page.JPG

Tell me where in that image you see any hint that “the relevant scientific community (in this case statisticians) have not yet reached consensus” as mathematician Devlin states.]

The paper wraps up the article by suggesting that the real probability of a coincidence is not 1 in 1.1 million, but 1 in 3:

In the end, however, jurors said they found the 1-in-1.1-million general-population statistic Merin had emphasized to have been the most “credible” and “conservative.” It was what allowed them to reach a unanimous verdict.

“I don’t think we’d be here if it wasn’t for the DNA,” said Joe Deluca, a 35-year-old martial arts instructor.

Asked whether the jury might have reached a different verdict if it had been given the 1-in-3 number, Deluca didn’t hesitate.

“Of course it would have changed things,” he said. “It would have changed a lot of things.”

By the way, in the case described in the L.A. Times article, there was more than just the cold hit. In addition to the fact that the defendant was a serial rapist who described his rapes as “making love” — the same terminology used by the murderer — the prosecution also showed the following:

[Defendant] Puckett “happened to be in San Francisco in 1972,” Merin told jurors in his opening argument. Merin could not place Puckett in [victim] Sylvester’s neighborhood on the day of the slaying. But Puckett had applied for a job near the medical center where Sylvester worked.

With the court lights dimmed and a photo of Sylvester’s naked body displayed on a screen, Merin argued that Puckett’s 1977 sexual assaults showed an “MO” consistent with Sylvester’s killing.

In each of those crimes, Puckett had posed as a police officer to gain the woman’s trust. The absence of forced entry to Sylvester’s apartment indicated her killer had also used a ruse, Merin said.

Puckett had kidnapped his victims by holding a knife or ice pick to their necks, leaving scratches similar to those found on Sylvester’s neck — what Merin called “his signature.”

I now throw open the matter for discussion.

UPDATE: Radley Balko has posted on this. He agrees with the L.A. Times experts. I have posted some counterarguments in his comments.

UPDATE x2: Follow-up post here with helpful responses from Prof. Kaye.

UPDATE x3: Statistics always opens the possibility of using language that doesn’t describe what’s really going on. For example, in this post I referred to “random match probability” as “in essence, the chance that two unrelated people will share the same genetic markers.” I’m not comfortable that this is right, and have removed the sentence. Random match probability refers to the expected frequency of a set of markers appearing in a population of unrelated individuals. I think it’s best to stick with that definition.

FLDS Statistics and Cultural Guide

Filed under: Civil Liberties,Law — DRJ @ 8:38 pm

[Guest post by DRJ]

The Texas Department of Family and Protective Services has published statistics that break down the children removed from the compound by age and gender. In addition, the website also has a Cultural Awareness Guide to help CPS workers and caregivers deal with the unique needs of the FLDS children.

The Guide notes that FLDS children, especially young boys, have made derogatory comments to “staff of color.” The children have become upset when they see people wearing jewelry, men with facial hair and men who aren’t wearing long-sleeved shirts.

The Guide also notes that the children have been socialized to believe sexual activity with adults is positive. They use the slang term “poofers” to refer to girls who suddenly disappear to take part in an arranged marriage.

Former FLDS member Carolyn Jessop told the Deseret News that FLDS members believe it is immoral to wear jewelry and have facial hair. She also said that Warren Jeffs’ taught racist ideology and banned books, the color red, and pork.

In related news, the Eldorado Success newspaper published the Bishops’ Records seized at the FLDS compound. There are 45 pages that includes columns for Name, Age, Relationship and Residence. The notation “R17″ under Residence is a reference to the Eldorado compound.

Many of the families listed in the Record seem to be traditional nuclear families but others are not. For instance, the Record lists one 67-year-old man with 21 wives ranging in age from 24 to 79, and 36 children from 6 months to 21 years of age.

— DRJ

Obama Wins Guam by 7 Votes (Updated)

Filed under: 2008 Election — DRJ @ 7:11 pm

[Guest post by DRJ]

Barack Obama beat Hillary Clinton by 7 votes in Guam. Obama finished with 2,263 votes to Clinton’s 2,257 votes, and they each picked up 2 pledged delegates.

Guam sends 4 pledged delegates and 5 superdelegates to the convention, illustrating again how quixotic the Democratic nominating procedures are. As a territory, Guam has no vote in the November election.

As I recall, Obama was expected to do better than Hillary in Guam because of his multi-ethnic background and because he was born in Hawaii and has lived in Indonesia. Maybe Clinton’s last minute promise to seek voting rights for Guam residents made a difference. Or maybe the Democrats on Guam are as conflicted about the candidates as mainland Democrats seem to be.

H/T Kishnevi.

UPDATE: And, of course, there are calls for a recount because of spoiled and missing ballots. In related news, the Democratic Party is considering a name change to Monty Python’s Totally Predictable Democratic Party.

— DRJ

Howard Dean: Florida and Michigan Delegations Will Be Seated

Filed under: 2008 Election,General — Patterico @ 12:32 pm

Howard Dean appeared on the Daily Show and said definitively that the Michigan and Florida delegations will be seated. (H/t Scott Jacobs.) The video is here and embedded below.

Representative quotes:

STEWART: If I were designing a plan to submarine your chances, and again, you don’t have to follow my advice here, I would take the state that was, let’s say crucial to the Republican election chances — lets, let’s call it Florida — and I would find a way to insult them. Maybe not seat them at the convention, that sort of thing. Then I would pick a Rust Belt state, maybe a Michigan, and say to them the same. Now you’ve got two states that are angry with you. Do you think that would be a good way?

DEAN: Well, we’re actually going to seat them at the convention.

STEWART: What?! This is news! Are you really going to do that?

DEAN: We’re going to find a way to seat them at the convention.

START: Are you really going to?

DEAN: Yeah.

STEWART: How — how can you do that when their results don’t count?

DEAN: Well, it’s a little hard, but we’re gonna do it.

. . . .

It’s gonna be quite a juggling act, but we’re gonna do it. You cannot have a Democratic convention without Florida and Michigan.

Stewart also asked Dean why Michigan and Florida don’t have to follow the rules. Dean replied: “They do. That’s why they lost their delegates.”

I don’t get it either.

Finally, Dean argued that the Democrats’ system is “still more democratic than the [system used by the] Republicans” — you know, the system where the voters choose all the delegates. Stewart let him get away with that one.

Watch it all, if you can stand it.

Hope for a Middle East Awakening

Filed under: International — DRJ @ 12:30 pm

[Guest post by DRJ]

Two stories from the Middle East caught my attention that I hope are early signs of a Middle East Awakening. The first was an AP story from Riyadh, Saudi Arabia, recounting the first public mixed-gender concert permitted by the government:

“It’s probably as revolutionary and groundbreaking as Mozart gets these days. A German-based quartet staged Saudi Arabia’s first-ever performance of European classical music in a public venue before a mixed gender audience.

The concert, held at a government-run cultural center, broke many taboos in a country where public music is banned and the sexes are segregated even in lines at fast food outlets.”

The second story from the New York Times concerns Turkish efforts to establish Islamic schools in Pakistan that teach co-existence with the West:

“The Turkish schools, which have expanded to seven cities in Pakistan since the first one opened a decade ago, cannot transform the country on their own. But they offer an alternative approach that could help reduce the influence of Islamic extremists.

They prescribe a strong Western curriculum, with courses, taught in English, from math and science to English literature and Shakespeare. They do not teach religion beyond the one class in Islamic studies that is required by the state. Unlike British-style private schools, however, they encourage Islam in their dormitories, where teachers set examples in lifestyle and prayer.

“Whatever the West has of science, let our kids have it,” said Erkam Aytav, a Turk who works in the new schools. “But let our kids have their religion as well.”

Some parents like the Turkish schools because they produce students who are good Muslims and have good educations. Others are suspicious because the Turkish teachers are clean-shaven, wear ties, and look like “math teachers from Middle America.” Still others, like Hakan Yavuz, a Turkish professor at the University of Utah, view the schools as a Turkish attempt to acquire power by shaping the Muslim world.

I hope Pakistani parents will awaken to the rest of the world the way Abrar Awan, whose son attends a Turkish school in Quetta, apparently has:

“[Awan] said he had grown tired of the attitude of the Islamic political parties he belonged to as a student. Now a government employee with a steady job, he sees real life as more complicated than black-and-white ideology.

“America or the West was always behind every fault, every problem,” he said, at a gathering of fathers in April. “Now, in my practical life, I know the faults are within us.”

— DRJ

Election Surprise in Britain

Filed under: International — DRJ @ 12:07 pm

[Guest post by DRJ]

Britain’s Conservative Party picked up 256 council seats in Parliament and Labor lost 331 seats, putting it in 3rd place among the nation’s parties. In addition, Conservative candidate Boris Johnson won an upset victory in the Mayoral race beating incumbent Ken Livingstone, a powerful politician who has been vilified “as a ‘loony left’ pariah within his own party.”

Except for the mayoral race, the Conservative victories are viewed as largely symbolic and a resounding public rebuke to the Labor government of Prime Minister Gordon Brown. The voters are displeased “with the economy, with 11 years of Labor rule, and with Mr. Brown himself.” Brown and his cabinet promptly acknowledged it was a disastrous election for Labor and pledged to listen to the voters and improve.

New Mayor Boris Johnson has been described as “funny, engaging and untested.” Educated at Eton and Oxford but born in the United States, Johnson has been a columnist for the Daily Telegraph, editor of the Spectator magazine, and served as an M.P. He often appears unkempt and is known for his politically incorrect statements:

“In his colorful career, the new London mayor has survived public airing of an extramarital affair whose existence he originally denied as an “inverted pyramid of piffle”; has apologized to whole cities, like Liverpool, that he offended in one way or another; and has been prone to saying things like: “Voting Tory will cause your wife to have bigger breasts and increase your chances of owning a BMW M3.”

He has developed a reputation for having a fearsome but un-serious intellect and for wading into and out of embarrassing scrapes. But a man who has previously poked fun at the political process, saying: “I can’t remember what my line on drugs is. What’s my line on drugs?” and “I’m backing David Cameron’s campaign out of pure, cynical self-interest,” has been kept under a tight rein this time around, sticking to issues like crime and transportation.”

The Labor government has to stand for election by 2010 and this election is not necessarily a harbinger of future results. The thing to watch is whether PM Gordon Brown makes any policy shifts as a result of these election results.

— DRJ

Future NYT Supreme Court Correspondent Shows His True Colors in Piece About Incarceration Rates

Filed under: General — Patterico @ 11:40 am

Adam Liptak has never been to Compton.

I know this because if he had been to Compton, he would have taken a different approach to his recent piece criticizing America’s high incarceration rate. If he came face to face with the devastation that violent crime has caused Compton and surrounding communities, he wouldn’t be so appalled by the fact that we’re doing our level best to lock up the people who are robbing and murdering people.

Liptak, you may recall, is the New York Times legal reporter who has been chosen to replace Linda Greenhouse as the paper’s Supreme Court correspondent. Regular readers of this blog will remember Liptak as the author of a piece that gravely misstated the law regarding peremptory challenges in jury selection. Ever since I read that piece, I knew that I would read all future Liptak pieces with a heavy measure of suspicion. That decision was only reinforced by Liptak’s piece bemoaning the fact that America puts a lot of criminals in prison.

Liptak’s piece was brought to my attention by an angry reader on April 23, the day it appeared on the front page of the New York Times. I haven’t blogged it until today because I’ve been busy 24/7 working to add to America’s prison population.

Liptak’s piece puts criticism of America front and center:

The United States has less than 5 percent of the world’s population. But it has almost a quarter of the world’s prisoners.

Indeed, the United States leads the world in producing prisoners, a reflection of a relatively recent and now entirely distinctive American approach to crime and punishment. Americans are locked up for crimes — from writing bad checks to using drugs — that would rarely produce prison sentences in other countries. And in particular they are kept incarcerated far longer than prisoners in other nations.

No, Adam Liptak, our main problem is that we are a violent society.

I know you’re used to people telling you that the prisons are filled mostly with first-time drug users and low-level property criminals. But the facts tell a different story. Here is a chart from the U.S. Department of Justice showing that over half of state prisoners in this country are incarcerated for violent offenses like “murder, negligent and nonnegligent manslaughter, rape, sexual assault, robbery, assault, extortion, intimidation, criminal endangerment, and other violent offenses.”

state-prisoners.gif

Now, an argument could be made that, as to the nearly half of crimes that fall into other categories (property crime, drug crime, etc.), we should be incarcerating fewer prisoners. That argument has less force when you start looking at the actual people who are serving these sentences. In virtually all cases, their records are lengthy, sometimes containing violent offenses in their past. The drug seller may have a record including felony assaults. The guy serving 32 months for car theft may have a carjacking on his record within the last ten years.

And there are almost no pure users in prison. Here in California, the vast majority of state prisoners incarcerated for simple possession are in prison because, within the last five years, they have a serious or violent felony on their record — crimes like arson, kidnapping, and rape. Therefore, they don’t qualify for the Proposition 36 drug treatment program, as virtually all other defendants with possession cases do.

So yeah, you could set free the property or drug criminals, but in many cases you’d be setting free potentially violent people. But even if you didn’t care and you kicked every last one of them out of prison, you’d still be left with over 600,000 state prisoners in prison for violent crimes. That would still be a high number compared to other countries.

That doesn’t mean we have an incarceration problem. We have a violent crime problem.

Exactly which violent criminals should we not be incarcerating?

Liptak games the numbers by mushing together statistics and facts about jail inmates and prison inmates. There is a difference.

Jails house people serving short sentences. In virtually all cases, jail inmates are either awaiting trial on any level of crime, or serving a sentence of one year or less. Prisons, by contrast, house people serving sentences of more than one year. In California, this could range from 16 months (again, they actually serve only half) to life, depending on the offense.

Throughout, Liptak mushes the two together when talking about the aggregate numbers (“The United States has, for instance, 2.3 million criminals behind bars“). But at other times he speaks as though all these numbers represent prisoners, as when he says that “Americans are locked up for crimes — from writing bad checks to using drugs — that would rarely produce prison sentences in other countries.”

Well, even here, crimes like writing bad checks and using drugs are typically dealt with by imposing local jail time. Here in Los Angeles, for example, first-time and even second-time shoplifters or bad-check writers will serve only a few days in jail. First-time PCP sellers will generally serve about 90 days (180 days at half-time). (Note that I said “sellers” — first-time PCP users will get a drug treatment program and no incarceration, under the state’s Proposition 36.) This is not what most people think of when they talk about the “horror” (as one of Liptak’s experts terms it) of American incarceration rates.

Prison is different.

Liptak continues:

Criminologists and legal scholars in other industrialized nations say they are mystified and appalled by the number and length of American prison sentences.

Guess what, Adam Liptak? I’m “mystified and appalled” by the number and length of European prison sentences — specifically, the mystifying and appallingly short sentences that too often result in cases of clear, premeditated murder.

For example, in Germany, activists bombed an American military base and killed a U.S. soldier, and received a “life” sentence. By August of last year, two had been paroled after serving only 21 years. In the Netherlands, Volkert Van der Graaf confessed to assassinating politician Pim Fortuyn and was sentenced to all of 18 years.

And I could go on.

I believe many Americans are also “mystified and appalled” by the leniency of these European sentences for premeditated murder. But somehow, Adam Liptak gives no prominence to their views.

Liptak’s article is filled with outrageous statements, but I don’t have the rest of the weekend to respond to them all, so I’ll document two. First, Liptak tells us that America is the worst offender in the world when it comes to incarcerating people — but his proof contains an odd parenthetical caveat:

China, which is four times more populous than the United States, is a distant second, with 1.6 million people in prison. (That number excludes hundreds of thousands of people held in administrative detention, most of them in China’s extrajudicial system of re-education through labor, which often singles out political activists who have not committed crimes.)

So if you put aside the inconvenient fact that China sentences hundreds of thousands of people to forced labor, without judicial due process, as punishment for political dissent — if you ignore that minor detail, so minor it really should be placed inside parentheses, because really, what does it have to do with whether China is inappropriately punitive? — if you ignore that, then America is the worst country in the world!!!

Aside from that, Mrs. Lincoln, how was the play?

Next, Liptak tells us that part of America’s problem is that we lack a social safety net:

Criminologists and legal experts here and abroad point to a tangle of factors to explain America’s extraordinary incarceration rate: higher levels of violent crime, harsher sentencing laws, a legacy of racial turmoil, a special fervor in combating illegal drugs, the American temperament, and the lack of a social safety net.

Huh?

Here in the United States, our federal social programs include food stamps, SSI, unemployment insurance, the Earned Income Tax Credit, school meals programs, low-income housing assistance, child-care assistance, and various other programs, adding up to 9% of the federal budget, or over $250 billion per year. If you toss in Social Security, Medicare, Medicaid, and the State Children’s Health Insurance Program, we’re now looking at about half the federal budget, or over $1.3 trillion.

Just imagine how expensive things would be if we did have a safety net!

Remember the guy I wrote about in March who makes a living off of unemployment? He said: “I’ve been on unemployment three times in the past six years. Each time was better than the last, and each time I stayed on until the last cent was exhausted. I didn’t even try to get a job; it was a paid vacation.” I bet he’d be surprised to learn that we lack a social safety net!

But I digress.

Liptak does provide some facts to give the appearance of balance, but these facts are, in most cases, buried. We have to read through almost all the quotes given above, and more — all tirades about how barbaric and out of kilter our penal system is — before Liptak tells us that our high incarceration rate has unquestionably reduced crime. We then get another nine paragraphs of more ranting about the “horror” of American incarceration before Liptak says — in a quote that I cannot prove appeared inside parentheses in the first draft — “The nation’s relatively high violent crime rate, partly driven by the much easier availability of guns here, helps explain the number of people in American prisons.”

That’s the 20th paragraph of the article. Don’t you think that’s kind of important?

Yet that nugget comes after quotes from three experts who say that “contemporary America is viewed with horror” and describe the United States as “a rogue state, a country that has made a decision not to follow what is a normal Western approach.”

The bottom line is that Liptak, our future New York Times Supreme Court correspondent, has written a piece that drips with sympathy for the views of Europeans who think we’re being far too harsh, while burying deep in the article (or in some cases omitting entirely) the facts that would provide a more balanced perspective.

I can’t wait to read his articles on the Supreme Court.


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