Forensic Thinking

What's wrong with being average?

2009-07-07T19:56:00.000-07:00

Yahoo finance has their own list of guest columnists that write opinion pieces on money and investing. They vary greatly in quality, by far the worst is "Rich Dad, Poor Dad" Author Robert Kiyosaki. Mr. Kiyosaki's mendacity is pretty well documented, so I won't comment on it here.

What is abundantly clear from his July 7 article is that Mr. Kiyosaki hasn't the faintest understanding of statistics. He tells investors "not to be average" as if average investors chose mediocrity.

No one chooses to be average.

If you try to make money from your investments, you are most likely to obtain average returns. This is because the average return is calculated based on the returns of people just like you. They're all shooting for the big returns, but most of them end up being average. Even worse, approximately as many of those few who get big returns instead get big losses.

Being a pro is no protection against average returns either. How many "pros" have lost so big that they're in a pickle now?

Why fight average returns anyways? You can, with a minimum of effort, obtain average returns from a well diversified portfolio. It has low transaction costs, low taxes, and typically does better than a non-diversified portfolio. It did far better during our current crisis unless you were one of the lucky few pros or amateurs to be in the right asset class at the right time.

Average returns, because they're a more likely result, are something you can plan around. You can plan your future on them, including knowing how much money to save and how to invest it. Not so for big returns - they're far less likely.

If you want to be above average, you could instead follow Kiyosaki's advice and work like a dog for those above average returns. Most likely, you'll still get average returns. You'll pay higher taxes and transaction costs, and depending on your strategy, have none of the benefits of diversification.

In his article, Kiyosaki talks about how his greater than average strategy led him to be homeless and broke in 1985. He left his wife with $2 while he went off to Australia on a business trip. His net income that year was $1500. I have no idea why anyone would want to replicate such a life. An average person will make more from average returns based on average savings from an average salary, without the homelessness and bone-crushing stress that comes with it.

One way you can become "above average" is to invest more than the average amount. You'll make more money because you're getting an average return from an above-average sized investment.

Politics and the "Dumb Electorate" Myth

2006-11-12T23:41:00.000-08:00

Around every election season, we routinely hear grumblings from folks that go something like this:

Man, people are stupid! If only people weren't so ignorant, the election would have gone the other way. What we really need to do, is make certain that we have an educated voting public rather than the stupid one we have now.

I've even heard people insist that we need a literacy test to keep the brainless electorate from ruining our lives.

I don't buy it. The idea that things would go my way if only people weren't such dopes is a very seductive concept, but ultimately it is a self serving one. I had many a strong political disagreement with well-educated colleagues, and the problem was definitely not a lack of education or misunderstanding of the issues.

It's difficult to determine how well-informed voters are on specific election issues, although I am working on finding out what I can. We can get a sense of how stupid our "dumb electorate" is by examining their educational status. Fortunately our wonderful data-compiling government collected statistics on various demographic data on those who register and those who vote. This data includes the educational status of our voting public.

You can pull up tables of who registered and who voted. I calculated percentages of the educational status of those who actually voted in the 2004 Presidential Election. What I found was:

11% have an advanced degree

21% have a bachelor's degree

31% have some college or an associates degree

28% have a high school diploma

You can then use these numbers of calculate some startling results.

91% who vote have at least completed k-12 successfully.

32% have either a bachelor's or advanced degree.

63% have some college, an associates degree, a bachelor's degree, or an
advanced degree.

They dwarf the 28% who only have a high school diploma and
the remaining 9% that have less than a k-12 education and still vote.

So, is this an uneducated voting populace?

To bring this full circle, I don't think some kind of barrier aimed at disenfranchising the less-educated is going to change much, even if it wasn't howled out of the room for a the ridiculous imposition upon the rights of the governed that it really is. Even if I assume that these people are a big problem, they're a very small percentage of the voters - a wee 9% of the vote.

I place the "Dumb Electorate" myth in same category along with the Eugenics hysteria of the first half of the 20th Century. The belief was that our country was being overrun by idiot immigrants because they hadn't passed an allegedly education and languange independent I.Q. test. Things got so out of hand that people were actually sterilized to stamp out their allegedly stupid genes. More on this topic is discussed in Stephen Jay Gould's The Mismeasure of Man.

To quote Mark Twain "There is something worse than ignorance, and that's knowing what ain't so."

Idle chatter about global warming

2006-05-14T17:51:00.000-07:00

The global warming debate rages on. Many folks think that it's a tempest in a teacup, others think that it's a real sign of human impact on the environment. I don't have much of an opinion on the subject, as I'm woefully ignorant of the science. However, the occaisonal debate catches my interest.

A recent discussion on a different message board included this statement:

Water vapor has always been the primary green house gas.

Let's assume this statement is true. The implication from this statement is that if water vapor is the primary greenhouse gas, that all of the CO2 we could possibly produce would never amount to much. Therefore, global warming is not due to human activity, and attempts to limit it are futile.

Maybe. It depends on what we mean when we say "primary". By primary green house gas do we mean that the primary gas has the largest amount in the atmosphere or the largest contribution to the warming effect?

The difference is essential.

A hypothetical example: assume water is 90% of the greenhouse gas by amount. CO2 is 5%, and all of the other gases are 5%. What if CO2 has 100 times the Green House Gas Activity than water?

Relative activity of water = 1 x 90 = 90

Relative activity of CO2 = 100 x 5 = 500

That 5% by volume would have over five times the net impact of water despite being 1/18th the relative amount.

Revisiting Prior Odds

2006-05-14T15:06:00.000-07:00

Remember our earlier examples of deciding whether we have a six or twenty sided die?

When I glibly divide 1/6 by 1/20 I assume that I am equally likely to choose a six sided or a twenty sided die. Let's instead assume a case where 101 dice are placed in a bag. 1 is a six sided die. The remainder are 20 sided. The odds of pulling a six sided die out of the bag is 1 in 100:

P of six sided die: 1/101

P of 20 sided die: 100/101

odds = (1/101)/(100/101) = 1 in 100.

We pull one die out of the bag and start rolling it to see what results we get and to determine how many sides it has. To be confident that we've pulled a six sided die out of our bag, we'd want the result of our rolls to overcome our 100 to one odds of being wrong. For one roll where the number is six or less, our calculation would be:

1/100 * 1/(6/20) = 1/100 * 3.333 = 0.03333

Which is a roughly 1 in 30 chance or 3.2%

For two rolls:

1/100 * 20/6 * 20/6 = 1/100 * 11.111 = 0.11111

About a 1 in 10 chance or 9.9%.

For three rolls:

1/100 * 20/6 * 20/6 * 20/6 = 1/100 * 37.037 = 0.37037

slightly less than 1 in 3 or 27%.

For four rolls:

1/100 * 20/6 * 20/6 * 20/6 * 20/6 = 1/100*123.456 = 1.23456

About 1.23 to one or about 55%.

For five rolls:

1/100 * (20/6)*(20/6)*(20/6)*(20/6)*(20/6) = 4.11

About 4 to 1 or 80%.

So in four rolls with numbers of six or less we could be 80% certain that we had a six sided die. If we rolled even one seven, we would be 0% certain that we had a six sided die.

If there were equal numbers of six and twenty sided dies in the bag, our numbers would be different. The prior probability would be 1/2, the prior odds would be 1 in 1. Therefore our result above would be 411 to one, with a probability of 99.75%.

No matter how compelling our scientific data, the particulars of our situation change the resulting probability.

My Math is Wrong and I Don't Care

2006-05-07T23:02:00.000-07:00

I'm not a mathematician. In fact, I would most likely irritate any mathematician worth his or her salt. This is because I am sampling from a mathematical buffet but am far too lazy to clean up after myself or, heaven forbid, prepare any of the buffet items.

A great deal of my thinking is influenced by something called Bayes's Theorem. Bayes's theorem and Bayesian Inference are often described as a guide on how to update or revise beliefs in light of new evidence.

I think that's fair statement of what I hope to accomplish.

I'm not too rigorous with the math, which means my calculations are most likely wrong at some level. I am cleverly selecting examples that I understand to illustrate my point before traveling into uncharted territory. This is much like a child who uses water wings before learning to swim. What is true is that my math is close enough so that my results make sense.

My earlier math appears wrong if you think about it carefully. Remember how we calculated odds?

Odds = P/(1-P)

Yet I was talking about odds of 3.3333 to one when dividing 1/6 by 1/20. The probability of not rolling a six on a six sided die is 5/6, not 1/20. So what gives?

It turns out that when I'm comparing the 1/6 and 1/20 probabilities, there is a Prior Odds hiding in the calculation that makes the math work. When I divide 1/6 by 1/20, I am assuming that I'd be equally likely to select a six or twenty sided die. This implies a prior odds of 1. It's there, we just don't notice it because it does not effect the calculation.

What that means is

Prior odds = P(selecting a six sided die)/P(selecting a non-six sided die)

Which is another way of saying

Prior Odds = P/(1-P)

Since

P = (1-P)

Therefore

Prior Odds = P/(1-P) = 1.

Therefore the only thing affecting the calculation is the DNA evidence.

In the earlier cases, where I merely divide 1/6 by 1/20, I'm assuming a prior odds of 1. Therefore even though 1/6 divided by 1/20 is not an odds calculation, because the prior odds are present the math will work out. Every calculation I've made without a Prior Odds in fact had one. The real calculation was

Odds of a six sided die = Prior Odds of Choosing a Six Sided Die x (Probability of rolling a six with a six sided die) / (Prob. of Rolling a six with a 20 sided die)

Odds of a six sided die = 1 x (1/6)/(1/20) = 20/6 = 3.3333

Odds, Schmodds.

2006-05-01T23:24:00.000-07:00

I've tried to avoid large amounts of arithmetic, but at this point it seems inescapable. The "odds" math I was talking about earlier can be expressed a little more formally.

Odds = (probability of an event)/(probability of non-event)

if we call probability P then odds becomes:

Odds = P/(1-P)

And therefore

P = Odds/(1 + Odds)

Let's revisit an earlier example where we rolled a die without knowing how many sides it has. Our earlier comparison looked like this:

Probability of rolling a six assuming a six-sided die: 1/6

Probability of rolling a six assuming a twenty-sided die: 1/20

or odds of about 3.333 to one.

But what do odds of about 3.333 to one mean, really? Perhaps if we could express this in terms of a probability, like 20%, 50%, of 90% we'd feel like we understood it better.

We already know the odds, we want to know the probability. Thanks to the awesome power of algebra, we can compute the probability from the odds. Our calculations go like this:

3.3333/(1+3.3333) = 3.3333/4.3333 = 0.7692

Therefore, odds of 3.333 to one mean a probability of about 77% that we have a six sided die.

Let's look at our earlier examples and convert them from odds to probabilities.

The "no DNA in the duke rape case" example: odds of 1.3333 to one: 57.1%

A standard rape case with one trillion to one odds: 99.9999999999%

Our trick die that rolled six sixes in a row: 99.9978%

Our example of rolling numbers six our less six times in a row on a six sided die versus a twenty sided die: 97.4%

This also gives us handy guide for thinking about odds and probability. If someone says the odds are 10 to one, we're talking roughly 91%. If we switch to 20 to one, we're talking about roughly 95%. If someone says 100 to one, 99%. One thousand to one, 99.9%, ten thousand to one, 99.99%, and so on.

Agatha Christie is for Chumps

2006-05-01T22:13:00.000-07:00

Okay, I'll admit it. I watch CSI. I only watch the original show, CSI:Miami and CSI:NY both leave me cold. I also love Quincy and Monk. I detest Colombo because they usually reveal the killer in the opening moments of the episode. I can't tolerate such nonsense. If I already know the identity of the killer, who cares if Columbo figures it out or not?

Along a similar line, I have zero respect for the Agatha Christie stories I've read or seen on TV. In most cases, one person is murdered by any one of a small number of people, perhaps as many as ten. Even if Poirot is a complete blunderer, outside of The Orient Express he has a one in ten chance of being correct assuming only one killer. This is admittedly a critical assumption, if we assume any combination of only five possible murderers are equally likely, Poirot's chances of determining the correct combination are much lower than 1 in 5, in the neighborhood of 1 in 30.

The real problem with Agatha Christie stories is that they fabricate a closed system to limit the scope of the problem to just a few possible criminals. With only ten people on the train, boat, or in the provincial English manor, only those few people may have contributed to the criminal event. In the real world, a crime is not a closed system, and many more than ten people might have contributed the evidence we find in a crime scene.

However, our much maligned author can contribute a useful idea to our toolbox: the notion of Prior Odds. I think about prior odds in the following fashion:

What is our chance of being "correct" if we choose a solution at random?

Prior odds are commonly utilized in mass disaster cases such as the World Trade Center disaster, Hurricane Katrina, and plane crashes. For example, if 301 people board a plane that later crashes, our expected chances of correctly identifying any one set of remains if we wildly guessed at random is about 1 in 301. The chances of identifying any one set of remains incorrectly is 300 in 301. So how do we get to prior odds from these two figures? The math is quite simple.

The odds of an event are the probability of the event divided by the probability of the non event. From above, our Prior Odds would be

(probability of correct ID)/(probability of incorrect ID).

So our prior odds are: (1/301)/(300/301) = 1 in 300.

To prevent nasty lawsuits, we want our scientific data that identifies remains as belonging to a passenger to have better odds than 300 to 1, maybe much better than 300 to one. It'd be a good idea to divide our statistics by 300 to see how well our data overcomes the 1 in 300 odds of being right.

What this means is that if our scientific analysis finds data that is 100 times more likely to belong to passenger #57 than a random person, there are only 1 out 3 odds of being correct because there are nearly 300 chances to be wrong. If there were only 10 people on the plane, the odds are instead around 10 to 1 in favor of being right.

A typical DNA profile matching an individual might be one trillion times more likely to be from that person than any one unrelated individual. However, when we are thinking about a large scale mass disaster like the 2004 Indian Ocean Tsunami where over one hundred thousand people were killed, prior odds that are at most 1/100,000 reduce our result to "only" ten million times more likely. If we imagine cases where a the missing person's toothbrush or other DNA-laden item is not available, we'd only have DNA from family members to identify a missing person. Typical DNA results might produce odds of one million to one, which when multiplied by our 1/100,000 number leaves only 10 to one.

Sounds pretty good, right? Here's the problem. If we have 10 to 1 odds of being right, that means we'll actually be wrong about 9% of the time. That means out of 100,000 dead people, we'd have on average 9000 wrong identifications. I suppose that might be acceptable to anyone other than the 9000 families with misidentified loved ones.

What follows next is some math to explain a little more of what I mean.

The Best Uses for DNA: The Duke Case Continued

2006-04-16T23:09:00.000-07:00

Another statement I disagree with from the original article:

The best use of DNA is excluding someone as the source of a particular sample," said Mark Rabil, a Winston-Salem lawyer who represented Darryl Hunt, a man freed in part by DNA evidence after serving 18 years in prison for a 1984 rape and murder.

I recoil at the use of the term "best". If DNA, as it currently existed, were "best" used as an exclusionary technique, then we could get by with a simple test that either said "match" or "no match". All of the statistics and studies of DNA profile rarity would be unimportant.

I won't belittle the benefit DNA has had for the wrongly convicted, but we shouldn't throw out the baby with the bathwater either. The primary benefit of forensic DNA technology as it exists today is not finding out who doesn't match the evidence, but understanding what it means when someone does match the evidence. The statistics that tell us that a profile is so rare it is found in only one out of ten trillion Caucasians allow us to interpret our results with confidence and present them honestly. We can then make intelligent statements about what fits best with the evidence.

If you read up on the current dust-up surrounding the admissibility of fingerprints into court under the Daubert standard, you'll understand why knowing what a match means is so important.

The Durham Lacrosse Team Rape Case

2006-04-15T15:44:00.000-07:00

A rape allegation involving Duke University's Lacrosse Team has quickly become a high-profile case. Scores of articles can be uncovered by searching news.google.com for "duke lacrosse rape". I don't have an opinion as to what happened, as I was not there and I have not personally reviewed any of the evidence. However, some egregious misstatements in a recent article have attracted my interest.

One belongs to the "willing the evidence into existence" category:

Lawyers representing some of the 46 players tested said the tests found no matching DNA on or in the woman. They contend that the results prove that no rape or sexual intercourse took place.

But the prosecutor disagrees, and the case isn't settled.

According to a U.S. Department of Justice study, DNA evidence from an attacker is successfully recovered in less than a quarter of sexual assault cases.

A statement in the Boston Globe directly attributes this figure to the DA:

Nifong said prosecutors were awaiting a second set of DNA results, but did not say how those differed from the tests reported Monday. Nifong added that in 75 percent to 80 percent of sexual assaults, there is no DNA evidence to analyze.

I can't tell from the media reports if no semen and no DNA were recovered from the victim, or if semen and DNA were found and the DNA that was found did not match any of the Lacrosse team. The difference is critical, as one finding supports rape by someone else while excluding the Lacrosse players, while the other does not support rape by anyone. What I'm stuck with is this: if semen and/or DNA had been found at all, why make the excuse that it's rarely found in the first place?

I'm unable to find any study that supports the DA's contention that DNA is rarely recoverable from rape cases. I know of reports (see below) that state that DNA from rape cases is rarely submitted to crime labs, but none that DNA is rarely recoverable. These two statements are completely different. Historically DNA was simply not collected or even submitted to crime labs due to any number of reasons, including that the victim had no idea who the attacker was. In the days before convicted offender DNA databanks, there was simply no way to know who the attacker might be without an eyewitness identification of some kind. Suspectless rape cases were simply a dead end. DNA was available, but without a suspect for comparison the results appeared useless.

I suspect that the 25% statement is a misquoting of a National Institute of Justice Report entitled The Unrealized Potential of DNA Testing, which states that of all of the reported rapes, about 40% were investigated by police, 9% provided DNA evidence to crime labs, and in 6% of cases was the DNA actually analyzed. If we adjust the numbers to include only those investigated by police, about 22% had DNA submitted to crime labs, and around 16% actually had the DNA processed. I'll add that these numbers are nine years old, and pre-date most of the "Cold Hit" programs that analyzed DNA evidence from suspectless rape cases. I wonder what the figures would be as of 2006?

The critical statement is that these numbers do not concern how much DNA is recoverable but actually recovered and analyzed.

Or maybe the figure came from somewhere else, since the quoted figure is 25% and not 20%. Maybe they're misreading this National Institute of Justice document entitled Convicted by Juries, Exonerated by Science: Case Studies in the Use of DNA Evidence to Establish Innocence After Trial, that in part states:

"Forensic DNA typing laboratories -- as numerous commentators have noted -- encounter rates of exclusion of suspected attackers in close to 25 percent of cases."

Which covers how often the initial suspect is the wrong man, not how often DNA is recovered from a case.

I cannot find any reference to a study that DNA is rarely recoverable from rapes. If anyone knows of the study, please let me know by posting to the comments of this article. I'll post a follow-up if I can find the study.

For the sake of giving the devil its due, let's do some math.

Not finding DNA in a rape case tells us plenty even when we take the 25% figure at face value. Proclaiming that "DNA is only recovered in 25% of rape cases" argues that a negative DNA result is essentially meaningless. This only makes sense if we refuse to examine alternative reasons for recovering no DNA. As before, let's assume that frequency and probability are the same.

Examined formally, this would be:

Probability of no DNA when rape did NOT occur: 100% or 1

Probability of no DNA when rape did occur: 100%-25% = 75% or .75

Relative probability of encountering no DNA when rape did not occur vs. rape did occur:

1/0.75 or 1.3333333... or about 1.3333 to one.

Therefore, not finding DNA is more likely if no rape occurred. The relative difference is small, but real.

Another way to think about this problem is in terms of reasonable doubt. Would the fact that no DNA was recovered make you cautious enough to have reasonable doubts? Or more appropriately, if we were the accused party, would we want the 1.33333 to one odds to play in our favor?

Even if DNA is recovered as rarely as 25% of the time in rape cases, the "no DNA" result is more likely if the rape did not occur. Before anyone gets angry with me, remember that I am not saying it's more likely that the rape did not occur, I'm saying that the fact that we have no DNA is more likely if the rape did not occur.

The Core Question

2006-04-01T15:21:00.001-08:00

From the previous post, the core question asked by the forensic analyst was:

How likely is the DNA profile we found if we assume the suspect committed the assault?

versus

How like is the DNA profile we found if we assume some unrelated person committed the assault?

How would we apply such thinking generally to non-forensic questions? Generalizing the core question looks like this:

How likely are the fact(s) I can truly verify if we assume one hypothesis?

versus

How likely are the fact(s) I can truly verify if I assume a competing hypothesis?

In the forensic case, the fact that can be verified and relied on is the resulting DNA profile. Everything else involved in the case the analyst was not around to witness and should be part of the "assumption" and not the facts.

In the general case, let's use a hypothetical model involving a contentious political issue. Let's say that the hypothetical state of Beatnikia bans all guns to alleviate their burgeoning gun crime problem. Some folks hate this law, claiming that it will disarm law-abiding citizens and cause crime to escalate. Other folks love this law, hoping that they'll finally be safe from gun-crazy criminals.

A federal study carefully monitors the results and finds that ten years after the ban was enacted that gun crime is roughly the same. What would be a clear-headed line of thinking? That gun crime would be lower if we hadn't disarmed the citizenry? That gun crime remained the same because gun nuts are hoarding their guns and selling them to criminals? Without further information, neither of these ideas are particularly clear-headed. These statements reek of confirmation bias, a beast discussed in an earlier posting.

the one fact we can verify is that gun crime rates are the same. Thinking forensically about that result might lead to the following questions:

How likely would that be if our law had any effect on gun crime vs. something else going on?

How likely would that be if one or the other group of concerned citizens were correct versus neither of them were correct?

How likely would that be if we really didn't understand the problem of gun crime?

This example sounds trite, but the core argument is profound. If we ask predictive questions only about the facts we can verify, we keep our heads even when things don't go our way. We no longer have to be "right" or "wrong", we merely transition from one honest idea to the next. Our theories, despite how dear they are to us, live and die on the facts we know are true.

It's a liberating idea. Imagine how much more interesting political debate would be if the participants first determined what facts they could rely on and weighed the probability of those facts given different sets of assumptions. It's a hopeless pipe dream to expect the talking heads who sell advertising for MSNBC and Fox News to embrace this idea, but most people aren't so completely compromised.

I'm not so naive as to expect some sea change in our political landscape. Politics will still be contentious and mean-spirited. Nonetheless, this "forensic" approach permitted thoughtful conversation and debate even when my fellow interlocutor disagreed with me completely. What's more, I almost always learned something from the discussion.

A Real World Example

2006-04-01T12:18:00.000-08:00

Forensic thinking is best explained with a real world example. As unpleasant as they are, rape cases often involve straightforward forensic thinking. I apologize in advance for anyone who might be upset by my blunt and clinical discussion of an extremely painful crime. A male assailant in a typical sexual assault leaves semen either on or inside the body of the victim. The assailant's DNA can be extracted from the semen and a DNA profile determined. If the DNA profile matches a suspect, the analyst must now determine what this match really means.

The forensic analyst asks two questions:

How likely is the DNA profile we found if we assume the suspect committed the assault?

vs.

How likely is the DNA profile we found if we assume a random person committed the assault?

The first question is simple. If the person whose DNA profile matches the profile recovered from the victim committed the rape, we'd expect to find his DNA profile every time. Therefore, the probability of his profile being found at a rape he committed would be one.

To determine how likely the DNA profile would be if someone else committed the crime, we need to know how often we'd expect to find a person unrelated to the suspect with a DNA profile matching the crime scene profile.

Population studies allow us to estimate the rarity of a DNA profile. In this case the crime scene profile is quite rare, the probability of encountering it is 0.000000000001. How small of a probability is that? Imagine the odds of rolling a "6" fifteen times in a row on a standard six-sided die. Imagine flipping a coin and have it turn up heads 147 times in a row. Get the general idea?

With a solid estimate of how rare the crime scene profile is, we can now evaluate our two scenarios.

The probability of encountering the DNA profile if the suspect committed the rape: 1

The probability of encountering the DNA profile if some random person committed the rape: 0.000000000001

Computing a ratio of the probabilities: 1/0.000000000001 = 1,000,000,000,000 or roughly one trillion to one.

In this case, the DNA evidence we found is one trillion times more likely if we assume that the suspect committed the rape than if we assume that some unrelated person did the deed.

Notice how the alternate hypothesis uses the word "unrelated" person. What if the suspect has a sibling or other blood relative that may have also committed the crime? Then our calculation changes significantly, because the two scenarios become:

The probability of encountering the DNA profile if the suspect committed the rape

The probability of encountering the DNA profile if a sibling of the suspect committed the rape

Thinking clearly about our assumptions is absolutely critical. For example, imagine if the suspect and victim were romantically involved. Finding a DNA profile matching the suspect would not be a surprise. The crime scene profile would not provide any useful information under such a scenario.

A Political Sidebar

2006-04-01T09:32:00.000-08:00

My brother contributes to a political blog based in Cincinnati. One of the local newspaper publications published a rather curious editorial by Professor Norbert at the Center for Environmental Genetics and Department of Pediatrics & Molecular Developmental Biology at the University of Cincinnati. He had asked me to contribute a response, which is linked by clicking on the title above.

As is always the case, I feel like I have more to say on the subject, bloated windbag that I am.

The fundamental thrust of Professor Norbert's argument is that the natural world demonstrates that homosexuality is an aberration:

Genetically and evolutionarily speaking, homosexuality is not normal - no matter how Hollywood and other secular progressives wish to spin it. "Normality" (in genetic or evolutionary terms) is defined as reproductive success that leads to future healthy generations of the species.

Apparently this professor has never heard of Bonobo chimps. I doubt their homosexuality arose from watching "Designing Women" and a morally ambiguous attitude. Bonobo chimps are sadly in danger of dying out, but not due to their sexual practices. Apparently their meat is highly prized.

Liberals reading this statement may cry "Victory! Homosexuality is validated by the natural world!" Not so fast - if we use the natural world to find moral approval, we've just validated rape, murder, theft, deception, incest, and adultery.

Our dear professor wrote an embarrassing pile of rubbish. The natural world does not give a tinker's cuss for our morality. People may glibly pick and choose what parts of nature to select for moral reinforcement, but they are playing a loser's game.

As a postscript, Professor Norbert's confusion of "normal" with "natural" and "morally good" was dealt with in my original response.

Sloppy Thinking Is Always Wrong

2006-03-22T21:32:00.000-08:00

Not too long ago I was at dinner with a forensic dentist, a forensic mathematician, and a forensic biologist. One member of the group mentioned that his wife was terrified to go camping because she feared abduction by UFOs. Being a pack of know-it-alls, we all had a good snicker at her absent expense.

The biologist piped up at this point:

While her fear sounds silly, it's very likely that there's life on other planets, and somewhat likely that there's intelligent life. So, therefore-

The forensic mathematician put his head in his hands and interrupted with a groan.

You have no idea how offensive that statement is to me. How can you say you know anything about the probability of finding life on other planets without knowing something about the frequency of life on other planets? And how can you determine this frequency of life on other planets without actually visiting them or somehow performing an experiment to test these planets for life? Unless, of course, you are trying to tell me that you're from another planet?

The mathematician's rebuke is harsh but fair. People carelessly assign probabilistic statements to events without any information other than their own wishes that something be true.

When we say something is "likely" we are in fact making a numerical judgment that the chances are greater than 50%. When we say that something is very likely, we make the statement that the chances are even greater than our estimate of "likely".

The fact that we refuse to be precise in our estimate does not excuse us from reaching a conclusion without any supporting information.

Someone might rejoinder that there's a chance our fuzzy-headed biologist might just be correct in his statement. Unfortunately, he's no more correct than the stopped clock that's right twice a day. "Correct" in this case is based on luck instead of knowledge.

A More Complex Example

2006-03-22T07:41:00.000-08:00

At first blush, forensic thinking may appear to strip us of all investigative power and abandon us in murky waters where every conclusion is predicated on weasel-worded assumptions. This is absolutely not true. To illustrate, let's return to our dice example again. Let's assume we roll six sixes in a row on what appears to be a normal six-sided die. This makes us suspect a trick die that will only roll a six. The chance of rolling six sixes on a trick die that always lands on six is 1, because that is the only result we'll get. The chance of rolling a six six times on normal die is:

(1/6)x(1/6)x(1/6)x(1/6)x(1/6)x(1/6), or approximately 0.0000214.

Therefore, our odds of rolling six sixes when we compare the assumption of a trick die versus a normal die becomes:

1 divided by 0.0000214 or approximately 46,700 to one.

Which is a very strong argument in favor of a trick die, as the six sixes in a row are 46,700 times more likely with that die.

The advantage to this type of thinking is that it separates our assumptions from our analysis and draws them out into the open. Even if your assumptions are wrong, you can still remain confident in your analysis. However, a change in your assumptions will often require a different conclusion.

New to this blog?

2006-03-22T00:48:00.000-08:00

I'd first read this posting:

What is Forensic Thinking?

Followed by

A Simple Example

Enjoy.

What is Forensic Thinking?

2006-03-22T00:36:00.000-08:00

Put plainly, forensic thinking is a way of considering complex problems in an honest and forthright fashion. Forensic thinking requires us to be explicit in our assumptions and only make definitive statements about facts that we can verify. Ideally, any good forensic scientist approaches their work in this manner.

When thinking about forensic analysis, the average person might understand the thought process to go something like this:

I extracted DNA from semen found inside a rape victim. The DNA profile from that semen matches a suspect. This DNA profile is so rare it is found in only one out of ten billion people, and therefore unlikely to be found in anyone else. Therefore, the chances against the suspect being innocent are approximately ten billion to one.

This sounds plausible, but is incorrect and not even remotely close to forensic thinking. A forensic scientist would instead present the question this way:

I extracted DNA from semen found inside a rape victim. The DNA profile from that semen matches a suspect. This DNA profile is so rare it is found in only one out of ten billion people, and therefore unlikely to be from anyone else. How relatively likely is it that I'd find this DNA profile when I compare two possibilities: The suspect contributed the semen found inside the rape victim versus some random, unrelated person contributed the semen?

The correct answer is approximately ten billion to one.

These two ways of thinking sound similar, but they are worlds apart. The first example mixes the analysis with the assumptions by leaping to the conclusion that the likely donor of the semen is the likely rapist. The suspect matching the DNA profile may be the victim's consensual partner and not a real assailant. At the same time the suspect could be both a frequent consensual partner of the victim AND the perpetrator of the rape. The DNA profile alone cannot distinguish between these two possibilities.

Making a definitive statement about events we were not around to observe is extremely perilous. The forensic scientist can only be certain of the evidence and analysis that he or she performed or examined directly. In this case, that would be the DNA profile resulting from the scientist's careful analysis.

One can only make informed statements about the probability of an event that has been observed or measured objectively. To do otherwise would be like trying to guess how likely a die roll will end up "6" without knowing how many sides the die has.

Forensic Thinking: A Simple Example

2006-03-22T00:34:00.000-08:00

One can only make informed statements about the probability of an event that has been observed or measured objectively. To do otherwise is like trying to guess how likely a die roll will end up "6" without knowing how many sides the die has.

The uncertainty behind such guesswork is obvious. The probability of rolling "6" is 1/6 for a six sided die, 1/20 for a 20 sided die, and zero for a four-sided die. Not knowing anything about the die renders it quite impossible to determine how likely a result would be, the probability would range anywhere from zero to 1/6. The die might even be a trick piece designed to roll "6" more often than any other number, which means the probability is even higher than 1/6.

Now imagine how far off you'd be with more complex problems, like how likely a crime scene DNA profile matches the "real killer" when you weren't present for any of the events that deposited the DNA in the first place.

However all hope is not lost. Let's return to the die example. We need to determine how likely a "6" would be when we roll this unseen die. Let's say that we know that the die in question either has six sides or twenty sides. We can compare the probabilities of rolling a "6" on a six versus a twenty sided die by thinking about the problem like this:

How likely am I to roll a six assuming a six-sided die versus rolling a six assuming a twenty-sided die?

Which would be:

1/6 divided by 1/20 = 20/6 or approximately 3.333

Assuming we have no other evidence regarding six or twenty sided dice being chosen for our experiment, the odds are approximately 3.333 to one in favor of rolling a "6" with a six sided die. Certain results are even more informative than the "6". For example, had we rolled a "7", the probability of getting that result assuming a six-sided die are zero, which would exclude the six sided die from our consideration.

We're not home yet, however. Odds of 3.333 to 1 mean you'll expect to be wrong approximately 23% of the time. What if we rolled the die three times and always came up with numbers of six or less? We'd certainly begin to suspect a six-sided versus a twenty-sided die, But how likely is it?

The probability of rolling any number on a six-sided die is 1/6. However, in this case we're asking the probability of rolling numbers of six or less three times in a row. Since the die can only produce numbers of six or less, the probability for each roll is 1.

1 x 1 x 1

The probability of rolling any number on a twenty-sided die is 1/20. However in this case, we're asking what the probability of rolling any number of six or less on a twenty sided die three times in a row. That becomes

(1/20) + (1/20) + (1/20) + (1/20) + (1/20) + (1/20) = 6/20

(6/20) x (6/20) x (6/20) = 0.027

If we divide the probability of getting numbers of six or less after three rolls on a six-sided die by the probability of the same result on a twenty sided die, we get

1/0.027 = 37.037

Or odds of about 37 to 1. Approximately 97% of the time you'd get this result with a six-sided die versus a twenty-sided die. After these results, we'd be reasonably confident of guessing that the die has six sides and the probability of rolling a "6" is 1/6.

2006-03-22T00:17:00.000-08:00

Forensic Scientists on TV do not utilize forensic thinking.

On television shows, forensic scientists generally fall into two types. Let's call the first Sherlock. Relying more on instinct and experience than any scientific skill, Sherlock only uses science to confirm what he or she already knows. It's almost as if Sherlock solved the crime at first glance, and the science is merely an amusing afterthought. Denzel Washington's character in "The Bone Collector" is a Sherlock. He sees things that no one else sees, and is always one step ahead of the science. He picks as his successor a beat cop with zero forensic experience who just happens to be born with the same instincts as Sherlock Washington.

The second type we can call the Deep Space Probe. The Deep Space Probe works in the lab and through miraculous techniques can determine the exact substance that was on the suspect's shoe and link it to the exact place of the crime. Results are produced immediately and eliminate all other possible explanations leaving only one possible culprit. CSI is a big fan of the Deep Space Probe forensic scientist, often paired up with a Sherlock working in the field. Sherlock's initial hunches are only disproved when the Deep Space Probe extracts miraculous (and impossible) amounts of information from the evidence.

Neither the Sherlock nor the Deep Space Probe utilize forensic thinking.

Confirmation Bias

Sherlock suffers from what is commonly known as confirmation bias.

Imagine a crime where thieves break into a donut shop and steal money from the register. Examination of the scene reveals fingerprints not belonging to the owner or current employees. Some prints at the scene match a man on parole for a felony burglary. Should we focus only our examination on this one man, or is it a mere coincidence?

Confirmation bias is a pernicious hound, stalking the intellect and striking when we least anticipate falling into its clutches. In its most basic form, confirmation bias is a form of bigotry. A very clear sign of confirmation bias are cases where a theory is proven regardless of the results of our investigation. If fingerprints matching our suspect are found, that means the suspect committed the crime. If fingerprints were not found, that means that only an experienced burglar such as our suspect committed the crime.

If you've seen the film In the Heat of the Night one of the opening scenes has a classic rendition of confirmation bias. A man is found murdered. A short distance a way, a black man is found trying to leave town on the next train with a large amount of cash in his wallet. The police are certain that they have their man because he fits their expectations and experience. They're horribly wrong, yet it takes great effort to convince them otherwise.

Politics are rife with confirmation bias. When the public votes for our favorite candidate, that means that the candidate is the right person for the job. When the public votes against our favorite candidate, the candidate is still the right person for the job, but the public is too stupid to recognize this.

Overzealous Interpretation of Evidence

The Deep Space Probe suffers from overzealous interpretation of evidence. A single hair or mote of dust is expanded into the entire fabric of the crime. In reality, minute traces of evidence found by the Deep Space Probe can rarely point to only one source. For example, a brown hair from the head of a Caucasian will not be easily confused with a hair from someone of African descent. However, one cannot look at a hair under a microscope and uniquely determine which person the hair came from.

DNA analysis can in many cases determine which person left a hair, bloodstain, or other biological evidence at a crime, but that does not mean the person committed the crime. Forensic DNA analysis is an excellent way to determine identity, but we cannot determine when the evidence was left at the scene. If a person sneezes on a tissue and leaves in a trashcan where someone is assaulted later on, overzealous interpretation of the DNA profile obtained from the tissue may unfairly implicate the sneezer in the crime.