How Useful is Additional Information?

As an informed and learned man, we are exposed to large amount of data and information all the time. Some of these data are incomplete, noisy; some are confusing and contradicting, and some are misleading or downright wrong.  Over time, with some filtering and learning, we formed our own (biased) opinions, and apply our judgment to event of interest.  While the intent and process may seem innocuous, our biases could and do sometimes have unintended and/or horrific consequences.  Take the recent news from Sanford, Florida as an example.  Trayvon Martin, a 17 years old, unarmed teen was shot dead by a neighborhood watch volunteer George Zimmerman.  While many details and facts are still unavailable to public, we do know that the tragic event started when George Zimmerman, according to his account, saw the hooded teen in the neighborhood and thought “he looks suspicious”.  

In his recent book Thinking, Fast and Slow, Professor Daniel Kahneman, 2002 Nobel Laureate in Economics, discussed how our brains struggle to balance our quick intuitions and slow analytics when making judgment.   We are proud of our build-in survival instincts and life experience that helped our quick intuitive responses.  We insist, while acknowledging such responses are not always correct, they are time tested and often sound.  We are perfectly ok to have such an efficient way of cutting through complex reality to get to the guts of the resolution.  And we can’t imagine how we can survive or live without such ability.  On the flip side, words such as profiling, stereotyping, bias, prejudice are often used to describe the same intuitive conclusions.   As we live in this information age and are constantly bombarded with noisy information and news, one must wonder how good is our gut reactions and how wrong could they be.  

In the chapter “Causes trump Statistics” of the said book, Professor Kahneman gave the following example:  “A cab was involved in a hit-and-run accident at night.  Two cab companies, the Green and the Blue, operate in the city.  You are given the following data: 85% of the cabs in the city are Green and 15% are blue.  A witness identified the cab as Blue.  The court tested the reliability of the witness under the circumstances that existed on the night of the accident and concluded that the witness correctly identified each one of the two colors 80% of the time and failed 20% of the time.”  Then Professor Kahneman asked us to answer intuitively to the question “What is the probability that the cab involved in the accident was Blue rather than Green?”

I don’t know about you.  But if I have to give an answer intuitively, I would probably put my bet on the taxi involved is Blue given the seemingly pretty solid witness’ account.  In real life, each of us runs into this type of situations from time to time and offers our guess freely.  But what if the answer matters (e.g., you are a juror in such a case in court) and what if we are wrong?  

So, what is the odd that I would win my bet in absence of any further information?  In this example, we were first given the fact that only 15% of taxi in this city is Blue.   If we knew nothing else, most of us probably would agree that a reasonable guess would be there is a 15% chance that it is a Blue taxi when an accident involving a taxi occurs.   The challenge comes when we are given further and additional information since we believe we now know a lot more about the event.  

In this example, we are told that there is an eye witness who said the taxi involved is Blue.   After all, the witness is 80% reliable that seems pretty good.  In a different setup, we might be told that Blue taxi is much more prune to having accident based on historical data, etc.   The core issue remains the same however: how can we incorporate such additional information properly?

More than 300 years ago, the 18^th century English mathematician Thomas Bayes addressed this very issue and developed an approach of how one could update one’s beliefs when given new evidence.   His work is fundamental to the theory of probability and statistics and bears names like Bayes’ Theorem, Bayes’ law, Bayesian Statistics, and Bayesian inference, etc.   If we applies Bayes’ Theorem to our taxi problem as Professor Kahneman suggested, we could update our estimate as follows once we are told the 2^nd piece of information that there is an eye witness who identified the taxi is Blue.  

The calculation is based on the simple observation that the probability of {the taxi is Blue} and {eye witness thinks it is Blue} can be expressed in two ways with priori or posterior probabilities:  this probability is equal to the product of the posterior probability of {that taxi is Blue, given eyewitness thinks it is Blue} of interest and the probability of {eye witness thinks it is Blue}.  It can also be expressed as the product of the probability of {eyewitness thinks it is Blue, given taxi is Blue} which is 0.8 and the priori probability of {that taxi is Blue} which is 0.15.  

But the eyewitness could be wrong.  The eyewitness can be thinking that the taxi is Blue when it is actually Green and he mistaken it to be Blue (20% chance), or taxi is indeed Blue and he got it right which is 80%.  Thus the latter probability of the evidence that eyewitness think it is blue is thus 0.20x0.85 + 0.80x0.15, or 0.29.  Therefore the posterior probability of our interest that the taxi is indeed Blue given eyewitness thinks it is Blue would be the ratio of 0.80x0.15 over 0.29, or 41%.  In other words, with the additional evidence provided by the eyewitness, the chance that the taxi is blue has risen almost three folds from 15% (based on the priori statistic) to 41%.  However, the resulted probability is still smaller than the obvious reference figure of 50% from a random toss of a fair coin if you had absolutely no information other than the fact there are two colors of taxi in the city.

What the example illustrates is that the additional information (in this example, the eyewitness account) may not give us nearly as much as we thought it would.  That is, we tend to give too much significance and weight to such additional information than it really deserves.   For this example, to have the updated estimate that the taxi is Blue be better than 50% (a totally uninformed random guess), the eye witness needs to be more than 85% reliable.   Note if we want to be 95% sure, the eyewitness reliability needs to be better than 98% in this case.

You can easily create examples like this with other subjects and numbers.  Perhaps you are visiting an area and you were told in advance that the minority population there is 15%.   Perhaps you are visiting an area and you were told that a particular group of certain profile is known to be responsible for 80% of the crimes in that area.  When there is a crime reported and a witness identified the perpetrator is of minority race or fits the profile of that group.  What is the chance that crime was indeed committed by a person of minority race or of that group as eye witness claimed?

When George Zimmerman of Sanford thought Trayvon Martin looked suspicious, when he began to follow him with a hand gun in his waist, the encounter ended with a tragic shooting death of the teen.   When the law enforcement and intelligence agencies collect statistics and profile groups, when institutions collect statistics about college admission of minority or under-represented groups, shouldn’t we all be concerned about how the data are used and if there is a rush to judgment?  Shouldn’t we all be worried about making proper inferences when we pick up new knowledge? 

Talk to you soon!

Bully and Beef

In my last blog, I touched upon the Second Opium War of China vs. British Empire in late 19^th century.  Interestingly, one hot button issue in recent weeks from Taiwan is the Second Beef War – popular protest of Taiwan government’s attempt in lifting the ban of importing beefs that contains (any) residue of ractopamine 瘦肉精.   When asked in his interview earlier today with local media in Taiwan, “America doesn’t bully,” said William Stanton, Director of the AIT (American Institute in Taiwan, the official representative of U.S. government in Taiwan).   You might think the most powerful nation of the world wouldn’t need to bully a small country like Taiwan, or would it?

Hearing and reading news like that, one can’t help but to conjure up this image of an bull running into a china shop, knocking down and breaking any objects around it.  According to the Online Etymology Dictionary however, the origin of the word bully had nothing to do with bulls.  It came from 16^th century Dutch and German and until late 19^th century, it was used with a positive meaning of "sweetheart" "lover, brother".  But Taiwan people are not likely to consider recent statements and actions by Mr. Stanton and other American officials/politicians an expression of brotherly love.

According to the Wikipedia entry, “Ractopamine is a drug that is used as a feed additive to promote leanness in pigs raised for their meat.”  It is the active ingredient in products known as Paylean for pigs and Optaflexx for cattle which were approved by FDA for finishing feeds before slaughter in 1999 and 2003 respectively (and for turkey in 2009).  The drug is now used in about 45% of the U.S. pigs and 30% of cattle.   The problem is that with the current industrial meat production process and regulations in U.S., there is no way for consumers to identify which is which. The obvious motivation behind the push is an economic one:   additional drug sales for Elanco Animal Health, a division of Eli Lilly and Company, additional revenue and profits for pig and cattle farmers/companies from (a few percent more) efficiency and resulting additional lean meat.  And when the domestic market is covered, why not reach out to international markets to sale the products?   

The first Beef War started in Oct 2009 when President Ma’s government reached an agreement with U.S. of a protocol under which Taiwan would import “risky” beef and beef offal (with higher risks of being infected by mad cow disease) from U.S.  In the end, Ma’s Nationalist government could not get the protocol ratified inspite of its supermajority in the Legislative Branch.  The Food Safety Act of Taiwan was amended to allow  more varieties of beef be imported but continue to ban virtually the risky beef and beef offal.  Since then, it is widely believed that Washington has been stalling and holding hostage the Trade and Investment Framework Agreement (TIFA) negotiation with Taiwan.  It is an open secret that Taiwan government wants TIFA badly to prevent itself from falling further into China’s grip economically and from falling behind in its competition with ASEAN countries.   Note since the first Beef War, U.S. beef export to Taiwan has increased significantly - from 27 thousand metric tons in 2009 to about 39 thousand metric tons in 2010.  It went down to 35.4 thousand metric tons in 2011 because of the strict regulation and zero tolerance inspection of imported beef for ractopamine, so complained by U.S. representatives.

Of course, no one would be making a big fuss if there weren’t financial and political interests involved.  $200 million dollars (that is the total value of the 2011 export of beef to Taiwan) may sound small, considering the total U.S. export to Taiwan in 2011 was 26 billion dollars.  Nevertheless, a dollar is a dollar and in U.S., there are particular business and farmers who stand to gain from increased export.  There are powerful lobbyists and politicians who represent these constituents and have allies who scratch each other's back.  On Taiwan side, there are pig farmers who worry about the “slippery slope” with pork next on the wish list, the politicians who seize on the popular sentiment and nationalism, and those of the opposition parties who wouldn’t miss the opportunity to attack the ruling party.

Shall we then ask the experts and trust the science like President Ma and Mr. Stanton of AIT suggested?  There are several arguments offered by both that would lead to the obvious conclusion that it is safe to import U.S. beef with limited residue of ractopamine.  Unfortunately some of these arguments such as “FDA approved”, “it is safe for Americans to consume“ only deepened the suspicion and resentment of the American Exceptionalism.  

Arguments have also been made to “bring it back to science” and “trust the experts” which are less than convincing in this case since experts do not have consensus on the risks of consumption of ractopamine fed pigs and beef.  Although limited studies and absence of serious health threat reports appear to support the claim that meat with small residue of ractopamine is safe for human, science cannot be expected to prove it is risk free.  That brings us to the real and fundamental problem – psychologists have recognized for some time that human are not very good in dealing with very small risks; we either ignore them completely or give them too much weight than any data would support.  

In his recent book Thinking, Fast and Slow, Daniel Kahneman, 2002 Nobel Laureate in Economics, devoted a whole section on the conflicting values of the Public and the Experts when it comes down to the judgment of risks like the case with the ractopamine.  Professor Kahneman sketched the opposing views of two of his esteemed colleagues:  Psychologist Paul Slovic does not believe in the existence of objective risk although risks are real.  At the other end of the spectrum, Harvard Law Professor Cass Sunstein believes it is possible to isolate decision makers from public pressure and to trust impartial experts who would not be swayed by irrational and emotional responses of public.  

Professor Kahneman agreed wisely with both.  He had this to say: “Rational or not, fear is painful and debilitating, and policy makers must endeavor to protect the public from fear, not only from real dangers.”  He went on to say “Psychology should inform the design of risk policies that combine the experts’ knowledge with the public’s emotions and intuitions.”  President Ma must be kicking himself for not handling this delicate issue better at the beginning.  It remains to be seen if his government can dig itself out of the hole it is in.  One thing is clear though: science alone cannot solve political problems.

Talk to you soon!

About Pain

Recently, I have had an episode of severe pain caused by a kidney stone in ureter (that propels urine from the kidneys to the bladder).  The pain was so intense that I was woken up in the middle of the night and after half an hour, I had to asked to be taken to the emergency room.  According to some statistics, there are more than 1 million incidents of kidney stone reported each year in U.S.  and one in ten people will experience such an episode at least once in their life time.

Of course, every one of us has had experienced pain of varying degrees in our lives.  Pain, while unpleasant, is a necessary mechanism to protect oneself to survive in the world.  Can you imagine the consequence of not feeling the pain when you are being burned, broke your leg, or sprain your ankle?  (By the way, I am limiting myself here to the discussion of physical pain which is already complicated enough.)

Yet, until 500 hundred years ago, pain was not well-understood.  Many well-respected scholars thought it was subjective and postulated it has something to do with external and spiritual world.  Some went as far as proclaiming it as a punishment by God.

With the advances of science, we now understand pain a lot more.  Significant discoveries have been and continued being made about the mechanisms of the sensing of pain and how to help relief and manage certain pains.  The basic model now tells us that there are millions of nerve endings with sensory neurons called nociceptors that can detect pain for skin, joints/bones, and body organs. When the received stimuli that are related to pain (including nerve damage) reach certain thresholds, particular neurons will signal and register the pain in the anterior cingulate gyrus of the brain and trigger appropriate responses.

Intuitively, pain has many dimensions and characteristics.  Obvious attributes include duration (short, long and continuous, and chronic), character (sharp, dull, throbbing), etc.  There are vivid verbal descriptions of experiences of distinct level of the intensity of pain too.  Among the severe pains, apparently it is true that pain can be so intense that one looses consciousness because of it, be it due to accident or torture.  Pain can also be so excruciating and have no obvious end to it that the thought of death is preferred to prolonged pain is real for many.  Severe pain with the hope of an end to it can still impair one’s judgment and potentially make one behave irrationally.  I would consider the pain caused by the kidney stone belong to this category.  First time in my life, I had reached the point of feeling so desperate that I was ready to plead for a powerful pain killer that would take my pain away immediately!

So what can we do about pain?  Pain killers come to mind immediately that is what most of us have done from time to time.  Over the counter pain killers come in various brand and packaging with ingredient such as aspirin, acetaminophen (e.g. Tylenol), ibuprofen (e.g., Advil, Motrin) and naproxen (e.g. Aleve).  These drugs all belong to the family of non-opioid analgesics that work to inhibit an enzyme known as cyclooxygenase (COX), a catalyst for the production of prostaglandins that causes pain, inflammation and fever.  Depending on where the inhabitation takes place (in central vs. peripheral nerve systems), some pain killers are more effective for headache and others are more effective for muscle or joint pains.  Except for acetaminophen, others examples above are NSAID (Non-Steroidal Anti-Inflamatory Drug) that can also reduce inflammation.  They all provide temporary reliefs for minor pains and are considered fairly safe albeit with some possible negative side effects. 

To manage more severe pains, potent and stronger pain killers are often prescribed by trained physicians.  Various opioid analgesics like morphine, hydrocodone and oxycodone come to mind.  They are either found in, or derived from, or synthesized from opiate alkaloids in natural opium poppy plants.  Remember the Opium Wars (the First Opium War from 1839 to 1842 and the Second Opium War from 1856 to 1860) between the British Empire and the Qing Dynasty of China that marked the beginning of the modern China?  Yes, Opium Wars woke up China from its deep isolation and ignorance.  Yes, the wars were triggered by the ban of opium and the seizures of the opium supplies of British and American merchants by Qing Government. 

As one of the world’s oldest known drugs, opioid works by binding to opioid receptors in our central and peripheral nervous systems and gastrointestinal tract.  The net effect is reduced the perception of pain, the decreased reaction to pain and an increase our pain tolerance.  It does have adverse side effects if not used properly.  It is addictive and often abused because of the euphoria it can produce.  But for medical use to treat acute and severe pains, it works magicv!   I was given some morphine through IV (Intravenous therapy) together with Zofran, an anti-nausea/vomiting drug to alleviate possible side effect of morphine.  Within a short time, I no longer feel any pain or discomfort (no, I did not reach euphoria)!  That was actually pretty much the end of my short kidney stone episode.  Two weeks later, the 3 mm long trouble making kidney stone was out of my body on its own without difficulty. 

In all, two things I learned from this painful experience.  I used to brag about my pain tolerance and tease those who take strong pain medications.  No more!  I have to admit that a little morphine brought me back from the hell of pain in the midst of my kidney stone episode.  I was able to breathe and talk normally not long after the IV.  Secondly, now I can honestly say I appreciate women’s worst physical pain.  The emergency room female doctor who treated me told us that pain due to kidney stone is considered comparable to that of giving a child birth.  The price I paid for this knowledge was no more sympathy from my wife.

Talk to you soon!