I was visiting the University of Utah this past week. I gave talks on the Kinetic Theory of Coupled Oscillators and on Deriving Moment Equations for Neural Networks. On my way to the airport I wondered what would be the optimal arrival time so that you spend the least amount of time waiting in the airport balanced by the cost of missing a flight. If you make some basic assumptions, it’s not too hard to derive a condition for the optimum. Let’s say the only thing we’re concerned about is minimizing wasted time. Then what we would want to do is to balance the average time waiting in airports with the average time lost to make up for a missed flight.
Month: April 2009
Monty Hall and Bayes
In the nineteen seventies there was a game show on TV called “Let’s Make a Deal”. The host was Monty Hall and for the game he would present three doors to a contestant. Behind one door was the grand prize (e.g. a living room set) and behind another door was a goat. The contestant would choose a door. Then Monty Hall would open one of the two doors not selected to show that the prize was not there. The contestant could then choose to keep their original door or switch doors. The problem became famous in 1990 because Marilyn Vos Savant, who reportedly had/has the world’s highest IQ at 228, wrote in her column in Parade magazine that you should switch doors because the probability of winning increased from 1/3 to 2/3. The column prompted thousands of letters, including many from those claiming to have statistics and mathematics PhDs, saying that she was wrong and that it didn’t matter since the probability of either door having the prize was 1/2. I must confess that when I first heard the problem (I didn’t know about Bayesian inference) I also believed that the probability of winning was 1/2 for either door so it didn’t matter and it took me awhile to understand the correct answer. Now, this has been written about hundreds of times in books and articles (just google Monty Hall Problem), so there is nothing more that I can really add. However, just in case you didn’t know about this problem, it is a very nice example of how Bayes theorem can come in handy in real life.
Worst Case Scenario
In light of Freeman Dyson’s skepticism of the dire effects of global warming (See his recent profile on the New York Times Magazine), I thought I would list in order what I thought would be the worst possible things that could happen as a result of global warming and also the worst possible things if we do something about it.
Worst possible outcomes of global warming
1. All life on earth goes extinct
2. Most life on earth goes extinct, including humans
3. Most life on earth goes extinct, but humans survive (depending on your philosophy, you may swap 2 with 3 in terms of priority)
4. Oceans become so acidic that ocean life goes extinct
5. Most arable farm land turns to deserts, eliminating civilization
6. Much arable land turns to desert, leading to mass starvation and wars
7. Ocean level rises by 30 metres flooding all coastlines and many low lying nations, requiring relocation for billions of people
8. Ocean level rises by a smaller amount leading to migration for less than a billion people
9. Climate drastically changes, leading to more droughts, more megafires, more massive storms, etc.
10. Gulf stream ceases putting Europe into a mini-ice age. (If you live in Europe you may swap 9 and 10)
Worst possible outcomes for acting
1. Increased cost of energy makes food production impossible and everyone starves to death
2. Increased cost of energy makes food production almost impossible and most people starve
3. Increased cost of energy plunges most of the world into extreme poverty and ends civilization
4. Increased cost of energy plunges most of the world into poverty including India and China
5. Increased cost of energy confines developing world to poverty, but India and China continue to grow
6. Carbon sequestration underground causes massive earthquakes
7. Terrorists take over laser fusion facility and turn it into a weapon of mass destruction
8. Increased cost of energy lowers everyone’s standard of living and changes transportation structure
9. Increased cost of energy makes air travel prohibitively expensive
10. Increased cost of energy makes suburbs and car culture obsolete (Some would say this is a good thing)
Personally, I’m actually not sure which of these scenarios will happen. I’m certain that global warming is occuring but I’m not sure of the consequences. It could be that none of these things happen on either of the lists and it wouldn’t make a difference if we acted or didn’t act although we will eventually run out of fossil fuels so we will need to switch to renewables at some point.
I think it’s fair to say that many physicists have little knowledge of statistics. As I posted previously, this mostly arises because there is little need for statistics in physics (see here and here). As a result, whenever they see someone attempting to explain data or extract information from data by fitting a statistical model, they’ll simply dismiss it as “merely curve fitting”. I’m going to argue here that this perceived dichotomy between a mechanistic model and a statistical model is artificial and in fact both camps could profit immensely by learning from each other. To a statistician, a model generally means capturing the data in terms of a smaller number of degrees of freedom. The model chosen will then depend on the data and any prior information. They then spend most of their effort testing the validity of their model and assessing the significance of the fit. To a physicist, a model implies some mechanistic description, often in the form of a function or differential equations that are based on prior knowledge that is independent of the particular data set.