Browsing "Statistics"
Aug 30, 2015 - Paradoxes, Probability, Statistics    Comments Off on Sleeping Beauty Plays the Lottery

Sleeping Beauty Plays the Lottery

I’ve already examined the classic Sleeping Beauty Problem and pointed out some of the pitfalls that many people fail to avoid when trying to solve the problem. I also examined Nick Bostrom’s so-called “Extreme Beauty” modification to the problem, in which Beauty wakes many, many times if the coin toss comes up tails. However, there is another “extreme” variant of this problem, the variant in which the coin toss is replaced with another two-result random process that has extremely uneven odds. That is, in this “extreme” problem, one of the possible results is extremely unlikely. Examining this variant with the methods of reasoning commonly used by the “thirders” can be enlightening and can provide some illustration of why they are wrong.

Since many “thirders” seem to be fond of relying on betting analogies to reason through the problem and explain their arguments, a useful substitute for the coin toss is a lottery. A typical lottery provides a very small chance of winning accompanied by a very large payoff (which is why lotteries are so popular). So here we shall examine what happens when Sleeping Beauty plays the lottery.

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Sleeping Beauty

For over 15 years, some people—particularly philosophers—continue to be confused by the so-called “Sleeping Beauty Problem.” This is a rather straight-forward exercise in conditional probability that should be accessible to a student in an undergraduate course on probability and statistics. Nevertheless, there are people who have managed to arrive at the wrong answer to this problem.

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Mar 3, 2014 - Climate, Statistics    Comments Off on Warming or Walking? – Stochastic Processes and Temperature Trends

Warming or Walking? – Stochastic Processes and Temperature Trends

Of all of the statistics that are cited to support the notion of “global warming,” the one that bothers me the most is the statistic claiming that \(n\) of the last \(m\) years have been the hottest years on record. For example, it’s not uncommon to hear that “10 of the last 12 years” are the warmest years in a temperature record that goes all the way back to 1880. This is often used as “irrefutable evidence” that mankind is driving up the Earth’s temperature and destroying the planet.

It is understandable that an activist would try to exploit this statistic. Most obviously, it emphasizes that recent global temperatures have been relatively high (where “high” corresponds to an increase of less than one degree Celsius over a 100-year period). The real purpose of repeating this factoid, however, is that it confuses and charms the numerically unsophisticated, leading them to assume that such a concentration of unprecedented, elevated temperatures in recent times is highly unlikely—unless some underlying cause is responsible.

This is quite misleading, however. In fact, it is not difficult to demonstrate that a relatively simple statistical model can account for this result, without requiring any bias toward warming.

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