STAT 330 October 16, 2012

I’ll get to the regular blog later, but I just looked at Steve Strogatz’s article in the New York Times today. Click here to get it. Then go down to the movie near the end of the article (but before the comments). It will take you about nine minutes to watch the whole thing, and (since this came up in our discussion today) give you a better idea of the scale of the universe. Please note, the visible universe is more than 100 times larger than the last frame showing galaxies, and we observe galaxies that are 50 times farther away than that last frame.

If you prefer to go directly to the movie without reading the Strogatz article, click here instead (although you’ll miss an interesting article).

Speaking of astronomy, here’s an article about false discoveries, and how some astronomers ethically admit mistakes, and others do not. This sort of thing happens in any field that depends on statistics (and many that do not). If you are an aspiring statistician, you should be aware of the comment that Richard Feynman made, and which was quoted in this article: “The first principle is that you should not fool yourself, and you are the easiest person to fool.”

We started out by looking at the problem of estimating the time that the leading edge of a burst of neutrinos from a supernova would have arrived, from the arrival times of the neutrinos that were detected (about two dozen of them). We looked at a 90% frequentist confidence interval based on three data points, and discovered that the time could not be in that confidence interval, which did not include the earliest neutrino. Although this confidence interval was based on an unbiased estimator, it was not based on a sufficient statistic. We looked at a Bayesian credible interval, which is not only easier to compute than the confidence interval, but also manifestly does not have the problem that the confidence interval did.

We then turned to estimation based on the normal distribution. The take-away is as follows: When not estimating the standard deviation of the errors $\sigma$ on the data, the posterior on $\mu$ is normal, but when estimating $\sigma$, the posterior is a t distribution, with a number of degrees of freedom equal to the number of data points minus the number of parameters being estimated. We saw that centered variables simplified the solution of basic linear regression of a straight line with slope and intercept by producing a posterior distribution in which the parameters are independent.

4 Responses to “STAT 330 October 16, 2012”

1. Ahmed Says:

Wow that was an amazing video. I liked the first part about the space but the one about the man’s hands were kind of creepy 🙂 You never know who is watching….

One thing I noticed while I was watching both parts, that they had similarities and my brain was tricked in a fraction of a second and couldn’t tell whether I was watching space or the man’s hand.

I was actually wondering today, as you were discussing the light year example, what would you see if you can see that much in time. I need to watch this video a few more times and perhaps I will notice more things. For now, I am good with the one time watching and my head spinning alright 🙂

Thanks again for sharing!

-Ahmed

2. Ahmed Says:

Hey guys,

I found an applet that simulates the MH sampling algorithm. It is really very interesting and I think will help us to visualize things from a more interactive point of view than just static pictures. You will need to have the Java plugin installed on your browser to see it. I hope you find it useful:

http://www.lbreyer.com/classic.html

-Ahmed

• bayesrules Says:

Thank you, Ahmed. This looks very interesting and I am glad you found it. There are many methods illustrated here, and we don’t have time to explore most of them, so I hope that using this applet will help all of you understand the many approaches to MCMC that are available, and choose the one that best solves your problem.

3. Jamey Says:

I saw that Nate Silver was on The Daily Show last night and since we have mentioned him a few times in class, I thought I’d share a link. He talks about how the campaigns are using polls and statistics.

http://www.thedailyshow.com/watch/wed-october-17-2012/exclusive—nate-silver-extended-interview-pt–1