In contrast to recent weeks, this has not been a slow week. It has, however, been a week of tunnel vision. I’ve really only done two things; even my alter-ego the kid has been short-changed.
I’ve spent a little time reading about probability distributions (t, chi-square, and F) derived from the normal distribution. Unfortunately, as a post for this coming Monday, this material is still at stage II – and I find it hard enough to go from stage III to a published post in one weekend. This should be a short post, however, so maybe I have shot at getting from stage II all the way to a published post.
(Stage III means that the mathematics is done, but is not yet even the beginning of a lecture. Stage II means I’m still reading and taking notes.)
Or maybe I should be looking for a more likely candidate for Monday’s post. But if I don’t put some time into probability distributions, I’ll find myself in the same sorry position next weekend. So I’m torn – oops, I of all people should not use that word. Start working on the probability distributions… but bail if the material doesn’t come together quickly?
As for actual computational mathematics, I’ve continued playing with ARMA (auto–regressive moving–average) time series – and that’s all I’ve done. Sooner or later, I’m going to start posting about this. I guess I’ve worked 4 examples… 3 of which are interesting – which is a euphemism for “this is not what I expected to see.” And when it’s 3 out of 4 that do not work out as expected, I have to wonder about both the theory and the computer code. (And, I hate to admit it, I have to wonder about operator error: did I do what I meant to, and was that what I was supposed to do?)
It’s also unfortunate that the time series functions are part of an add-on package to Mathematica®, and isn’t free (last time I looked)… the wavelets package and the control systems package were incorporated into version 8, so I expect that the time series package will soon become part of the standard distribution. It would not feel good to pay for it one year and discover that it was free the next.
In the meantime, when I discuss it, I’ll be talking about functions that you may not have access to in Mathematica.
Along the way, I’ve had to install the latest version of the time series package… learned that I needed to use the legacy random number generator in order to replicate the original help system examples… learn how to compute residuals – and discover that the computed residuals are not consistent with the option which permits me to specify observations or noise or both before time = 0. That inconsistency is not surprising, but essential to know.
(Oh, the package computes residuals upon request… I just had to know exactly how they were computed.)
I’ve also seen the maximum likelihood estimation completely fail… or come up with parameter estimates of different signs from all of the preliminary estimates.
Anyway, time series analysis is just about the only thing I’ve been doing since the last diary post… that, and reading about probability distributions.
In other ongoing business, there were 2 earthquakes in my vicinity during the past week… one of them a 3.4… and that brings the total to 9 so far in June. I may stop counting after today, and just call it “one every 3 days”, about 10 a month – based on my thorough record-keeping for 2 whole months!
Now let me see what math I can do today.