Laplace the Bayesianista and the Mass of Saturn

I'm reviewing Bayes' theorem and related topics for the upcoming GDAT class. In its simplest form, Bayes' theorem is a statement about conditional probabilities. The probability of A, given that B has occurred, is expressed as: \begin{equation} \Pr(A|B) = \dfrac{\Pr(B|A)\times\Pr(A)}{\Pr(B)} \label{eqn:bayes} \end{equation} In Bayesian language, $\Pr(A|B)$ is called the posterior probability, $\Pr(A)$ the prior probability, and $\Pr(B|A)$ the likelihood (essentially a normalization factor).

Source: Wikipedia

GDAT Class October 14-18, 2013

This is your fast track to enterprise performance and capacity management with an emphasis on applying R statistical tools to your performance data.

Early-bird discounts are available for the Level III Guerrilla Data Analysis Techniques class Oct 14—18.

As usual, all classes are held at our lovely Larkspur Landing location in Pleasanton. Attendees should bring their laptops to the class as course materials are provided on a flash drive. Larkspur Landing also provides free wi-fi Internet in their residence-style rooms as well as the training room.

What's Wrong with This Picture?

Here are some examples of how not to display performance data. Remember: collecting and analyzing your performance data is only half the battle. The other, equally difficult, half is presenting your performance data and conclusions.

Example 1

This first example is an oldie but a baddie. It will also provide some context for the second example below.

Figure 1 (click to enlarge)

See the problem?

Capacity Planning Classes in August 2013

Bookings are open for both Guerrilla Boot Camp (GBoot) and Guerrilla Capacity Planning (GCaP) classes in August 2013 at the Early Bird rate.

As usual, classes will be held at our lovely Larkspur Landing location. Click on the image for booking information. Here are some comments contributed by Guerrilla alumni.

Attendees should bring their laptops, as course materials are provided on CD or flash drive. The venue also offers free wi-fi to the internet.

Exponential Cache Behavior

Guerrilla grad Gary Little observed certain fixed-point behavior in simulations where disk IO blocks are updated randomly in a fixed size cache. For his python simulation with 10 million entries (corresponding to an allocation of about 400 MB of memory) the following results were obtained:

• Hit ratio (i.e., occupied) = 0.3676748
• Miss ratio (i.e., inserts) = 0.6323252

In other words, only 63.23% of the blocks will ever end up inserted into the cache, irrespective of the actual cache size. Gary found that WolframAlpha suggests the relation: \begin{equation} \dfrac{e-1}{e} \approx 0.6321 \label{eq:walpha} \end{equation} where $e = \exp(1)$. The question remains, however, where does that magic fraction come from?

Visual Proof of Little's Law Reworked

Back in early March, when I was at the Hotsos Symposium on Oracle performance, I happened to end up sitting next to Alain C. at lunch. He always attends my presentations, especially on USL scalability analysis. During our lunchtime conversation, he took out his copy of Analyzing Computer System Performance with Perl::PDQ and opened it at the section on the visual proof for Little's law. Alain queried (query ... Oracle ... Get it?) whether the numbers really added up the way they are shown in the diagrams. It did look like there could be a discrepancy but it was too difficult to reanalyze the whole thing over lunch.

Book Review: Botched Erlang B and C Functions

As a consequence of looking into a question on the GCaP google group about the telecom performance metric known as the busy hour, I came across this book.

A new copy comes with a $267.44 price tag!!! Here is my review; slightly enhanced from the version I wrote on Amazon.