An application of Bloom filters

It is said that Google's BigTable uses Bloom filters to reduce the disk lookups for non-existent rows or columns.

A suffix tree implementation with Unicode support

It seems that there is currently no suffix tree implementation with Unicode support publicly available online. So I adapted Thomas Mailund's suffix tree implementation in C with a Python binding and put it here. The changes that I made to the code were mainly to make it support Unicode text and be compatible with new version Python. It also includes an example program all_comsubstr.py that illustrates the extraction of common substrings from two Chinese strings (encoded in UTF-8).

Longest Common Substring

Given two strings, S of length m and T of length n, their longest common substrings can be found in O(m+n) time using a generalised suffix tree, or in O(mn) time through dynamic programming (e.g., the Python code here).

Bayesian inference for the Gaussian

Given the prior probability
$p(\mu) = \mathcal{N}(\x_0,\sigma_0^2)$
and the likelihood
$p(x_1|\mu) = \mathcal{N}(\mu,\sigma_1^2)$,
the expectation of the posterior probability
$p(\mu|x_1)$
has a very simple and elegant form:
$(\alpha \x_0 + \beta x_1) / (\alpha + \beta)$
where
$\alpha = 1/(\sigma_0^2)$ and $\beta = 1/(\sigma_1^2)$
are the precisions.

Please refer to Bishop's PRML book section 2.3.6.

Comparing Data Analysis Packages

A succinct comparison of data analysis packages including R, Matlab, SciPy, Excel, SAS, SPSS and Stata, can be found here. I recently tried Stata, but found its language syntax ugly and awkward.