Statistics

• pymc
  pymc implements the Metropolis-Hastings algorithm as a python class. Bayesian estimation, Markov chain Monte Carlo (MCMC)
• PyMVPA
  A Python package offers algorithms for classification, regression, feature selection, data import and export
  Works well with scikit-learn, and MDP. 

Natural Language Processing

• Natural Language Toolkit (NLTK) 3.0
  Text processing libraries for classification, tokenization, stemming, tagging, parsing, and semantic reasoning, and etc. Also, check out a book Natural Language Processing with Python in the library.

Machine Learning

• scikit-learn
  Python library for machine learning, data mining and analysis
• mlpy - Machine Learning Python
  mlpy provides machine learning methods for supervised and unsupervised problems.

Social Media

• Twython
  Twython is the premier Python library providing a method to access Twitter data.

Visualization

• Orange 
  Open source data visualization and analysis tool. Data mining through visual programming or Python scripting. Add-ons for bioinformatics and text mining are available.