On The Dirichlet Distribution

The Dirichlet distribution is a multivariate generalization of the Beta distribution. It is an important multivariate continuous distribution in probability and statistics. In this report, we review the Dirichlet distribution and study its properties, including statistical and information-theoretic quantities involving this distribution. Also, relationships between the Dirichlet distribution and other distributions are discussed. There are some different ways to think about generating random variables with a Dirichlet distribution. The stick-breaking approach and the Pólya urn method are discussed. In Bayesian statistics, the Dirichlet distribution and the generalized Dirichlet distribution can both be a conjugate prior for the Multinomial distribution. The Dirichlet distribution has many applications in different fields. We focus on the unsupervised learning of a finite mixture model based on the Dirichlet distribution. The Initialization Algorithm and Dirichlet Mixture Estimation Algorithm are both reviewed for estimating the parameters of a Dirichlet mixture. Three experimental results are shown for the estimation of artificial histograms, summarization of image databases and human skin detection.

Healthcare and the Common Good: Restructuring the Economy of Medical Knowledge through Communitarian Political Theory

The pharmaceutical industry wields disproportionate power and control within the medical economy of knowledge where the desire for profit considerably outweighs health for its own sake. Utilizing the theoretical tools of political philosophy, this project restructures the economy of medical knowledge in order to lessen the oligarchical control possessed by the pharmaceutical industry. Ultimately, this project argues that an economy of medical knowledge structured around communitarian political theory lessens the current power dynamic without taking an anti-capitalist stance. Arising from the core commitments of communitarian-liberalism, the production, distribution, and consumption of medical knowledge all become guided processes seeking to realize the common good of quality healthcare. This project also considers two other theoretical approaches: liberalism and egalitarianism. A Medical knowledge economy structured around liberal political theory is ultimately rejected as it empowers the oligarchical status quo. Egalitarian political theory is able to significantly reduce the power imbalance problem but simultaneously renders inconsequential medical knowledge; therefore, it is also rejected.