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.

‘Black Settlers’: Hybridity, Neoliberalism and Ecosystemic Change Among Tonga Farmers of Southern Zambia, 1964-2008

This dissertation examines a process of indigenous accumulation among Tonga farmers in Zambia’s Southern Province. In the 1970s multiple authors concluded that capitalist farmers had emerged among Tonga agro-pastoralists, predominantly within private titled holdings. Relying on archival research, newspapers, secondary sources and extensive oral testimony this thesis fills a 35-year gap on the topic, providing insights into the social and environmental impacts of neoliberal policy among African peasants and capitalist farmers. In contrast to dominant narratives of the post-independence period, this study argues that Zambia did experience a developmental process post-independence, which saw significant achievements made in the agricultural sector, including the doubling of national cattle stocks. The data reveals a painful process of disarticulation beginning in the late 1980s. Following neoliberal adjustment, we observe significant heterogeneity in production systems, some regional specialization, and processes of migration. Most importantly, the thesis uncovers processes of overwhelming ecosystemic change that contributed to livestock epidemics of severe scale and scope. Amazingly, this went largely undocumented because of the simultaneous crisis of the state, which left the national statistics office and other state bodies incapable of functioning from the late 1980s into the 2000s. In response, the Zambian state has introduced a number of neodevelopmental initiatives in the sector, yet the lack of animal traction remained up to 2008 and agricultural production declined, while more capitalized farmers (largely white, and/or with foreign direct investment) have become more significant players in the country. This thesis provides compelling evidence to challenge dominant economic thinking of the Washington institutions as well as many of the common Marxian formulations.