The relationship of E. coli and total coliform culture to the quantitative molecular detection of various fecal indicators, sources, and pathogens in private drinking water wells

Water remains a predominant vector for human enteric pathogens not just for developing countries but also developed nations, where numerous infectious disease outbreaks, linked to the contamination of drinking water have been documented. Private drinking water wells are a source of drinking water that is largely unstudied even though a significant percentage of the population in Ontario relies on wells as their primary water source. As there exists little to no systematic surveillance for enteric infections or outbreaks related to well water sources, these individuals may be at higher risk of waterborne infectious diseases. The relationships between various fecal indicators in the water of private drinking water wells, including E. coli, Total Coliforms (TC) and Bacteroides, and enteric pathogens, including Campylobacter jejuni, Salmonella spp., and Shiga toxin producing E. coli, were studied. Convenience private well water samples collected from various regions of interest during the summer of 2014 underwent membrane filtration and culture to determine quantities of E. coli and TC colony forming units. 289 E. coli positive and 230 TC-only waters were successfully analyzed by individual qPCR assays for the aforementioned enteric pathogens. Microbial source tracking methods targeted to specific Bacteroides were used to determine the source of fecal contamination as either human or bovine. The source of fecal contamination varied by geographic region and is thought to be due to such things as differences in septic tank density and underlying geology, among others. Fecal indicators, E. coli and Bacteroides, were significantly correlated. E. coli as measured by qPCR was more strongly correlated to both total and human-specific Bacteroides genetic markers than culturable E. coli. Lastly, 1.9% of samples showed molecular evidence of contamination with enteric pathogens. Although low, this finding is significant given the limited volume of water available for testing, and suggests a potential health risk to consumers. Knowing the extent of contamination, as well as the biologic source, can better inform risk assessment and the development of potential intervention strategies for private well water in specific regions of Ontario.

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.