On classical and other methods of discriminant analysis and estimation of log-odds

For two multinormal populations with equal covariance matrices the likelihood ratio discriminant function, an alternative allocation rule to the sample linear discriminant function when n1 ≠ n2 ,is studied analytically. With the assumption of a known covariance matrix its distribution is derived and the expectation of its actual and apparent error rates evaluated and compared with those of the sample linear discriminant function. This comparison indicates that the likelihood ratio allocation rule is robust to unequal sample sizes. The quadratic discriminant function is studied, its distribution reviewed and evaluation of its probabilities of misclassification discussed. For known covariance matrices the distribution of the sample quadratic discriminant function is derived. When the known covariance matrices are proportional exact expressions for the expectation of its actual and apparent error rates are obtained and evaluated. The effectiveness of the sample linear discriminant function for this case is also considered. Estimation of true log-odds for two multinormal populations with equal or unequal covariance matrices is studied. The estimative, Bayesian predictive and a kernel method are compared by evaluating their biases and mean square errors. Some algebraic expressions for these quantities are derived. With equal covariance matrices the predictive method is preferable. Where it derives this superiority is investigated by considering its performance for various levels of fixed true log-odds. It is also shown that the predictive method is sensitive to n1 ≠ n2. For unequal but proportional covariance matrices the unbiased estimative method is preferred. Product Normal kernel density estimates are used to give a kernel estimator of true log-odds. The effect of correlation in the variables with product kernels is considered. With equal covariance matrices the kernel and parametric estimators are compared by simulation. For moderately correlated variables and large dimension sizes the product kernel method is a good estimator of true log-odds.

Effects of synbiotics on cancer risk biomarkers

Colorectal cancer (CRC) is the fourth most common cause of death from cancer in the world and second most common (behind lung cancer) in developed countries. In recent years there has been much interest in the potential use of prebiotics, probiotics and synbiotics in the prevention and treatment of CRC. We have previously shown that synbiotic consumption in Azoxymethane treated rats modulates the immune system, influences the genotoxic potential of caecal contents and reduces the number of colonic tumours compared to control rats who did not receive the synbiotic. The aim of the current study was to identify biomarkers suitable for use as cancer risk markers and as intervention markers. A second aim was to determine the influence of synbiotic consumption on cancer risk biomarkers such as in vivo colonic mucosal proliferation and genotoxic damage along with examining the genotoxic, cytotoxic and tumour promoting potential of faecal water (FW). Synbiotic consumption altered the composition of the gastrointestinal flora and reduced in vivo genotoxic damage and the genotoxic potential of FW in cancer and polyp subjects. Synbiotic consumption also reduced the proliferative activity in the colonic mucosa in polyp subjects. In both cancer and polyp subjects gene expression in the colonic mucosa was modulated in synbiotic consuming subjects. In this and other studies the activity of natural killer cells, the level of PGE2 in FW, IL-12 production by PBMCs, genotoxic damage in the colonic mucosa and the tumour promoting activities of FW have been identified as possible biomarkers of cancer risk. Future large scale studies investigating these parameters in healthy and diseased individuals are needed to confirm the suitability of these markers in assessing cancer risk and the role of synbiotics in modulating them.

A king for the queene: Samuel Sheppard's the faerie king and his reception of Spenser's epic authority

This thesis is the study of the use and abuse of Edmund Spenser as an authority in native English epic literature of the early seventeenth century, within fifty years of his death. It focuses on attempts to emulate or adapt his seminal text, The Faerie Queene (1596), and offers a comparative analysis of two such approaches by the liminal authors, Ralph Knevet and Samuel Sheppard. The former, a tutor to the wealthy Norfolk Paston family, produced his A Supplement of the Ferie Queene in the pre-Civil War period (c.1630-1635), while the latter wrote The Faerie King at the very end of the social upheaval of the war (c.1648-54). The thesis privileges the study of the holograph manuscripts (Cambridge University Library, MS Ee.3.53 and Bodleian Library MS Rawl. Poet. 28 respectively) over the basic editions of these neglected texts. It argues for the need to re-evaluate the significance of such texts within the Spenserian canon and, through new readings of the texts' structures and contexts, the thesis questions the legitimacy of canon formation and continuation, as well as the influence editorial policies and decision making can have on subsequent readers and receptions of the text