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.

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

Realism and national identity in 'Y Tu Mamá También': an audience perspective

When referring to cinema and its emancipatory potential, realism, like Plato’s pharmakon, has signified both illness and cure, poison and medicine. On the one hand, realism is regarded as the main feature of so-called classical cinema, inherently conservative and thoroughly ideological, its main raison d’être being to reify and make a particular version of the status quo believable and to pass it out as ‘reality’ (Burch, 1990; MacCabe, 1974). On the other, realism has also been interpreted as a quest for truth and social justice, as in the positivist ethos that informs documentary (Zavattini, 1953). Even in the latter sense, however, the extent to which realism has served colonizing ends when used to investigate the ‘truth’ of the Other has also been noted, rendering the form profoundly suspicious (Chow, 2007, p. 150). For realism has been a Western form of representation, one that can be traced back to the invention of perspective in painting and that peaked with the secular worldview brought about by the Enlightenment. And like realism, the nation state too is a product of the Enlightenment, nationalism being, as it were, a secular replacement for the religious - that is enchanted or fantastic - worldview. In this way, realism, cinema and nation are inextricably linked, and equally strained under the current decline of the Enlightenment paradigm. This chapter looks at Y tu Mamá También by Alfonso Cuarón (2001), a highly successful road movie with documentary features, to explore the ways in which realism, cinema and nation interact with each other in the present conditions of ‘globalization’ as experienced in Mexico. The chapter compares and contrasts various interpretations of the role of realism in this film put forward by critics and scholars and other discourses about it circulating in the media with actual ways of audience engagement with it.