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 non-classical LysR-type transcriptional regulator PA2206 is required for an effective oxidative stress response in Pseudomonas aeruginosa

LysR-type transcriptional regulators (LTTRs) are emerging as key circuit components in regulating microbial stress responses and are implicated in modulating oxidative stress in the human opportunistic pathogen Pseudomonas aeruginosa. The oxidative stress response encapsulates several strategies to overcome the deleterious effects of reactive oxygen species. However, many of the regulatory components and associated molecular mechanisms underpinning this key adaptive response remain to be characterised. Comparative analysis of publically available transcriptomic datasets led to the identification of a novel LTTR, PA2206, whose expression was altered in response to a range of host signals in addition to oxidative stress. PA2206 was found to be required for tolerance to H2O2 in vitro and lethality in vivo in the Zebrafish embryo model of infection. Transcriptomic analysis in the presence of H2O2 showed that PA2206 altered the expression of 58 genes, including a large repertoire of oxidative stress and iron responsive genes, independent of the master regulator of oxidative stress, OxyR. Contrary to the classic mechanism of LysR regulation, PA2206 did not autoregulate its own expression and did not influence expression of adjacent or divergently transcribed genes. The PA2214-15 operon was identified as a direct target of PA2206 with truncated promoter fragments revealing binding to the 5'-ATTGCCTGGGGTTAT-3' LysR box adjacent to the predicted -35 region. PA2206 also interacted with the pvdS promoter suggesting a global dimension to the PA2206 regulon, and suggests PA2206 is an important regulatory component of P. aeruginosa adaptation during oxidative stress.