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- ItemLinear models with perturbed and truncated Laplace response functions: The asymptotic theory of MLE with application to epigenetics(Hindawi Publishing Corporation, 2012-11-20) Hassell-Sweatman CZW; Wake GC; Pleasants T; McLean CA; Sheppard AM
Show more The statistical application considered here arose in epigenomics, linking the DNA methylation proportions measured at specific genomic sites to characteristics such as phenotype or birth order. It was found that the distribution of errors in the proportions of chemical modification (methylation) on DNA, measured at CpG sites, may be successfully modelled by a Laplace distribution which is perturbed by a Hermite polynomial. We use a linear model with such a response function. Hence, the response function is known, or assumed well estimated, but fails to be differentiable in the classical sense due to the modulus function. Our problem was to estimate coefficients for the linear model and the corresponding covariance matrix and to compare models with varying numbers of coefficients. The linear model coefficients may be found using the (derivative-free) simplex method, as in quantile regression. However, this theory does not yield a simple expression for the covariance matrix of the coefficients of the linear model. Assuming response functions which are 2 except where the modulus function attains zero, we derive simple formulae for the covariance matrix and a log-likelihood ratio statistic, using generalized calculus. These original formulae enable a generalized analysis of variance and further model comparisons.Show more - ItemPopulation growth as a nonlinear process(2003-12-01) Soboleva TK; Pleasants T
Show more The evolution of the probability density of a biological population is described using nonlinear stochastic differential equations for the growth process and the related Fokker-Planck equations for the time-dependent probability densities. It is shown that the effect of the initial conditions disappears rapidly from the evolution of the mean of the process. But the behaviour of the variance depends on the initial condition. It may monotonically increase, reaching its maximum in the steady state, or have a rather complicated evolution reaching the maximum near the point where growth rates (not population size) is maximal. The variance then decreases to its steady-state value. This observation has implications for risk assessments associated with growing populations, such as microbial populations, which cause food poisoning if the population size reaches a critical level.Show more - ItemPre- and Postnatal Nutritional Histories Influence Reproductive Maturation and Ovarian Function in the Rat(Public Library of Science, 2009-08-25) Sloboda DM; Howie GJ; Pleasants T; Gluckman PD; Vickers MH
Show more While prepubertal nutritional influences appear to play a role in sexual maturation, there is a need to clarify the potential contributions of maternal and childhood influences in setting the tempo of reproductive maturation. In the present study we employed an established model of nutritional programming to evaluate the relative influences of prenatal and postnatal nutrition on growth and ovarian function in female offspring.Show more