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The most important parameter of a histogram is the bin width, since it controls the trade-oo between presenting a picture with too much detail (\un-dersmoothing") or too little detail (\oversmoothing") with respect to the true distribution. Despite this importance there has been surprisingly little research into estimation of the \optimal" bin width.(More)
SUMMARY A study into geographical variability of reproductive health outcomes (e.g. birth-weight) in Upper Cape Cod, Massachusetts, USA, benefits from geostatistical mapping or kriging. However, also observed are a number of continuous covariates (e.g. maternal age) that exhibit pronounced non-linear relationships with the response variable. To properly(More)
Fully simplified expressions for Multivariate Normal updates in non-conjugate variational message passing approximate inference schemes are obtained. The simplicity of these expressions means that the updates can be achieved very efficiently. Since the Multivariate Normal family is the most common for approximating the joint posterior density function of a(More)
Often, the functional form of covariate effects in an additive model varies across groups defined by levels of a categorical variable. This structure represents a factor-by-curve interaction. This article presents penalized spline models that incorporate factor-by-curve interactions into additive models. A mixed model formulation for penalized splines(More)
We examined the influence of two common polymorphic forms of the beta(2)-adrenergic receptor (beta(2)AR): the Gly16 and Glu27 alleles, on acute and long-term beta(2)AR desensitization in human airway smooth muscle (HASM) cells. In cells from 15 individuals, considered without respect to genotype, pretreatment with Isoproterenol (ISO) at 10(-7) M for 1 h or(More)
Multivariate kernel density estimation provides information about structure in data. Feature significance is a technique for deciding whether features – such as local extrema – are statistically significant. This paper proposes a framework for feature significance in d-dimensional data which combines kernel density derivative estimators and hypothesis tests(More)
There are a number of applied settings where a response is measured repeatedly over time, and the impact of a stimulus at one time is distributed over several subsequent response measures. In the motivating application the stimulus is an air pollutant such as airborne particulate matter and the response is mortality. However, several other variables (e.g.(More)
We present a simple semiparametric model for fitting subject-specific curves for longitudinal data. Individual curves are modelled as penalized splines with random coefficients. This model has a mixed model representation, and it is easily implemented in standard statistical software. We conduct an analysis of the long-term effect of radiation therapy on(More)