Adrian Bowman

Applied smoothing techniques for data analysis : the kernel approach with S-plus illustrations

1. Density estimation for exploring data 2. Density estimation for inference 3. Nonparametric regression for exploring data 4. Inference with nonparametric regression 5. Checking parametric regression models 6. Comparing regression curves and surfaces 7. Time series data 8. An introduction to semiparametric and additive models References

Intrauterine growth restriction with absent end-diastolic flow velocity in the umbilical artery is associated with maldevelopment of the placental terminal villous tree

OBJECTIVE Our purpose was to evaluate the structure of placental terminal villi and their capillaries in pregnancies complicated by intrauterine growth restriction with absent end-diastolic flow velocity in the umbilical artery. STUDY DESIGN Glutaraldehyde-perfusion-fixed villous tissue and a plastic cast of the vessels in at least two cotyledons were prepared from 10 cases with intrauterine growth restriction and 9 gestational age-matched control placentas. The structure and dimensions of 20 terminal capillary loops per cast were determined by scanning electron microscopic examination, and their appearances were correlated with the peripheral villi of the perfusion-fixed villous tissue. RESULTS Capillary loops in the growth-restricted cases were sparse in number and significantly longer than in the control cases (218 microns [72] vs 137 microns [30], mean and SD, p < 0.05). They exhibited fewer branches (4.0 [1.9] per loop vs 6.1 [2.2], p < 0.05) and a majority of loops were uncoiled (79% vs 18%, p < 0.05). The villous tissues from the growth-restricted cases demonstrated elongated villi, consistent with the cast findings. The trophoblast surface was wrinkled and in some areas covered by fibrin plaques. CONCLUSIONS The terminal villous compartment of the placenta appears to be maldeveloped in preterm intrauterine growth restriction pregnancies where absent end-diastolic flow velocity is demonstrated in the umbilical artery before delivery. These findings are consistent with an increase in fetoplacental vascular impedance at the capillary level and may account for the impaired gas and nutrient transfer in this disorder.

3D Computational Imaging with Single-Pixel Detectors

Cheap Pix Three-dimensional (3D) images can be captured by, for example, holographic imaging or stereoimaging techniques. To avoid using expensive optical components that are limited to specialized bands of wavelengths, Sun et al. (p. 844; see the Perspective by Faccio and Leach) projected pulses of randomly textured light onto an object. They were able to reconstruct an image of the 3D object by detecting the reflected light with several photodetectors without any need for lenses. The patterned light beams can thus in principle be substituted for light sources of any wavelength. A computational imaging method is used to reconstruct a three-dimensional scene, without the need for lenses. [Also see Perspective by Faccio and Leach] Computational imaging enables retrieval of the spatial information of an object with the use of single-pixel detectors. By projecting a series of known random patterns and measuring the backscattered intensity, it is possible to reconstruct a two-dimensional (2D) image. We used several single-pixel detectors in different locations to capture the 3D form of an object. From each detector we derived a 2D image that appeared to be illuminated from a different direction, even though only a single digital projector was used for illumination. From the shading of the images, the surface gradients could be derived and the 3D object reconstructed. We compare our result to that obtained from a stereophotogrammetric system using multiple cameras. Our simplified approach to 3D imaging can readily be extended to nonvisible wavebands.

An ultrasound study of gestational and postural changes in the deep venous system of the leg in pregnancy

Objective To investigate gestational and postural changes in diameter and blood flow in the proximal deep leg veins during pregnancy.

Bootstrapping in nonparametric regression: Local adaptive smoothing and confidence bands

Abstract The operation of the bootstrap in the context of nonparametric regression is considered. Bootstrap samples are taken from estimated residuals to study the distribution of a suitably recentered kernel estimator. The application of this principle to the problem of local adaptive choice of bandwidth and to the construction of confidence bands is investigated and compared with a direct method based on asymptotic means and variances. The technique of the bootstrap is to replace any occurrence of the unknown distribution in the definition of the statistical function of interest by the empirical distribution function of the observed errors. In a regression context these errors are not directly observed, although their role can be played by the residuals from the fitted model. In this article the fitted model is a kernel nonparametric regression estimator. Since nonparametric smoothing is involved, an additional difficulty is created by the bias incurred in smoothing. This bias, however, can be estimated...

A look at some data on the old faithful geyser

An analysis of data on the duration times and waiting times for eruptions from the Old Faithful Geyser reveals an interesting time series structure. A tentative physical model, derived from Rinehart, is outlined and a corresponding first‐order Markov chain examined. It is shown that a second‐order model is necessary to explain the observed correlations in the data. A curious clustering effect is apparent in the autocorrelation function when plotted over a large range of lags. Similar patterns are observed in simulations from the fitted second‐order model.

Respiratory dysfunction after uncomplicated cardiopulmonary bypass

Respiratory dysfunction is a well-recognized complication of cardiac operations. To quantify its current incidence and severity after uncomplicated cardiopulmonary bypass, serial measurements of arterial oxygen tension (PaO2), alveolar-arterial oxygen gradient (AaO2), and percentage pulmonary shunt fraction (%PSF) measured by a noninvasive technique were made in 129 patients (age, 59 +/- 8 years (mean +/- standard deviation) with good left ventricular function (left ventricular end-diastolic pressure < 15 mm Hg) undergoing isolated coronary artery operations (group 1) and 30 patients undergoing general surgical procedures (group 2). Measurements were made before operation and on the first, second, and sixth postoperative days. Seven patients in group 1 who required prolonged ventilation were excluded from further study. In group 1, between the preoperative and second postoperative days, there was a marked fall in PaO2 [89 +/- 11 versus 57 +/- 9 mm Hg; p < 0.001] and a marked increase in the AaO2 gradient [18 +/- 10 versus 50 +/- 11 mm Hg; p < 0.001)] and %PSF [3 +/- 1% versus 19 +/- 6%; p < 0.001)] with only modest improvement by the sixth postoperative day [PaO2, 67 +/- 11 mm Hg; AaO2, 45 +/- 11 mm Hg; %PSF, 15 +/- 4]. There were similar but less severe changes in PaO2 and AaO2 gradients in group 2 patients, with a return to baseline values by day 6.(ABSTRACT TRUNCATED AT 250 WORDS)

Testing monotonicity of regression

Abstract This article provides a test of monotonicity of a regression function. The test is based on the size of a “critical” bandwidth, the amount of smoothing necessary to force a nonparametric regression estimate to be monotone. It is analogous to Silvermans test of multimodality in density estimation. Bootstrapping is used to provide a null distribution for the test statistic. The methodology is particularly simple in regression models in which the variance is a specified function of the mean, but we also discuss in detail the homoscedastic case with unknown variance. Simulation evidence indicates the usefulness of the method. Two examples are given.

NON-PARAMETRIC ANALYSIS OF COVARIANCE

An analysis of covariance model where the covariate effect is assumed only to be smooth is considered. The possibility of different shapes of covariate effect in different groups is also allowed and tests of equality and of parallelism across groups are constructed. These are implemented using Gasser-Maller smoothing, whose properties enable problems of bias to be avoided. Accurate moment-based approximations are available for the distribution of each test statistic. Some data on Spanish Onions are used to contrast the non-parametric approach with that of a nonlinear, but parametric, model. A simulation study is also used to explore the properties of the non-parametric tests.

Adaptive Smoothing and Density-Based Tests of Multivariate Normality

Abstract Methods of adaptive smoothing of density estimates, where the amount of smoothing applied varies according to local features of the underlying density, are investigated. The difficulties of applying Taylor series arguments in this context are explored. Simple properties of the estimates are investigated by numerical integration and compared with the fixed kernel approach. Optimal smoothing strategies, based on the multivariate Normal distribution, are derived. As an application of these techniques, two tests of multivariate Normality—one based on integrated squared error and one on entropy—are developed, and some power calculations are carried out.