The GUM perspective on straight-line errors-in-variables regression

Abstract Even in the simple case of univariate linear regression and prediction there are important choices to be made regarding the origins of the noise terms and regarding which of the two variables under consideration that should be treated as the independent variable. These decisions are often not easy to make but they may have a considerable impact on the results. A unified probabilistic (i.e., Bayesian with flat priors) treatment of univariate linear regression and prediction is given by taking, as starting point, the general errors-in-variables model. Other versions of linear regression can be obtained as limits of this model. The likelihood of the model parameters and predictands of the general errors-in-variables model is derived by marginalizing over the nuisance parameters. The resulting likelihood is relatively simple and easy to analyze and calculate. The well-known unidentifiability of the errors-in-variables model is manifested as the absence of a well-defined maximum in the likelihood. However, this does not mean that probabilistic inference cannot be made; the marginal likelihoods of model parameters and the predictands have, in general, well-defined maxima. A probabilistic version of classical calibration is also included and it is shown how it is related to the errors-in-variables model. The results are illustrated by an example from the coupling between the lower stratosphere and the troposphere in the Northern Hemisphere winter.

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Microdensitometer—computer correlation analysis of ultrastructural periodicity

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100081024 ◽

1978 ◽

Vol 36 (2) ◽

pp. 32-33

Author(s):

D.R. Ensor ◽

C.G. Jensen ◽

J.A. Fillery ◽

R.J.K. Baker

Keyword(s):

Correlation Analysis ◽

Background Noise ◽

Computer Control ◽

Optical Diffraction ◽

Screw Thread ◽

Straight Line ◽

Computer Storage ◽

Correlation Process ◽

Electron Microscope Image ◽

Fixed Beam

Because periodicity is a major indicator of structural organisation numerous methods have been devised to demonstrate periodicity masked by background “noise” in the electron microscope image (e.g. photographic image reinforcement, Markham et al, 1964; optical diffraction techniques, Horne, 1977; McIntosh,1974). Computer correlation analysis of a densitometer tracing provides another means of minimising "noise". The correlation process uncovers periodic information by cancelling random elements. The technique is easily executed, the results are readily interpreted and the computer removes tedium, lends accuracy and assists in impartiality.A scanning densitometer was adapted to allow computer control of the scan and to give direct computer storage of the data. A photographic transparency of the image to be scanned is mounted on a stage coupled directly to an accurate screw thread driven by a stepping motor. The stage is moved so that the fixed beam of the densitometer (which is directed normal to the transparency) traces a straight line along the structure of interest in the image.

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Freeze fracture imaging and computer simulation of liposome structure: Membrane geometry and defects

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100076834 ◽

1983 ◽

Vol 41 ◽

pp. 646-647

Author(s):

Joseph A. Zasadzinski

Keyword(s):

Liquid Crystalline ◽

Freeze Fracture ◽

Continuum Theory ◽

Closed Surfaces ◽

Straight Line ◽

Low Weight ◽

Concentric Spheres ◽

Membrane Geometry ◽

Dupin Cyclides ◽

Limiting Case

At low weight fractions, many surfactant and biological amphiphiles form dispersions of lamellar liquid crystalline liposomes in water. Amphiphile molecules tend to align themselves in parallel bilayers which are free to bend. Bilayers must form closed surfaces to separate hydrophobic and hydrophilic domains completely. Continuum theory of liquid crystals requires that the constant spacing of bilayer surfaces be maintained except at singularities of no more than line extent. Maxwell demonstrated that only two types of closed surfaces can satisfy this constraint: concentric spheres and Dupin cyclides. Dupin cyclides (Figure 1) are parallel closed surfaces which have a conjugate ellipse (r1) and hyperbola (r2) as singularities in the bilayer spacing. Any straight line drawn from a point on the ellipse to a point on the hyperbola is normal to every surface it intersects (broken lines in Figure 1). A simple example, and limiting case, is a family of concentric tori (Figure 1b).To distinguish between the allowable arrangements, freeze fracture TEM micrographs of representative biological (L-α phosphotidylcholine: L-α PC) and surfactant (sodium heptylnonyl benzenesulfonate: SHBS)liposomes are compared to mathematically derived sections of Dupin cyclides and concentric spheres.

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Human Enamel Replication

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100090889 ◽

1976 ◽

Vol 34 ◽

pp. 180-181

Author(s):

Norman L. Dockum ◽

John G. Dockum

Keyword(s):

Organic Matrix ◽

Human Teeth ◽

Human Enamel ◽

Straight Line ◽

Ultrastructural Characteristics

Ultrastructural characteristics of fractured human enamel and acid-etched enamel were compared using acetate replicas shadowed with platinum and palladium. Shadowed replications of acid-etched surfaces were also obtained by the same method.Enamel from human teeth has a rod structure within which there are crystals of hydroxyapatite contained within a structureless organic matrix composed of keratin. The rods which run at right angles from the dentino-enamel junction are considered to run in a straight line perpendicular to the perimeter of the enamel, however, in many areas these enamel rods overlap, interlacing and intertwining with one another.

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