We deal with the situation covered by the univariate general linear model, that is, it is intended that n observations be generated in accordance with the usual model y = Xβ + ε however, it is feared that k of the observations are spurious, that is, not generated in the manner intended, so that for an unknown set of k distinct integers, say (i 1, … ik ), a subset of the first n integers, we have, specifically, that ytj , = x tj ′, β + a j , + ∊ tj , where in general x t ′ denotes the t-th row of X, and where (a 1, …, a k ), so called shift parameters, are such that – ∞ < a j , < ∞. In this paper, we discuss the posterior distribution of β, when indeed it is assumed a priori that any given set of k observations has uniform probability I/( n k ) of being spurious. The properties of the posterior of β are discussed, and the results used in an example using data generated from a response surface design. Ad hoc procedures are discussed for gaining information on k, when k is unknown. These ad hoc procedures are illustrated using a famous set of data from Darwin

The general behaviour of stiff pastes is discussed in order to select the most suitable form of apparatus for rheological measurements. Two new instruments, each of the concentric cylinder type, which can be applied to different types of stiff paste, are described. The first relies on the use of a narrow annulus to enable absolute calculations to be made, and incorporates a novel method of filling by using a split outer cylinder. It cannot be used satisfactorily with systems showing very rapid shear hardening, for which the second instrument was designed. This instrument enables the shear to be determined at all points across a wide annulus. Measurements show that, for some systems, Bingham's law of plastic flow is obeyed for each value of the shear, the effect of the shear hardening being to give an increasing value to the yield stress, as the amount of shear increases. Two new ideal rheological bodies are suggested and the effect of hydrostatic pressure on the flow properties of materials is discussed.