Summary
The incidence of an anaesthetic drug error can be directly observed in large trials. In an alternative approach, we developed a probabilistic mathematical model in which the anaesthetist is ...modelled as a ‘fallible entity’ who makes repeated drug administration choices during an operation. This fallibility was factored in the model as an initial ‘intrinsic error rate’. The choices faced included: dose; timing of administration; and the routes available for injection (e.g. venous, arterial, epidural, etc.). Additionally, we modelled the effect of fatigue as a factor that magnifies the cumulative error rate. For an initial intrinsic error rate of 1 in 1000 (which from first principles we consider a reasonable estimate), our model predicted a cumulative probability of error over a ~12 h operation of ~10%; that is, 1 in 10 operations this long results in some drug error. This is similar to the rate reported by large observational trials. Serious errors constitute a small fraction of all errors; our model predicts a Poisson distribution for the uncommon serious errors, also consistent with independent observations. Even modest assumptions for the development of fatigue had a dramatic and adverse impact on the cumulative error rate. The practice implications of our modelling include: exercising caution or avoiding starting work if under par; added vigilance in unfamiliar environments; keeping anaesthetic recipes simple; and recognising that operation durations > 5–6 h constitute a time of exaggerated risk. These implications are testable predictions in observational trials. If validated, our model could serve as a potential research tool to investigate the impact of safety interventions on the rate of intrinsic error using simulation.
Statistics lectures have been a source of much bewilderment and frustration for generations of students. This book attempts to remedy the situation by expounding a logical and unified approach to the ...whole subject of data analysis. This text is intended as a tutorial guide for senior undergraduates and research students in science and engineering. After explaining the basic principles of Bayesian probability theory, their use is illustrated with a variety of examples ranging from elementary parameter estimation to image processing. Other topics covered include reliability analysis, multivariate optimization, least-squares and maximum likelihood, error-propagation, hypothesis testing, maximum entropy and experimental design. The Second Edition of this successful tutorial book contains a new chapter on extensions to the ubiquitous least-squares procedure, allowing for the straightforward handling of outliers and unknown correlated noise, and a cutting-edge contribution from John Skilling on a novel numerical technique for Bayesian computation called 'nested sampling'.
The opportunities for doing scattering experiments at synchrotron and neutron facilities have grown rapidly in recent years and are set to continue to do so into the foreseeable future. This text ...provides a basic understanding of how these techniques enable the structure and dynamics of materials to be studied at the atomic and molecular level. Although mathematics cannot be avoided in a theoretical discussion, the aim has been to write a book that most scientists will still find approachable. To this end, the first two chapters are devoted to providing a tutorial background in the mathematics and physics that are implicitly assumed in other texts. Thereafter, the philosophy has been one of keeping things as simple as possible.
The analysis of data in particle physics often involves systematic uncertainties, and the results entail the setting of limits on inferred parameters. This paper illustrates the former with a simple ...example, building on the introduction to the Bayesian approach given in Sivia 1, and offers a novel suggestion for the latter.
The kinematic approximation to specular reflectivity is very useful for understanding neutron and X-ray scattering observations, because it provides a simple analytical formula that relates the ...scattering-length density profile of a layered surface or interface, β(z), to the data, R (q
z
). Although its derivation from the wave equation, or the optical transfer model, for large q
z
, is straightforward, the origin of the q
z
-factor in the denominator is less obvious when the problem is viewed in the limit of Fraunhofer diffraction from the outset. This paper, which is principally educational, aims to bring clarity to the issue.
A novel method for the estimation of the background in a powder diffraction pattern has been developed using a robust Bayesian analysis. In formulating a probabilistic approach to background fitting, ...the diffraction peaks are considered to be nuisance data that must be taken into account. The underlying probability theory is discussed in terms of going beyond the Gaussian approximation normally associated with counting statistics and least‐squares analysis. Various examples are presented that illustrate the general applicability of this approach.
The superionic properties of the compounds RbAg4I5, KAg4I5 and KCu4I5 have been investigated by powder neutron diffraction and complex impedance spectroscopy. RbAg4I5 and KAg4I5 have room-temperature ...ionic conductivities of σ=0.21(6) and 0.08(5) Ω−1 cm−1, respectively, which increase gradually on increasing temperature. KCu4I5 is only stable in the temperature range between 515(5) K and its melting point of 605 K, and its ionic conductivity is σ=0.61(8) Ω−1 cm−1, at T=540 K. At lower temperatures, KCu4I5 disproportionates into KI+4CuI and the ionic conductivity falls by over three orders of magnitude. Least-squares refinements of the powder neutron diffraction data for RbAg4I5 at ambient temperature confirm the reported structure (space group P4132, Z=4, a=11.23934(3) Å), though with some differences in the preferred locations of the mobile Ag+. KAg4I5 and KCu4I5 are found to adopt the same basic structure as RbAg4I5, with the I− forming a β-Mn-type sublattice, with the K+ located in a distorted octahedral environment and the Ag+(Cu+) predominantly distributed over two sites which are tetrahedrally co-ordinated to I−. The implications for the conduction mechanism within these compounds are discussed, using a novel maximum entropy difference Fourier technique to map the distribution of the Ag+(Cu+) within the unit cell.
The number of `statistically independent' observations in a powder diffraction pattern has been the topic of some discussion over the past few years. It is argued that while this notion is ...tantalizing, it is illusory in principle, and it is suggested that a more appropriate measure of the quality of the data is the number of `good' reflections. By way of explanation, a tutorial on the underlying concepts of correlation and covariance, which are a surprisingly common source of confusion, is provided. A practical procedure for implementing the theoretical ideas is proposed.
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