Optimal designs for multivariable spline models

In this paper, we investigate optimal designs for multivariate additive spline regressionmodels. We assume that the knot locations are unknown, so must be estimated from thedata. In this situation, the Fisher information for the full parameter vector depends on theunknown knot locations, resulting in a non-linear design problem. We show that locally,Bayesian and maximin D-optimal designs can be found as the products of the optimaldesigns in one dimension. A similar result is proven for Q-optimality in the class of allproduct design

Multivariate emulation of computer simulators: model selection and diagnostics with application to a humanitarian relief model

We present a common framework for Bayesian emulation methodologies for multivariate-output simulators, or computer models, that employ either parametric linear models or nonparametric Gaussian processes. Novel diagnostics suitable for multivariate covariance-separable emulators are developed and techniques to improve the adequacy of an emulator are discussed and implemented. A variety of emulators are compared for a humanitarian relief simulator, modelling aid missions to Sicily after a volcanic eruption and earthquake, and a sensitivity analysis is conducted to determine the sensitivity of the simulator output to changes in the input variables. The results from parametric and nonparametric emulators are compared in terms of prediction accuracy, uncertainty quantification and scientific interpretability

The early career of the Magister Equitum Jacobus

Claudian's carm. min. 50 which is addressed ‘In Jacobum Magistrum Equitum’ has recently been the subject of a detailed study by J. Vanderspoel. In it he reviews what little we know about the career of Jacobus using as his second source in this matter the letter of Vigilius, bishop of Tridentum, to John Chrysostom, bishop of Constantinople, the heading of which reports that the relics of the martyrs Sisinnius, Alexander and Martyrius reached Constantinople ‘per Jacobum virum illustrem’. Whilst I am willing to accept the argument that the relics must have been delivered by about A.D. 400, if not earlier, and that Jacobus received the office of magister equitum subsequent to this, I have some misgivings about the treatment afforded the earlier career of Jacobus, and it is to this matter which I wish to draw attention here

An unnoticed official: the Praepositus Saltus

The Passio Typasii survives in only one manuscript and was published for the first time in 1890. It purports to describe the trial and death of a Mauretanian martyr, a military veteran by the name of Typasius, during the Diocletianic persecution. However as recently demonstrated its literary borrowings, from the Breviarium of Eutropius and the Vita Martini of Sulpicius Severus, suggest that it is a mere fiction and that it should be dated after c. A.D. 396. It is the purpose of this note to draw attention to its preservation of an otherwise unattested title, that of the praepositus saltus, and to expand upon the significance of this title for the interpretation of the work. This title only occurs fully in one passage, being elsewhere abbreviated to praepositus, and this passage is of some interest therefore

The fate of the Magister Equitum Marcellus

In A.D. 357 while at Antioch the sophist Libanius wrote a letter to his friend Anatolius in which he congratulated him on his appointment as praefectus praetorio Illyrid. He expressed his pleasure at the conduct of Anatolius in his new appointment, and related a story which he had heard at Antioch from Musonianus, the praefectus praetorio Orientis. On his appointment, Anatolius had promised Constantius II that he would not ignore the misconduct of any official, whether civilian or military, whatever his rank. This promise had been put into effect almost immediately when one of the military commanders who showed cowardice against the barbarians was arrested

The Constantinian origin of Justina (Themistius, Or.3.43b)

Themistius says that Constantius saved Rome by defeating Magnentius and his ‘bastard and spurious successors’ who are recognizable as his future children. This description is in contrast to the ‘legitimate and unsullied blood line’ represented by Constantius. This concedes that Magnentius’ children would have been related by blood to Constantius. Since Magnentius was of ‘barbarian’ origin, this could only have happened through his wife at the time of his death, Justina, who has long been recognized as probably of Constantinian descent. Themistius’ passage constitutes the only ancient statement of Justina’s membership of the Constantinian dynasty, and confirms now what had been deduced from circumstantial evidence alone previously