Aeroengine performance is determined by temperature and pressure profiles along various axial stations within an engine. Given limited sensor measurements, we require a statistically principled approach for inferring these profiles. In this paper we detail a Bayesian methodology for interpolating the spatial temperature or pressure profile at axial stations within an aeroengine. The profile at any given axial station is represented as a spatial Gaussian random field on an annulus, with circumferential variations modelled using a Fourier basis and radial variations modelled with a squared exponential kernel. This Gaussian random field is extended to ingest data from multiple axial measurement planes, with the aim of transferring information across the planes. To facilitate this type of transfer learning, a novel planar covariance kernel is proposed. In the scenario where frequencies comprising the temperature field are unknown, we utilise a sparsity-promoting prior on the frequencies to encourage sparse representations. This easily extends to cases with multiple engine planes whilst accommodating frequency variations between the planes. The main quantity of interest, the spatial area average is readily obtained in closed form. We term this the Bayesian area average and demonstrate how this metric offers far more representative averages than a sector area average---a widely used area averaging approach. Furthermore, the Bayesian area average naturally decomposes the posterior uncertainty into terms characterising insufficient sampling and sensor measurement error respectively. This too provides a significant improvement over prior standard deviation based uncertainty breakdowns.

The Literary remains of Christophe de Longueil (Longolius, ca. 1490-1522) were published by Junta in Florence in December 1524. The volume had no collective title, but may be listed as Orationes. It included the writing which Longueil did in Padua during his stay there 1520-1522: 'Orationes duae pro defensione sua in crimen lese maiestatis,' or, as the title appeared over the work itself, 'Perduellionis rei defensio,' a third version of his answer to the charge of treason to the Roman people.