Well-posed Bayesian inverse problems and heavy-tailed stable quasi-Banach space priors

This article extends the framework of Bayesian inverse problems in infinite-dimensional parameter spaces, as advocated by Stuart (Acta Numer. 19:451--559, 2010) and others, to the case of a heavy-tailed prior measure in the family of stable distributions, such as an infinite-dimensional Cauchy distribution, for which polynomial moments are infinite or undefined. It is shown that analogues of the Karhunen--Lo\`eve expansion for square-integrable random variables can be used to sample such measures on quasi-Banach spaces. Furthermore, under weaker regularity assumptions than those used to date, the Bayesian posterior measure is shown to depend Lipschitz continuously in the Hellinger metric upon perturbations of the misfit function and observed data.Comment: To appear in Inverse Problems and Imaging. This preprint differs from the final published version in layout and typographical detail

Well-posedness of Bayesian inverse problems in quasi-Banach spaces with stable priors

The Bayesian perspective on inverse problems has attracted much mathematical attention in recent years. Particular attention has been paid to Bayesian inverse problems (BIPs) in which the parameter to be inferred lies in an infinite-dimensional space, a typical example being a scalar or tensor field coupled to some observed data via an ODE or PDE. This article gives an introduction to the framework of well-posed BIPs in infinite-dimensional parameter spaces, as advocated by Stuart (Acta Numer. 19:451--559, 2010) and others. This framework has the advantage of ensuring uniformly well-posed inference problems independently of the finite-dimensional discretisation used for numerical solution. Recently, this framework has been extended to the case of a heavy-tailed prior measure in the family of stable distributions, such as an infinite-dimensional Cauchy distribution, for which polynomial moments are infinite or undefined. It is shown that analogues of the Karhunen--Lo\`eve expansion for square-integrable random variables can be used to sample such measures on quasi-Banach spaces. Furthermore, under weaker regularity assumptions than those used to date, the Bayesian posterior measure is shown to depend Lipschitz continuously in the Hellinger and total variation metrics upon perturbations of the misfit function and observed data.Comment: To appear in the proceedings of the 88th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM), Weimar 2017. This preprint differs from the final published version in pagination and typographical detai

Using Experiments to Foster Innovation and Improve the Effectiveness of Energy Efficiency Programs

This paper argues that the establishment of a process designed to manage innovation must be developed in California to foster the creation of needed program improvements and develop new and more effective energy efficiency delivery programs. This paper discusses several key institutional problems that must be overcome to achieve significant progress

A review of the genus Megalographa Lafontaine and Poole (Lepidoptera: Noctuidae: Plusiinae) with the description of a new species from Costa Rica

The classification of the genus Megalographa Lafontaine and Poole, 1991, is reviewed and the five known species diagnosed. The genus is essentially restricted to the New World, although one species M. biloba (Stephens) is migratory and has occasionally straggled to western Europe. A new species (Megalographa talamanca Lafontaine and Sullivan) endemic to the Talamanca Mountain Range in Costa Rica is described. Adults and genitalia are illustrated

Nuclear emulsion measurements of the astronauts' radiation exposures on Skylab missions 2, 3, and 4

On the Skylab missions, Ilford G.5 and K.2 emulsions were flown as part of passive dosimeter packs carried by the astronauts on their wrists. Due to the long mission times, latent image fading and track crowing imposed limitations on a quantitative track and grain count analysis. For Skylab 2, the complete proton energy spectrum was determined within reasonable error limits. A combined mission dose equivalent of 2,490 millirems from protons, tissue stars and neutrons was measured on Skylab 2. A stationary emulsion stack, kept in a film vault drawer on the same mission, displayed a highly structured directional distribution of the fluence of low-energy protons (enders) reflecting the local shield distribution. On the 59 and 84-day mission 3 and 4, G.5 emulsions had to be cut on the microtom to 5-7 microns for microscopic examination. Even so, the short track segments in such thin layers precluded a statistically reliable grain count analysis. However, the K.2 emulsions still allowed accurate proton ender counts without special provisions

Radiation monitoring with nuclear emulsions on project Gemini. 1. Experimental design and evaluation procedures - Partial results on missions 4 and 5

Radiation monitoring with nuclear emulsions and other radiation sensors on Gemini projec

Radiation monitoring with nuclear emulsions on Project Gemini. II. Results on the 14-day mission Gemini VII

Radiation monitoring results of small nuclear emulsion packs worn by astronauts on Gemini VI

Nuclear emulsion measurements of the astronauts radiation exposure on Apollo 7

Nuclear emulsion measurements of astronaut radiation exposure on Apollo 7 fligh