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

Environmental Activism, Social Networks and the Internet

Social networks and the internet both have a substantial individual effect on environmental activism in China. In this article, we speculate that social linking patterns between environmental actors, which often facilitate activism on the ground, may also exist in cyberspace in the form of an online network. The article addresses the following empirical questions. Does such an online network exist? If so, who are the constituent actors? Are these the same actors observed on the ground? In addressing these questions the article aims to contribute to the growing debate on the implications of the internet for the potential emergence of social movements in China

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

Evaluation of a Stirling engine heater bypass with the NASA Lewis nodal-analysis performance code

In support of the U.S. Department of Energy's Stirling Engine Highway Vehicle Systems program, the NASA Lewis Research Center investigated whether bypassing the P-40 Stirling engine heater during regenerative cooling would improve engine performance. The Lewis nodal-analysis Stirling engine computer simulation was used for this investigation. Results for the heater-bypass concept showed no significant improvement in the indicated thermal efficiency for the P-40 Stirling engine operating at full-power and part-power conditions. Optimizing the heater tube length produced a small increase in the indicated thermal efficiency with the heater-bypass concept

Risk management and nonbank participation in the U.S. retail payments system

The retail payments system in the United States has changed significantly in recent years. Advances in technology have caused a greater reliance on electronic payment networks. And the industrial structure of the payment services industry has evolved, as more and more nonbanks deliver payment products to end users and supply back-end processing. In general, these changes have made the payments system more efficient and given more choices to consumers and more payment options to merchants and businesses. ; At the same time, however, the rapid pace of change has introduced new risks to the payments system. First, as more and more banks market payment services to nonbanks and outsource payments processing, the differences in information possessed by payments participants can magnify difficulties in managing risk. Second, electronic payments have a significantly different risk profile than paper checks. Third, greater complexity of the payments network potentially reduces incentives to manage risk and may cause difficulties in coordinating risk mitigation. ; Sullivan lays the groundwork for a dialogue on policy to control risk in the U.S. retail payments system. He concludes that a thorough review of supervisory authority relevant to retail payments would be valuable. In particular, the original authority to supervise nonbank payment processors was established over 40 years ago, when the primary reason for establishing that authority was the use of computer technology applied to bank accounting systems. Is that authority adequate given the revolutionary changes in the payments technology seen over the last four decades?Payment systems

The changing nature of U.S. card payment fraud: industry and public policy options

As credit and debit card payments have become the primary payment instrument in retail transactions, awareness of identity theft and concerns over the safety of payments has increased. Traditional forms of card payment fraud are still an important threat, but fraud resulting from unauthorized access to payment data appears to be rising, and we are only beginning to get a sense of the dimensions of the problem. ; Thus far, the role of public policy has been to encourage the card payment industry to limit fraud by developing its own standards and procedures. Whether this policy stance is sufficient depends on the effectiveness of industry efforts to limit fraud in light of the dramatic shift toward card payments. ; Sullivan provides an overview of card payment fraud in the United States. He develops a preliminary estimate of the rate of U.S. card payment fraud and suggests that such fraud is higher than in several other countries for which data are available. The U.S. payment industry is taking steps to combat payment fraud, but progress has been slowed by conflicts of interest, inadequate incentives, and lack of coordination. Thus, policymakers should monitor the card payment industry to see if it better coordinates security efforts, and if not, consider actions to help overcome barriers to effective development of security.