Nurturing Talent HE STEM Project Report

This is the final report outlining the findings of our evaluation of a Widening Participation initiative involving young members of the Somali community in Brent, London

Improved Adaptive Rejection Metropolis Sampling Algorithms

Markov Chain Monte Carlo (MCMC) methods, such as the Metropolis-Hastings (MH) algorithm, are widely used for Bayesian inference. One of the most important issues for any MCMC method is the convergence of the Markov chain, which depends crucially on a suitable choice of the proposal density. Adaptive Rejection Metropolis Sampling (ARMS) is a well-known MH scheme that generates samples from one-dimensional target densities making use of adaptive piecewise proposals constructed using support points taken from rejected samples. In this work we pinpoint a crucial drawback in the adaptive procedure in ARMS: support points might never be added inside regions where the proposal is below the target. When this happens in many regions it leads to a poor performance of ARMS, with the proposal never converging to the target. In order to overcome this limitation we propose two improved adaptive schemes for constructing the proposal. The first one is a direct modification of the ARMS procedure that incorporates support points inside regions where the proposal is below the target, while satisfying the diminishing adaptation property, one of the required conditions to assure the convergence of the Markov chain. The second one is an adaptive independent MH algorithm with the ability to learn from all previous samples except for the current state of the chain, thus also guaranteeing the convergence to the invariant density. These two new schemes improve the adaptive strategy of ARMS, thus simplifying the complexity in the construction of the proposals. Numerical results show that the new techniques provide better performance w.r.t. the standard ARMS.Comment: Matlab code provided in http://a2rms.sourceforge.net

Order theory and interpolation in operator algebras

We continue our study of operator algebras with and contractive approximate identities (cais). In earlier papers we have introduced and studied a new notion of positivity in operator algebras, with an eye to extending certain C*-algebraic results and theories to more general algebras. Here we continue to develop this positivity and its associated ordering, proving many foundational facts. We also give many applications, for example to noncommutative topology, noncommutative peak sets, lifting problems, peak interpolation, approximate identities, and to order relations between an operator algebra and the C*-algebra it generates. In much of this it is not necessary that the algebra have an approximate identity. Many of our results apply immediately to function algebras, but we will not take the time to point these out, although most of these applications seem new.Comment: 27 pages. arXiv admin note: substantial text overlap with arXiv:1308.272

Operator algebras with contractive approximate identities II

We make several contributions to our recent program investigating structural properties of algebras of operators on a Hilbert space. For example, we make substantial contributions to the noncommutative peak interpolation program begun by Hay and the first author, Hay and Neal. Another sample result: an operator algebra has a contractive approximate identity iff the linear span of the elements with positive real part is dense. We also extend the theory of compact projections to the most general case. Despite the title, our algebras are often allowed to have no approximate identity.Comment: 18 pages. To appear J. Functional Analysi

Exploring the role of messenger effects and feedback frames in promoting uptake of energy-efficient technologies

The persuasive potential for varying messenger types and feedback frames to increase pro-environmental choice was explored in a 2 (feedback frame: financial vs. environmental) × 5 (messenger type: neighbour, government, industry, utilities vs. control) factorial design experiment. Using the context of home heating choice, 493 non-student participants were given information on either the financial or environmental benefits of selecting an energy-efficient heat pump versus a standard boiler, as described by one of four messenger types (versus a no-messenger control). Likelihood of selecting the ‘green’ technology was assessed, as well as any carry-over effects on real-life behavioural intentions. Additionally, we assessed the messenger attributes that appeared to be most important in this context, in terms of whether sources that were perceived to be trustworthy, knowledgeable, or a combination of both dimensions, would hold greater sway over preference formation. Overall, no evidence was found for any impact of messenger type on either preference formation or behavioural intentions. However, message content (i.e. how information on the benefits of pro-environmental choice was framed), was found to have substantial impact on behaviour; with the financial versus environmental decision frame being significantly more likely to encourage uptake of the energy-efficient versus standard technology. We suggest that the level of processing required for the kinds of large-scale purchase decisions we consider here may explain the lack of any messenger effect on choice behaviour. Implications for the development of behaviour change interventions designed to promote consideration of energy-efficient technologies in this context are discussed