Efficient Monte Carlo sampling by parallel marginalization

Markov chain Monte Carlo sampling methods often suffer from long correlation times. Consequently, these methods must be run for many steps to generate an independent sample. In this paper a method is proposed to overcome this difficulty. The method utilizes information from rapidly equilibrating coarse Markov chains that sample marginal distributions of the full system. This is accomplished through exchanges between the full chain and the auxiliary coarse chains. Results of numerical tests on the bridge sampling and filtering/smoothing problems for a stochastic differential equation are presented.Comment: 7 figures, 2 figures, PNAS .cls and .sty files, submitted to PNA

"The mad", "the bad", "the victim":gendered constructions of women who kill within the criminal justice system

Women commit significantly fewer murders than men and are perceived to be less violent. This belief about women’s non-violence reflects the discourses surrounding gender, all of which assume that women possess certain inherent essential characteristics such as passivity and gentleness. When women commit murder the fundamental social structures based on appropriate feminine gendered behaviour are contradicted and subsequently challenged. This article will explore the gendered constructions of women who kill within the criminal justice system. These women are labelled as either mad, bad or a victim, by both the criminal justice system and society, depending on the construction of their crime, their gender and their sexuality. Symbiotic to labelling women who kill in this way is the denial of their agency. That is to say that labelling these women denies the recognition of their ability to make a semi-autonomous decision to act in a particular way. It is submitted that denying the agency of these women raises a number of issues, including, but not limited to, maintaining the current gendered status quo within the criminal law and criminal justice system, and justice both being done, and being seen to be done, for these women and their victims

Building a sustainable approach to mental health work in schools

Sustainability is a major challenge to mental health work in schools, and many initiatives started by well-meaning individuals and agencies fade quickly. This paper outlines some key actions that can be taken to ensure that mental health work is sustained, as well as introduced, in schools. These actions include demonstrating that mental health work meets educational goals such as learning and the management of behaviour, using a positive model of mental well-being to which it is easy for those who work in schools to relate, using mentalhealth experts as part of a team, forging alliances with other agencies and working with a whole-school approach. Such approaches are more likely to meet the needs of people with more severe mental problems and provide a more stable platform for specialist interventions than targeted programmes. The paper goes on to suggest some practical steps to sustain work at the school level. These steps include assessing the current position, developing the vision, identifying the gaps, determining readiness and assessing the scene for change, securing consensus, planning the change, establishing criteria, and managing, evaluating and maintaining the change

The Brownian fan

We provide a mathematical study of the modified Diffusion Monte Carlo (DMC) algorithm introduced in the companion article \cite{DMC}. DMC is a simulation technique that uses branching particle systems to represent expectations associated with Feynman-Kac formulae. We provide a detailed heuristic explanation of why, in cases in which a stochastic integral appears in the Feynman-Kac formula (e.g. in rare event simulation, continuous time filtering, and other settings), the new algorithm is expected to converge in a suitable sense to a limiting process as the time interval between branching steps goes to 0. The situation studied here stands in stark contrast to the "na\"ive" generalisation of the DMC algorithm which would lead to an exponential explosion of the number of particles, thus precluding the existence of any finite limiting object. Convergence is shown rigorously in the simplest possible situation of a random walk, biased by a linear potential. The resulting limiting object, which we call the "Brownian fan", is a very natural new mathematical object of independent interest.Comment: 53 pages, 2 figures. Formerly 2nd part of arXiv:1207.286

Fast randomized iteration: diffusion Monte Carlo through the lens of numerical linear algebra

We review the basic outline of the highly successful diffusion Monte Carlo technique commonly used in contexts ranging from electronic structure calculations to rare event simulation and data assimilation, and propose a new class of randomized iterative algorithms based on similar principles to address a variety of common tasks in numerical linear algebra. From the point of view of numerical linear algebra, the main novelty of the Fast Randomized Iteration schemes described in this article is that they work in either linear or constant cost per iteration (and in total, under appropriate conditions) and are rather versatile: we will show how they apply to solution of linear systems, eigenvalue problems, and matrix exponentiation, in dimensions far beyond the present limits of numerical linear algebra. While traditional iterative methods in numerical linear algebra were created in part to deal with instances where a matrix (of size $\mathcal{O}(n^2)$) is too big to store, the algorithms that we propose are effective even in instances where the solution vector itself (of size $\mathcal{O}(n)$) may be too big to store or manipulate. In fact, our work is motivated by recent DMC based quantum Monte Carlo schemes that have been applied to matrices as large as $10^{108} \times 10^{108}$. We provide basic convergence results, discuss the dependence of these results on the dimension of the system, and demonstrate dramatic cost savings on a range of test problems.Comment: 44 pages, 7 figure