Approximate Bayesian computation (ABC) gives exact results under the assumption of model error

Approximate Bayesian computation (ABC) or likelihood-free inference algorithms are used to find approximations to posterior distributions without making explicit use of the likelihood function, depending instead on simulation of sample data sets from the model. In this paper we show that under the assumption of the existence of a uniform additive model error term, ABC algorithms give exact results when sufficient summaries are used. This interpretation allows the approximation made in many previous application papers to be understood, and should guide the choice of metric and tolerance in future work. ABC algorithms can be generalized by replacing the 0-1 cut-off with an acceptance probability that varies with the distance of the simulated data from the observed data. The acceptance density gives the distribution of the error term, enabling the uniform error usually used to be replaced by a general distribution. This generalization can also be applied to approximate Markov chain Monte Carlo algorithms. In light of this work, ABC algorithms can be seen as calibration techniques for implicit stochastic models, inferring parameter values in light of the computer model, data, prior beliefs about the parameter values, and any measurement or model errors.Comment: 33 pages, 1 figure, to appear in Statistical Applications in Genetics and Molecular Biology 201

The conductance of a multi-mode ballistic ring: beyond Landauer and Kubo

The Landauer conductance of a two terminal device equals to the number of open modes in the weak scattering limit. What is the corresponding result if we close the system into a ring? Is it still bounded by the number of open modes? Or is it unbounded as in the semi-classical (Drude) analysis? It turns out that the calculation of the mesoscopic conductance is similar to solving a percolation problem. The "percolation" is in energy space rather than in real space. The non-universal structures and the sparsity of the perturbation matrix cannot be ignored.Comment: 7 pages, 8 figures, with the correct version of Figs.6-

Computer program for determination of natural frequencies of closed spherical sandwich shells

Solutions for the axially symmetric motion of an elastic spherical sandwich shell have been obtained from a theory of shells which includes the effects of transverse shear deformation and rotary inertia. Frequency equations and mode shapes are derived for the full vibrations of a closed spherical shell

New deal for young people: evaluation of unemployment flows

Summary: The New Deal for Young People (NDYP) was introduced in Great Britain in January 1998 as one of the key parts of the government's welfare to work strategy. The aims of the programme were to help the young unemployed people into work and increase their employability. NDYP is for 18-24 year-olds who have been claiming Jobseeker's Allowance (JSA) for six months or more (including those getting NI credits only). It provides opportunities to work, get new skills and/or get work experience in the voluntary and environmental sectors of the economy. NDYP starts with a period known as the Gateway. On the Gateway participants receive up to four months of intensive, personalised help and support, initially designed to help find an unsubsidised job. If the participant does not get a job straight away, they will be directed towards one of four New Deal Options. The Options available are subsidised work, full-time education and training, work in the voluntary sector or work with the Environment Task Force. The Options typically last for six months, after which participants enter a period known as Follow through, which provides similar support to that available under the Gateway. NDYP is a mandatory programme, there is no option to not participate and continue to claim JSA. The aim of this paper is to derive estimates of the extent to which outcomes for individual participants in NDYP were changed by participation in the programme, by comparison with what would have happened to them without the programme. Evaluating the separate effects of the Options is not an aim of this paper. A separate evaluation study, using a different approach, was commissioned to assess the effectiveness of the Options relative to one another (see Bonjour et al., 2001). The structure of the report is as follows. The next section discusses the methods used in the evaluation. Section Three introduces the data to be used in the analysis and provides some basic descriptive information that highlights the method of analysis. Section Four presents estimated results prior to the introduction of NDYP, this analysis is used to choose the appropriate baseline period against which NDYP is to be assessed. Section Five presents the estimated results for the impact of NDYP on the probability of being unemployed after entering the programme. Section Six considers pre-programme effects. Section Seven considers the destinations upon leaving unemployment. Section Eight concludes

Geometrically necessary dislocation densities in olivine obtained using high-angular resolution electron backscatter diffraction

© 2016 The AuthorsDislocations in geological minerals are fundamental to the creep processes that control large-scale geodynamic phenomena. However, techniques to quantify their densities, distributions, and types over critical subgrain to polycrystal length scales are limited. The recent advent of high-angular resolution electron backscatter diffraction (HR-EBSD), based on diffraction pattern cross-correlation, offers a powerful new approach that has been utilised to analyse dislocation densities in the materials sciences. In particular, HR-EBSD yields significantly better angular resolution (<0.01°) than conventional EBSD (~0.5°), allowing very low dislocation densities to be analysed. We develop the application of HR-EBSD to olivine, the dominant mineral in Earths upper mantle by testing (1) different inversion methods for estimating geometrically necessary dislocation (GND) densities, (2) the sensitivity of the method under a range of data acquisition settings, and (3) the ability of the technique to resolve a variety of olivine dislocation structures. The relatively low crystal symmetry (orthorhombic) and few slip systems in olivine result in well constrained GND density estimates. The GND density noise floor is inversely proportional to map step size, such that datasets can be optimised for analysing either short wavelength, high density structures (e.g. subgrain boundaries) or long wavelength, low amplitude orientation gradients. Comparison to conventional images of decorated dislocations demonstrates that HR-EBSD can characterise the dislocation distribution and reveal additional structure not captured by the decoration technique. HR-EBSD therefore provides a highly effective method for analysing dislocations in olivine and determining their role in accommodating macroscopic deformation

Counterfactual reasoning for regretted situations involving controllable versus uncontrollable events: The modulating role of contingent self-esteem

We report a study that examined the modulating impact of contingent self-esteem on regret intensity for regretted outcomes associated with controllable versus uncontrollable events. The Contingent Self-Esteem Scale (e.g., Kernis & Goldman, 2006) was used to assess the extent to which a person’s sense of self-worth is based on self and others’ expectations. We found that there was an influence of self-esteem contingency for controllable but not for uncontrollable regret types. For controllable regret types individuals with a high contingent (i.e., unstable) self-esteem reported greater regret intensity than those with a low contingent (i.e., stable) self-esteem. We interpret this finding as reflecting a functional and adaptive role of high contingent self-esteem in terms of mobilizing the application of counterfactual reasoning and planning mechanisms that can enable personal expectations to be achieved in the future

Energetics of the Quantum Graphity Universe

Quantum graphity is a background independent model for emergent geometry, in which space is represented as a complete graph. The high-energy pre-geometric starting point of the model is usually considered to be the complete graph, however we also consider the empty graph as a candidate pre-geometric state. The energetics as the graph evolves from either of these high-energy states to a low-energy geometric state is investigated as a function of the number of edges in the graph. Analytic results for the slope of this energy curve in the high-energy domain are derived, and the energy curve is plotted exactly for small number of vertices $N$. To study the whole energy curve for larger (but still finite) $N$, an epitaxial approximation is used. It is hoped that this work may open the way for future work to compare predictions from quantum graphity with observations of the early universe, making the model falsifiable.Comment: 8 pages, 3 figure